id
string | setting_key
string | difficulty
string | level
int64 | messages
list | ground_truth
string | dataset
string | omega_split
string | __index_level_0__
int64 |
|---|---|---|---|---|---|---|---|---|
math_arithmetic_matrix_svd_level_7_7_800
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-25, -1, -18, -10, 8, 19, -24, -21, 16, -4, 8, -12],\n [-19, 5, 7, -16, 19, -24, 2, -17, -9, -9, -15, 0],\n [24, -8, 14, 6, -2, 17, -25, -25, -22, -5, 6, 17],\n [-22, 1, -13, 13, 16, 23, -17, 14, -12, -17, -23, 16],\n [22, -9, -10, 4, 6, -2, -15, 20, -6, -10, -7, 2],\n [-24, -20, 6, -1, -7, 16, 10, 5, 8, -6, 25, 26],\n [14, -19, -25, 24, 21, -11, 0, 9, -17, 1, -10, -2],\n [-12, -9, 1, -25, 13, 15, 4, 4, -2, -26, -9, -11],\n [15, 10, 14, 15, 10, -20, -21, -13, -5, 23, 4, 18],\n [-17, 19, 13, 19, 9, 14, 11, 7, -24, -4, 16, -10],\n [2, -26, -24, -13, -16, 3, -6, -11, 19, 24, -18, -25],\n [-1, 15, -24, -12, -15, -8, 14, -13, -12, -4, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
math
|
train
| 425,032 |
math_arithmetic_matrix_svd_level_7_7_801
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-24, 16, -26, -23, -6, -2, -7, -17, -9, 6, 26, 8],\n [-2, -24, 24, 23, -14, 8, -2, -9, 24, 3, 13, 19],\n [3, -3, -1, -26, 6, -19, -15, -19, -16, -13, -9, 17],\n [13, -26, -6, -17, 10, 2, 19, 13, -3, 17, 9, -9],\n [-12, 5, 11, 16, 18, -7, 7, -18, 14, 7, 8, 0],\n [15, -9, -6, -9, 0, 4, 1, 6, -12, 18, 20, 9],\n [-8, 8, 5, 18, 12, -15, 2, 7, -11, -5, -19, -15],\n [7, -11, 20, -18, 0, 20, 8, -16, -8, 4, -12, 26],\n [0, 6, -20, -4, 9, -5, -26, 0, 25, -16, 24, -15],\n [-6, -19, -14, 10, 6, 23, -25, -18, -14, -1, 18, 20],\n [25, -18, -12, -20, 16, 10, -18, -13, 3, 24, 20, 21],\n [-7, 20, -4, -12, 4, -23, -2, 24, -8, 10, 7, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
math
|
train
| 425,033 |
math_arithmetic_matrix_svd_level_7_7_802
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 4, 13, 17, 8, 0, -6, -19, -9, -4, 14, 9],\n [2, -11, 23, -17, -10, -5, 13, -25, 15, 3, 17, 12],\n [12, 18, -8, -17, -7, -3, -21, 18, -9, -11, 12, 13],\n [13, -11, 13, -12, 13, -21, 6, 21, -14, -23, 5, 23],\n [2, -20, 6, -22, 13, -23, -20, -11, 10, 22, -16, 23],\n [-22, 2, -2, -24, 5, 3, -7, 3, -24, 17, -12, 14],\n [-13, 13, 23, -17, -10, -12, 2, 26, 7, 8, -18, 24],\n [-10, -25, -1, 11, 16, 1, 3, 16, -18, 1, -11, -3],\n [-5, -7, 25, -13, 25, 16, 5, -17, -25, -20, -26, 10],\n [-12, -16, -7, 23, 14, 6, 25, 11, -7, -17, 5, 9],\n [23, -15, -2, -18, 22, -10, -13, -3, 14, 24, 18, -24],\n [23, 14, -11, -9, 12, 23, -13, -17, -17, -21, -24, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
math
|
train
| 425,034 |
math_arithmetic_matrix_svd_level_7_7_803
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, -25, 12, -15, -26, 25, 10, -14, 5, -2, 24, 11],\n [-22, 10, -9, -17, 26, -8, 7, 3, 5, -16, -5, 3],\n [-26, -21, -13, -24, 12, -12, 4, -8, -5, -20, 0, 8],\n [16, -22, 19, 8, 9, 10, -4, 9, -23, -25, 10, 8],\n [19, -23, 21, -23, -21, 24, -10, -23, -5, -6, -15, -20],\n [21, 1, 19, -14, 16, 16, 6, 13, -14, -23, -2, 24],\n [-7, 11, 8, -18, 24, 3, 12, -4, -16, -12, 20, 26],\n [-5, -10, 20, -15, 24, 8, 7, -26, 5, -23, -3, -20],\n [-15, -5, 22, 8, -6, 2, 22, -10, 1, 15, 20, 14],\n [-10, -23, 14, -21, -12, 17, -3, -19, 14, 0, 4, -18],\n [-9, 26, -25, -5, -7, 15, -23, 11, 17, -14, 22, -7],\n [25, -21, -12, -19, 3, 9, 9, -24, 0, 3, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
math
|
train
| 425,035 |
math_arithmetic_matrix_svd_level_7_7_804
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[13, 11, -7, 18, -11, -6, -9, 14, 4, -25, -3, -21],\n [19, -10, -1, 20, 25, 10, -25, -1, 17, 10, -26, -25],\n [6, -16, 3, 7, 0, 16, 7, -20, 12, 12, -25, 3],\n [21, -24, -25, 3, 10, 2, 8, 11, -5, 10, -9, 13],\n [18, 7, 18, 22, 11, 3, -25, -7, 17, -11, -23, 21],\n [-14, -13, -18, 17, -13, -16, -17, 3, -20, -21, -10, -14],\n [20, -23, -1, 5, -24, -16, -7, 25, 2, -25, 16, -23],\n [5, 22, 22, -6, -10, 18, -14, 5, 24, -24, 15, 21],\n [25, 4, 4, -26, 1, -4, 25, -22, -26, -11, -16, 9],\n [10, -11, -15, 3, 17, -23, 22, 14, 11, -19, -19, -6],\n [13, -19, 2, -12, -13, 11, -17, 0, 13, 26, 0, 15],\n [13, 8, 9, -16, -14, 8, 26, -6, 10, 17, -15, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
555
|
math
|
train
| 425,036 |
math_arithmetic_matrix_svd_level_7_7_805
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, 1, 17, -9, -17, 12, -24, -22, -15, -13, 18, 14],\n [5, 15, 6, -21, 3, -21, 4, -25, -1, 21, 5, -22],\n [19, 21, 14, 16, -11, 25, -15, -12, -6, 10, -6, -2],\n [-10, -19, 3, 6, -25, 6, 25, 1, -1, 14, -26, 8],\n [21, 16, 12, -7, -14, 4, 11, -4, -15, -21, -3, 7],\n [6, -20, 24, -13, 9, -11, 19, -4, -9, 2, -20, -23],\n [-2, 6, 24, -3, -4, 23, -6, 12, -6, 21, 0, -10],\n [26, -1, -8, 6, 21, 25, -20, 4, 12, -12, -25, 18],\n [-25, -10, 7, 20, 19, -2, 21, -16, 17, -18, -20, -16],\n [24, -23, 10, -1, 26, 7, -11, 14, 20, 3, 19, -11],\n [-21, 6, 23, -12, -7, -15, -3, 13, 5, 14, 6, 21],\n [19, -15, -12, -19, -23, 0, 10, 26, -13, 12, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
75
|
math
|
train
| 425,037 |
math_arithmetic_matrix_svd_level_7_7_806
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[26, -13, -20, -21, 7, -3, -2, 14, -2, 23, 20, -12],\n [15, -24, 9, -25, -5, 1, 5, 12, -2, -26, 17, -4],\n [-22, 21, 8, -16, -12, -22, 11, -23, 17, -17, -18, 6],\n [15, -21, 19, 0, 16, 1, 19, 16, 7, 2, 5, -5],\n [-12, 0, -17, -2, -16, -19, -6, -19, 10, -3, 19, 21],\n [-4, 26, -3, -14, 12, -22, -12, -3, -16, -10, -19, 15],\n [-3, 11, 0, 15, 24, -20, 25, -3, 0, 10, 18, -24],\n [-5, 21, 11, -5, 13, 21, 22, 2, -17, -10, 15, -20],\n [16, 8, 13, -24, -14, -21, -10, -25, 12, 11, 6, 15],\n [-4, 25, 6, -2, -13, 8, 3, -18, 3, -20, -19, -20],\n [15, 0, -2, 20, 24, -3, 1, 7, 25, -17, 9, -12],\n [11, -24, -15, 6, -1, 14, 14, -21, -24, 0, 14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
99
|
math
|
train
| 425,038 |
math_arithmetic_matrix_svd_level_7_7_807
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[22, 22, 23, -16, 25, 24, -10, 19, 21, 25, -11, 16],\n [-26, 21, -21, -12, 6, -20, -19, 26, 15, 3, -20, 13],\n [18, -13, -24, -1, 17, 7, 3, 3, 2, 10, 17, -2],\n [-23, -26, -19, 26, 25, -25, -10, 14, 25, 16, 22, -4],\n [-6, 2, -22, 5, -6, -18, -20, -9, -12, -2, 21, -11],\n [-7, 18, 10, 7, 24, -22, 6, -26, 21, 22, -20, 15],\n [-23, -23, 18, -14, 8, 16, -9, 25, 16, 23, 19, -16],\n [-14, 16, 4, 12, 15, -21, 11, 23, -16, -6, -1, -12],\n [-3, -9, -19, 14, 8, 1, 2, 20, 25, 19, -25, -9],\n [-26, -25, 18, 18, -13, 1, 17, -6, -7, 7, 7, 19],\n [12, -23, 16, 1, 12, -26, 18, -19, -11, 24, 21, 18],\n [4, -20, 24, -22, -25, 14, 21, 26, -23, -17, 8, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
605
|
math
|
train
| 425,039 |
math_arithmetic_matrix_svd_level_7_7_808
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[12, -24, 16, 18, -1, -10, 15, -19, 3, -19, 2, 24],\n [24, -9, -3, -18, -7, 25, 17, -14, 10, -8, -22, 9],\n [-3, 26, 25, 7, 20, -19, 19, -23, 17, 11, -19, -18],\n [14, 21, 14, 4, 4, 24, 13, -20, -2, -14, -22, 25],\n [-9, -20, 11, 15, -12, 22, 18, 6, 25, 4, 26, -18],\n [-8, -21, 9, 5, 1, 23, 11, -17, 8, 19, -3, 7],\n [24, -18, 0, 7, -12, 0, 0, 5, 18, 0, -1, 17],\n [-10, -11, 8, -1, 11, 3, 15, 10, -13, -9, 1, 13],\n [-11, -25, -7, 3, -18, 24, -26, 0, -18, -7, 0, 12],\n [8, 6, -14, -13, 26, -26, 23, -20, 20, 6, 12, 25],\n [25, 7, 19, 26, 1, -20, 19, 25, -3, -12, -3, 0],\n [12, -24, -17, -15, 14, 2, -19, -17, -10, -18, 15, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
| 425,040 |
math_arithmetic_matrix_svd_level_7_7_809
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-23, -6, -20, 21, -19, 19, -7, -20, 19, -21, -18, -13],\n [21, 9, 25, 2, -24, 18, 4, -3, -3, 21, 9, 8],\n [-2, 12, -6, -12, 7, -18, -24, -17, 23, -12, -11, -14],\n [17, 17, -26, 20, 6, -19, -11, 21, 8, 24, -13, 14],\n [0, 17, 21, -26, 12, 23, 16, 3, 8, -17, 4, -15],\n [13, 8, 7, 12, 5, -15, 18, 1, -8, -3, -7, -5],\n [-16, 1, 18, 13, -7, -22, 24, 25, 13, -20, -5, 10],\n [14, 2, -15, 2, 9, 8, 16, -5, -9, -5, -8, 7],\n [-18, -17, -8, 11, -18, 24, 1, 3, -2, -9, 25, -1],\n [-8, 0, 9, -23, 22, -1, 18, -24, 26, 26, 9, -20],\n [-17, 18, -23, -20, -5, 3, -5, 26, 2, -16, -11, 17],\n [-21, 10, -14, 6, 20, 24, -19, -16, 6, 6, 17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
73
|
math
|
train
| 425,041 |
math_arithmetic_matrix_svd_level_7_7_810
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[13, 0, 19, 12, -9, 18, 5, 18, 14, -3, -5, 23],\n [-24, -24, -13, 5, -18, -11, -2, -22, -14, 4, -6, 13],\n [24, -18, -6, -18, -17, 14, 17, -15, -16, -7, 23, 12],\n [6, -20, -26, -13, 18, -6, 18, 22, -19, -10, 18, 22],\n [-12, -25, -14, 25, 2, 1, -19, 8, -3, -20, 1, -5],\n [-1, -10, 11, -21, -16, 11, -25, 5, -1, 4, 5, 8],\n [-25, -24, 6, -20, -6, 21, -2, -11, -4, -10, 6, -9],\n [12, -4, -18, -24, 21, 8, -3, -21, -8, -13, -24, -21],\n [-10, 9, -5, 26, -23, -17, 5, 20, 22, 25, 22, 16],\n [-23, -14, -8, 19, 16, 11, 21, -1, 3, 16, 4, 24],\n [11, -15, -8, -4, 23, 19, 14, -17, -12, 23, -10, 25],\n [-14, -3, -11, 12, 11, 3, 18, 17, -12, -23, 17, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
545
|
math
|
train
| 425,042 |
math_arithmetic_matrix_svd_level_7_7_811
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-17, 13, 19, 19, 5, -6, 2, 3, -20, 15, 2, -17],\n [23, -5, -10, -9, 19, -22, 12, -10, 7, -23, 14, -19],\n [-1, -2, 9, 16, 12, -16, -24, 17, 13, 1, 12, -2],\n [-5, -14, -23, 1, -8, -24, 0, -16, -21, 21, 4, 2],\n [-19, -16, -18, 4, -26, -20, -17, -18, -14, 0, -9, -11],\n [-23, 3, 11, -7, 14, -15, 1, 17, -26, -18, 15, 22],\n [6, 26, -26, 15, -18, -5, -18, -22, -25, -13, -15, 2],\n [-11, 21, -18, 24, 5, 26, -3, 26, -7, -7, 26, 24],\n [15, 16, 25, -22, -7, -11, -8, -15, -10, 7, 0, 14],\n [-1, 23, 7, -6, 15, 14, -24, 14, 9, 2, 18, -8],\n [-6, -15, 17, -4, 20, 1, -15, -25, 3, -15, 12, 12],\n [-9, -3, -15, -9, -21, -19, 22, -12, 17, -20, 2, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
575
|
math
|
train
| 425,043 |
math_arithmetic_matrix_svd_level_7_7_812
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-2, -14, 5, -15, 21, -2, -8, 15, -11, -15, 8, 9],\n [-3, 6, 9, -23, 8, 23, 23, -19, -19, -20, 13, -2],\n [21, 8, -12, -9, -16, 3, 2, -4, 7, -8, -11, -21],\n [14, -12, -18, 2, 15, -25, 20, 6, 11, -4, -14, -7],\n [-20, -10, 24, -6, 1, 3, -4, -6, 22, -26, -10, 5],\n [-3, -20, 8, 9, -13, -15, 12, -4, -13, -2, -5, 18],\n [22, 10, 2, -19, -16, 3, -5, -12, -6, 20, -2, -14],\n [-20, 22, -9, -15, 20, -1, -22, 24, -19, 9, -22, -5],\n [-4, -19, 24, -8, 7, -21, 23, 22, -10, -10, -12, 12],\n [10, 4, -5, -2, -8, -20, -25, -12, -5, 19, 11, 26],\n [-20, 14, -4, -25, 25, 6, -9, 17, -20, -3, -16, -15],\n [-9, 10, -26, 26, -26, 0, -18, -26, 1, -15, 22, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
| 425,044 |
math_arithmetic_matrix_svd_level_7_7_813
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[22, -20, 8, 14, -4, 8, -11, 21, 15, -19, 21, -11],\n [-21, 9, 4, 20, 1, 8, -10, 20, 3, 25, -18, -4],\n [18, -26, -15, -10, 19, 6, -5, -17, -1, -13, -2, 20],\n [-16, -8, 16, 24, 1, 0, -16, -5, -2, 3, -8, 12],\n [-20, -21, -18, -9, 4, -21, 19, 26, -5, -18, 4, -5],\n [26, -6, 8, 2, -6, 26, 8, -4, 13, 17, -4, -9],\n [-4, -26, 24, 17, -7, -11, -18, -2, 11, -2, 11, -20],\n [19, -11, 8, 4, -26, -7, 22, 0, -26, 10, -3, 22],\n [-22, -16, 8, 2, -4, -17, 3, 4, -3, -13, 24, -16],\n [-26, 17, -1, -7, -25, 6, 20, 18, 18, 18, -10, -21],\n [-15, -12, -24, -5, 11, -6, 8, 17, 16, 0, -21, -16],\n [-10, 9, 4, 16, -14, 21, 2, 11, -7, 11, 22, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
math
|
train
| 425,045 |
math_arithmetic_matrix_svd_level_7_7_814
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, -26, 17, 23, -14, 0, -24, -7, 1, -21, 19, 19],\n [-18, 18, 6, -23, -14, 25, 11, -26, 19, -2, -26, 5],\n [15, 22, -8, -10, 25, 12, 14, -15, -7, -5, 18, 4],\n [7, -4, 17, -8, 22, -25, -25, 11, 12, 10, -15, 1],\n [-16, 15, 22, 2, -6, 2, 2, 13, 15, -15, -25, 13],\n [11, 6, 18, 19, -17, 14, -16, -11, -19, 20, 26, 19],\n [-23, 17, 1, -10, -9, 26, -22, -19, 26, -22, 8, -4],\n [-5, 21, 26, -25, 9, -24, 1, 17, -4, -18, -8, -4],\n [-14, 19, -18, -22, 13, 3, -4, 6, -6, 21, -14, 15],\n [14, 21, 14, -15, -5, -23, -18, 4, 23, 21, -25, 19],\n [9, -16, 2, 9, 7, 20, 23, -18, -15, -6, -22, -20],\n [17, 10, 24, -24, -12, -8, 22, -24, -7, -12, 11, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
574
|
math
|
train
| 425,046 |
math_arithmetic_matrix_svd_level_7_7_815
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-13, -23, 8, -19, -6, 8, -23, 9, -13, 17, -24, -7],\n [-19, 24, -13, -26, -7, -13, 24, 1, 12, 18, -18, -4],\n [-11, 21, 0, 13, -19, 1, -9, 7, -25, -3, -17, 22],\n [13, -19, -22, -24, 6, 3, 25, 12, -20, 18, -6, 11],\n [-14, -2, -25, -25, -25, -12, -12, -9, -22, -1, 3, -13],\n [-22, 13, -6, 16, -19, -21, -1, -23, 25, 3, 8, 0],\n [0, 17, 16, -22, 13, -16, 16, 25, 8, -16, 11, 11],\n [23, -22, 10, 24, 10, -1, 6, 6, -4, -20, 5, -18],\n [-11, -18, 17, 16, 1, -4, -15, 15, -18, 18, -15, -18],\n [-8, 9, 6, -14, -25, 13, 17, -2, -14, -14, 6, 0],\n [13, 10, -8, -5, 25, -10, 24, -25, -15, 6, 1, -1],\n [-2, 1, 4, 17, 4, 0, 24, 17, -26, 8, 6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
math
|
train
| 425,047 |
math_arithmetic_matrix_svd_level_7_7_816
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, 6, 17, 26, 10, 20, -12, -12, 22, 2, 14, -6],\n [19, -9, -11, 2, 14, 0, -12, 25, 26, 20, -18, 1],\n [-25, -6, -16, 5, -5, 8, 15, 14, -11, 4, -17, 13],\n [9, -6, -19, 20, 15, 17, 20, 6, 13, -5, 3, -4],\n [25, -12, 20, 16, -1, -11, -17, 9, 1, 15, -1, 4],\n [-9, -10, 21, 25, 5, 12, 24, 24, -22, 15, 2, 9],\n [12, 23, -16, 6, -23, 21, 6, -26, -6, -10, 7, 2],\n [-24, 22, -3, 7, -25, 4, 13, -20, 24, 2, 26, 24],\n [-16, 16, 26, -2, -8, -16, 18, 8, 6, -22, 8, -24],\n [4, -15, -23, 5, 23, 23, -3, 24, 9, -25, -22, -15],\n [-2, 14, -3, -2, 17, 18, 18, -9, 24, -7, 6, 2],\n [2, -5, -15, 7, -23, -22, 25, -17, -5, -2, -26, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
550
|
math
|
train
| 425,048 |
math_arithmetic_matrix_svd_level_7_7_817
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-12, 13, 4, 26, -10, -15, -22, 11, 21, 12, 24, -18],\n [24, -10, 2, 24, 15, -10, 19, -13, -7, 20, 0, 24],\n [12, 21, -7, -4, -18, 26, 24, 22, -8, 5, 25, -15],\n [-25, 9, -6, 13, 16, -16, 1, -15, -22, 23, -12, 5],\n [-10, 14, 9, -13, 14, -18, -10, 17, -20, 5, 17, 17],\n [-21, -11, -25, -17, -23, -22, 10, 12, -1, 3, -25, 24],\n [-9, -20, 19, 20, -4, -7, -12, 25, 1, 19, -24, -24],\n [-15, 7, 9, -19, -18, 8, -3, -3, 8, -16, -21, -2],\n [-26, -18, -15, -14, 2, 19, 5, 4, -1, 13, -3, -12],\n [15, 24, -21, 2, 4, -11, -17, 18, 13, -23, 2, -19],\n [13, -16, -26, 16, 10, -4, 3, -12, 2, -3, -18, 16],\n [-16, -12, 17, 19, 11, 21, -1, 18, 10, -3, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
83
|
math
|
train
| 425,049 |
math_arithmetic_matrix_svd_level_7_7_818
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, 2, 5, -15, 14, -10, -2, 26, -13, -2, 0, -14],\n [10, -17, -18, -14, -20, -13, 9, 13, -22, -14, -7, 1],\n [24, 25, -12, 12, -6, -10, -21, 19, 19, -2, -17, -13],\n [-8, 25, -16, 5, -17, 20, 7, 24, 17, 26, 2, 2],\n [-5, 23, -13, -25, -15, -5, -26, 23, -15, -15, -23, -10],\n [26, 21, -8, -26, 25, -10, 7, 16, -20, 6, -21, 25],\n [-21, 5, 1, 10, 2, 16, 3, -5, -22, 2, -25, -17],\n [19, -7, 25, 26, -9, 18, 8, 26, 9, 24, -9, -15],\n [23, 19, -2, 9, 15, 14, 26, -7, 21, -16, -7, 6],\n [-17, -2, -17, -3, 14, 6, 7, -12, 13, -3, -12, 22],\n [-17, -22, -5, 10, 4, -4, -16, -17, 8, -5, 14, -5],\n [10, 0, -26, -22, -16, 6, -11, 13, 3, 1, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
551
|
math
|
train
| 425,050 |
math_arithmetic_matrix_svd_level_7_7_819
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-26, -19, -23, 24, 9, -9, -8, 9, -18, -1, -25, -24],\n [1, 18, -7, -8, -8, 14, 10, -12, 14, -21, 15, -26],\n [-14, 22, 19, -24, 18, -19, -4, 1, 6, 7, 7, -2],\n [14, -26, 16, -20, 26, 11, 1, -10, 11, 21, 3, -26],\n [1, 9, -9, -25, 6, -20, 21, 18, 23, 12, -9, -20],\n [-23, -10, -8, -22, 12, 11, 10, -14, -15, 10, -23, -2],\n [4, 13, -12, 1, -16, 2, -22, 16, 15, -25, -7, -5],\n [13, 0, -6, -7, 5, 9, 21, 19, -24, -19, 3, -23],\n [-20, -3, -18, 7, 8, -18, 12, 25, -12, 22, -15, -23],\n [-10, -18, 4, 3, 26, 11, -9, -6, -10, 8, -10, -10],\n [-2, -14, -3, -12, -6, -15, -13, 20, 19, 1, -2, 1],\n [4, 9, -11, 13, 2, -16, -1, 0, 3, 26, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
math
|
train
| 425,051 |
math_arithmetic_matrix_svd_level_7_7_820
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[25, -17, 5, -22, -18, -1, 8, -22, -11, -14, 3, -16],\n [3, 22, -6, -23, -10, 6, 4, -21, 6, 25, 12, 16],\n [15, 23, 0, -2, 15, -8, -25, -26, -13, 17, -12, 24],\n [-5, -10, 23, 14, 5, 6, -26, 14, -8, 11, 24, 23],\n [8, -23, -16, 22, -24, -25, 9, -4, -16, 8, 2, -20],\n [-8, -21, -2, -11, -4, 26, -16, 6, -19, 9, 23, -2],\n [8, -14, -21, 8, 19, 12, 23, -23, 18, 16, 15, -11],\n [-16, -3, -13, 13, -19, 3, 4, -21, -3, -26, 11, 19],\n [-6, -21, -12, 5, -9, 20, 5, -15, -16, 7, -25, 17],\n [-5, -6, -21, -21, -15, -23, -20, -15, 3, -18, -20, 21],\n [20, -5, 0, 8, 11, -3, -13, 13, 9, -14, 10, 25],\n [23, -16, 5, -22, -10, -25, 5, -4, -22, 13, 11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
585
|
math
|
train
| 425,052 |
math_arithmetic_matrix_svd_level_7_7_821
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -25, 13, -20, 13, 23, -5, -20, 20, -18, 19, 18],\n [8, 11, -3, 9, 26, -9, 16, -1, 12, -12, -5, -2],\n [16, 24, -2, 14, -2, 11, -2, -20, 13, 17, -3, -8],\n [-5, 19, -4, -7, -7, -20, 7, -16, 16, -19, 11, -16],\n [16, -2, 4, 10, -1, -17, 6, -20, 9, 18, -7, -12],\n [-11, 8, -6, 8, 13, 21, 7, 12, -26, -18, 14, 3],\n [-6, -9, -5, 17, -1, -15, 4, 10, 16, 9, 21, 17],\n [-25, 10, 13, -11, 23, -4, 8, -21, 9, -5, -16, 7],\n [-6, -14, 18, -9, 18, 17, 3, 14, -3, -26, 10, 1],\n [-23, -23, -13, -16, -4, 19, -15, 21, 20, 15, -23, -26],\n [24, 13, -17, -20, -25, -4, 7, 24, -15, 24, -15, 18],\n [-11, -19, 15, -21, -12, 22, -16, 24, 3, -17, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
524
|
math
|
train
| 425,053 |
math_arithmetic_matrix_svd_level_7_7_822
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-18, -18, 23, -21, -11, -15, -25, -10, -1, -18, -22, 1],\n [3, -10, 20, 12, -8, -21, -23, 17, 24, 11, -13, -11],\n [10, 5, 4, -22, -10, -23, 16, -3, -21, 3, 17, -16],\n [0, -18, -3, -7, -14, 1, 20, 4, 5, 8, 10, -8],\n [20, -20, -24, 13, 3, 4, 18, 21, 13, -18, 7, -5],\n [0, 25, 0, 6, 25, 18, 18, 16, 15, 25, -21, 21],\n [0, 5, 11, -5, 25, 26, -14, 5, 0, 17, 13, 3],\n [8, -14, -26, 15, 0, -5, 20, 16, 21, -3, 26, -4],\n [26, 8, -18, 0, -20, -3, -11, -4, -20, 13, -5, 2],\n [-7, 10, -21, 4, 0, 14, 10, -18, -2, 15, 11, 6],\n [-14, 10, 0, -8, -11, 20, -13, 19, -23, 12, -5, 20],\n [10, -26, 24, -6, 23, 3, 0, 19, 7, 2, -23, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
math
|
train
| 425,054 |
math_arithmetic_matrix_svd_level_7_7_823
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -15, 6, 19, -3, 11, -26, 7, -10, 13, 23, -5],\n [22, 21, 0, -12, -12, -4, -15, 0, 22, 23, 13, -18],\n [20, 18, 2, 10, -6, -26, 26, -15, -26, 0, -3, -3],\n [22, 7, 12, 8, 23, 19, -17, -3, 0, -20, -13, 8],\n [16, -12, 24, 17, 5, 10, -18, 12, 20, 6, 6, 11],\n [5, -6, -22, 16, -16, 2, 19, -19, 0, 19, 14, 16],\n [16, 25, 26, 21, -15, -20, 8, 17, -21, -8, 9, 15],\n [13, 15, -11, -16, 9, 1, 18, 25, -4, 8, 8, -10],\n [12, 16, -23, 21, -20, 21, -9, 26, 17, -4, 1, 14],\n [15, 9, 11, -8, 23, 17, 23, -6, 8, 23, -25, 24],\n [-10, -16, -14, 14, 1, -10, 18, 26, -3, 18, 7, 22],\n [10, -13, 22, -21, 14, 17, -5, -7, -4, 17, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
550
|
math
|
train
| 425,055 |
math_arithmetic_matrix_svd_level_7_7_824
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, 23, -4, -7, 10, 16, 19, 12, 16, 7, -10, -12],\n [-6, -26, 18, 11, 7, 2, -25, -7, 15, 23, 17, 24],\n [-14, -19, -4, 21, -16, -4, 25, 9, 1, -10, -19, -26],\n [2, 25, -24, -14, 6, -4, -4, 7, -1, -22, -19, -10],\n [-2, -4, 1, 7, -19, 16, -8, -14, -1, 12, 24, -21],\n [-14, 22, 25, -4, 9, 16, -10, -26, 16, 24, -14, 1],\n [-13, 21, -13, -20, 10, 14, 16, -9, 14, -18, 11, -7],\n [-6, 11, 9, -2, 16, -25, 17, 3, -19, -2, 3, 3],\n [-14, 4, 5, 9, 14, 2, 21, 7, -8, -1, -22, -7],\n [-13, 16, 2, -24, -7, -2, 14, -22, 2, 23, 14, 14],\n [-25, -21, 9, -26, 4, 0, 18, 10, 19, 19, -8, -26],\n [4, -9, -20, 22, 5, 8, 5, -26, 6, -15, 18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
math
|
train
| 425,056 |
math_arithmetic_matrix_svd_level_7_7_825
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-23, -12, 5, -3, -4, -2, 22, -1, -6, -21, -5, 18],\n [12, 10, -16, 10, 3, 4, 6, 18, -15, 0, -13, 26],\n [-26, 18, 23, 22, -19, -19, 13, 2, -1, -1, 22, -7],\n [17, 16, 22, 25, -20, 5, 15, 22, -9, -5, 2, 5],\n [22, -7, 4, 16, 14, -19, 16, 9, 24, -19, -18, -13],\n [19, 6, -12, 3, 3, 13, 4, -22, -8, 21, 15, -16],\n [10, -17, 21, 9, 6, -3, -12, 2, 12, 0, -7, 9],\n [-13, 10, 22, 9, 10, -3, 22, 16, 9, 2, -12, 12],\n [-22, 19, 6, 12, 18, 18, -26, 20, 7, 13, -19, -3],\n [19, -4, 9, -14, 10, 19, -9, -17, -23, -20, 9, -5],\n [16, 16, -15, -3, 20, 10, -19, -7, 16, -9, -2, 23],\n [-4, 11, -9, 24, 19, -16, 12, -13, 21, -5, 18, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
526
|
math
|
train
| 425,057 |
math_arithmetic_matrix_svd_level_7_7_826
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, -22, 22, -22, 23, 15, -8, 7, 26, -11, -6, 18],\n [5, 26, -8, -3, 8, -9, -13, -5, 12, 3, -15, 22],\n [-15, 3, -24, 13, 5, 0, 1, -9, 26, 26, -2, -12],\n [24, 18, 21, 0, -12, 3, -16, 18, 26, -13, 18, 1],\n [-19, -16, -13, 24, 20, -5, -2, -17, 9, 12, -3, -21],\n [6, -5, -7, -16, 24, 8, 8, -26, 15, -1, -13, 22],\n [-25, 19, -22, 12, -12, -6, 2, 24, -6, 11, 25, 9],\n [-13, 6, -4, -19, -7, 11, 20, 11, 20, -26, 15, -23],\n [-13, -5, -15, -2, 25, 21, 25, -20, -20, 12, -21, -8],\n [20, -4, -17, 17, -19, 9, -20, -24, -19, -14, 4, -14],\n [-1, 21, 21, -25, -24, -12, 22, -25, -10, 11, -16, -22],\n [-21, -24, -4, 5, -23, 20, 2, -10, 4, 8, 21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
math
|
train
| 425,058 |
math_arithmetic_matrix_svd_level_7_7_827
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 21, 4, 26, -26, 26, -16, -26, -20, 14, -14, -7],\n [-21, 3, 22, 25, -21, 7, 8, -7, 11, 3, 24, 6],\n [-3, 4, -11, 13, -11, 0, 9, -5, -12, 19, -26, 1],\n [6, 9, -12, 4, -21, -23, -7, -23, -17, -20, 0, -21],\n [4, 9, 0, -14, -16, 26, -18, -19, -17, -25, -3, 8],\n [7, 23, -16, 25, -26, -22, 0, -20, 23, 10, 25, 11],\n [-26, 5, -10, -9, -23, 22, -14, -22, -5, -1, -23, -4],\n [-22, -18, -14, -18, -23, -1, -13, -25, 4, 23, 24, -1],\n [-25, 14, 19, 17, 25, 10, -25, 13, 1, -4, -20, 12],\n [13, 25, -5, 9, -26, 7, -23, 14, 8, 26, 4, 6],\n [-22, 16, 16, -16, 5, 20, -26, 16, -21, 1, -10, 23],\n [-16, 14, 0, -15, -14, 4, 8, -2, 3, 9, -6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
math
|
train
| 425,059 |
math_arithmetic_matrix_svd_level_7_7_828
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, 1, 0, -15, -17, -1, 2, 18, -21, -2, -19, -16],\n [-10, 11, 20, -14, 14, -12, -8, -8, -17, 1, 10, -2],\n [-12, 8, -11, 10, 0, -22, -3, -25, 13, 22, 26, 8],\n [26, 6, 15, 5, 5, -11, 18, 11, 18, 17, -4, -1],\n [-22, -20, 7, 23, -17, -5, -6, -8, 25, 15, 12, 18],\n [-2, -14, 16, -8, -20, 4, -25, 17, 18, -23, -26, 25],\n [20, 23, -4, 20, -10, -5, 8, -19, -20, -26, -2, 24],\n [-3, 23, 6, -16, 5, 2, -26, 20, -19, 18, 2, 4],\n [8, -20, 4, 18, 23, 5, 3, -15, 8, -17, -1, -22],\n [-4, -18, 6, 10, 3, 6, -25, 15, -23, -1, 3, 8],\n [-17, 4, -12, -6, -21, -26, -17, -25, -18, -10, -11, -25],\n [-11, 8, 1, 24, -14, -21, -2, 12, -1, 17, 19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
math
|
train
| 425,060 |
math_arithmetic_matrix_svd_level_7_7_829
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-25, -5, 15, 1, -10, -4, -12, 11, 7, 3, -26, 14],\n [-11, -2, 21, 19, -4, 6, 7, -18, -11, 10, 23, 21],\n [-22, 22, 15, -15, -22, -4, -19, 16, 8, -11, -7, 1],\n [3, -16, 23, -10, -17, -3, 4, -16, 20, -19, 4, 10],\n [10, 6, -18, 19, -24, 22, -14, 25, 1, 25, -3, -17],\n [15, 10, -12, 15, 1, 10, -26, -14, -23, 13, 3, 25],\n [-24, -7, 8, 0, 21, -15, 18, 24, 14, -11, 5, 24],\n [6, -11, 2, 0, 4, 24, -3, 4, -18, 18, 9, -21],\n [3, -1, 13, -20, -19, -16, -24, -23, 6, -7, -22, 7],\n [-13, -14, 22, 18, 26, -3, 3, 13, -16, -18, -14, -14],\n [5, -20, -16, 22, 15, -26, 1, -19, -12, -22, -5, -7],\n [-23, 18, -2, -11, 13, 19, 0, 2, -15, 25, -20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
534
|
math
|
train
| 425,061 |
math_arithmetic_matrix_svd_level_7_7_830
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-22, 20, 15, 6, 11, 13, 16, -21, -19, -5, 23, -13],\n [-18, -14, 23, 5, -13, 8, -2, 4, 22, 16, 18, 25],\n [-7, 15, 10, -20, 26, -17, -21, -2, 23, -21, 18, -10],\n [-5, -4, 2, -20, 8, 12, 25, -7, -1, 2, 2, -20],\n [7, -22, -14, -21, 5, 9, 6, 16, 6, -8, 14, -9],\n [-13, -6, 12, 7, 4, -10, -20, -6, -20, -26, -5, -5],\n [-4, 1, 13, 19, 3, 18, -17, -15, 18, -11, -6, -14],\n [20, -23, 10, 3, -1, -13, 10, -2, 12, 0, -13, -25],\n [-25, 6, -25, 7, 26, -2, 18, 10, 0, -1, 25, 20],\n [-5, 25, 20, -20, -14, 21, 24, 1, 18, 1, -3, 8],\n [6, 10, -18, 23, -24, 25, -25, -5, -6, 10, -3, -13],\n [6, -10, -6, -14, 17, 24, 17, 13, -16, -25, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
83
|
math
|
train
| 425,062 |
math_arithmetic_matrix_svd_level_7_7_831
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-24, -12, 19, -3, -19, -21, 5, 14, 24, 8, -14, 1],\n [15, -23, 4, -26, 3, -19, 13, 19, 26, -13, 17, 1],\n [7, 12, -23, -3, 0, 15, -16, -4, 15, 5, 23, 26],\n [-23, -8, -20, 6, -13, -14, -21, -8, -18, 8, 22, 24],\n [21, -1, -23, 21, 1, 0, 24, 17, -20, 25, -18, 7],\n [-19, -17, -26, 23, -19, 18, 12, 19, 12, -10, -9, 7],\n [8, 24, -24, -15, -23, 9, -18, 8, -24, -2, 25, -1],\n [10, 21, 0, 1, -8, -3, 10, 13, 17, 11, -2, 7],\n [-12, -11, -23, -1, 20, 12, 20, -1, 21, 1, 22, 10],\n [11, 9, -17, 6, -19, 11, 15, 9, -6, 18, 23, -7],\n [7, 11, 16, 1, 5, -15, -18, 16, -12, -14, -25, -7],\n [-13, 15, -12, 2, -6, -17, 26, 26, 14, 11, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
math
|
train
| 425,063 |
math_arithmetic_matrix_svd_level_7_7_832
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[17, -10, 17, -23, -13, 13, 5, -9, 7, 5, -13, 9],\n [7, -21, 13, 8, -12, 24, -7, 1, 10, 24, 11, -6],\n [-3, -17, 9, -18, -5, 15, 10, -11, 16, -3, -23, 17],\n [-4, 15, -5, -25, 1, 26, -8, -7, 1, 15, -3, 0],\n [17, -25, -20, -26, -16, 24, 4, 3, -14, -3, -9, -14],\n [-10, 19, 21, 3, -8, -15, -1, -9, -15, 17, 23, 15],\n [-25, -7, -21, -26, -1, -20, 5, 6, -17, 18, 14, -12],\n [4, -3, 2, -9, -20, 7, -13, -7, 2, 10, 15, 4],\n [-8, -4, -20, -21, 8, 2, -14, 12, -2, 7, -8, -23],\n [-3, 6, 16, -25, -25, -13, 23, -16, 7, 11, 1, 12],\n [-5, 15, 6, 11, 25, 4, -13, 11, -18, -3, 2, -22],\n [15, 12, 0, -19, 2, 26, -15, -19, 15, 14, -6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
| 425,064 |
math_arithmetic_matrix_svd_level_7_7_833
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[20, -18, -13, -26, 4, -11, 12, 0, -16, -25, 4, 23],\n [-3, 12, -24, 21, -23, 3, -24, -23, -14, 26, -13, -17],\n [-13, -10, -5, 19, 10, -6, -2, -24, -8, 5, -12, 14],\n [-3, -18, -17, 21, 5, 13, -20, 19, 23, 0, -12, 17],\n [-6, -17, -4, -22, 22, -21, -5, 1, -8, 22, -13, 21],\n [-20, -12, 5, -5, 19, -6, -8, -14, -5, -17, 19, 19],\n [17, -3, -19, -19, 22, 22, 12, 23, -8, 15, -9, 6],\n [21, 10, 2, 5, -19, 5, -15, -5, -7, 18, -1, -10],\n [15, 7, 4, -9, -24, -9, -7, 25, -6, 8, 15, 16],\n [3, 9, -23, -12, 21, -20, 5, 6, -14, -10, 26, 13],\n [11, -21, 23, -23, -12, -19, 7, 24, 3, -4, -18, -3],\n [17, -19, 23, -21, -2, -14, 7, -2, -9, -18, 6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
528
|
math
|
train
| 425,065 |
math_arithmetic_matrix_svd_level_7_7_834
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-13, -21, -9, 16, 12, -1, 9, 9, -16, -9, -12, 3],\n [14, -2, -11, -15, -13, 20, -14, 12, 3, 9, 19, -11],\n [-26, 14, 2, 0, -14, -10, 1, -7, 24, 26, -22, -3],\n [-18, 6, 7, 19, 0, 10, 6, 21, 11, 2, 11, 8],\n [-7, -8, -22, -2, 2, -1, 19, 24, -25, -12, 18, -21],\n [-26, -18, 16, -11, -13, -17, -8, 24, -19, 21, -15, -21],\n [8, -21, -21, 8, 17, -16, 11, 0, -1, 1, -19, -2],\n [-8, -11, 23, -1, 17, -12, 12, -15, -3, -14, -10, -14],\n [-10, 16, -26, -16, -7, 4, 17, 8, 12, -21, 8, 1],\n [24, 26, 25, 14, 17, -26, -11, 22, 18, -15, 1, 26],\n [-12, -19, -23, 4, 19, 3, 8, -21, 11, -6, 3, -11],\n [-19, 0, 6, 16, -15, 16, 18, 15, 25, -4, 19, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
math
|
train
| 425,066 |
math_arithmetic_matrix_svd_level_7_7_835
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[19, 24, 24, -26, -20, 9, -2, -6, 10, -15, 5, 22],\n [11, -11, -26, 17, -1, -13, -21, 14, 24, -7, -24, 26],\n [16, -15, 6, 22, 23, 18, -26, -8, -25, -4, 18, -19],\n [7, -23, -19, 0, -1, 6, 16, 13, 18, 21, 13, 23],\n [-24, -18, -17, 2, -6, 26, 15, 23, -9, -10, -6, -24],\n [0, 5, 15, 2, 20, 2, -1, -18, 0, -15, -11, 20],\n [-25, 24, 12, 0, -18, 19, -25, 15, -20, -19, 11, -21],\n [-8, -12, 18, 1, 3, 0, -17, 18, 4, -26, 23, 5],\n [-11, -21, -25, 15, -25, -24, -8, -23, 14, 16, -9, -9],\n [20, 19, 18, 19, -6, -6, 12, 3, 14, -10, -22, -22],\n [26, -18, -16, 11, 21, 13, -13, 11, -21, -13, -19, 3],\n [-26, -2, -14, 0, -2, -23, 20, 4, 22, -9, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
585
|
math
|
train
| 425,067 |
math_arithmetic_matrix_svd_level_7_7_836
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-15, -24, -12, -21, -22, 4, -19, -17, -24, -15, 1, -15],\n [15, 3, -8, -6, -10, -13, 12, 24, -16, 2, 23, -20],\n [22, -26, 14, -20, -13, -11, 8, -11, -6, -14, -9, 2],\n [-6, -18, 4, 10, 18, -10, 4, -3, 20, 20, -21, 5],\n [4, -9, 21, -18, -24, 10, -20, -1, -14, 7, 16, 2],\n [6, -22, 9, -12, -17, -23, 12, 10, 20, 10, 18, 11],\n [5, -3, -7, 21, 14, 11, 13, -23, 14, -16, -16, -11],\n [14, -26, 6, -20, -24, -20, -26, 6, -20, -23, -9, 26],\n [10, -13, 25, -12, -2, -9, -23, -25, 16, -1, -7, -12],\n [-21, 10, 16, 15, -14, -11, 15, 11, -25, -26, -22, 3],\n [4, 16, 5, -24, -24, 15, -22, 8, -5, 5, -4, 11],\n [15, -19, -23, -21, 0, 18, -8, 15, 17, 17, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
104
|
math
|
train
| 425,068 |
math_arithmetic_matrix_svd_level_7_7_837
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[17, -21, -24, 5, 21, -11, 6, -25, 16, -1, 8, 1],\n [16, 22, -16, 19, -3, -11, -2, -4, 12, 8, -2, 14],\n [26, 12, 18, 6, -5, -17, -26, 19, 11, -5, 5, -4],\n [3, -4, 16, 20, -15, -8, -20, 0, -1, -9, 1, -16],\n [-25, -10, 19, 2, 5, 23, -12, -9, 1, 0, 14, 24],\n [20, 6, 17, 23, -17, -3, 7, 16, 0, -7, 14, -2],\n [22, -1, 16, 26, -6, 23, -14, 22, 6, -17, 1, 6],\n [-16, -13, -7, 9, 14, -7, -19, -12, 6, -8, 21, -15],\n [-10, 6, 24, -7, 19, 4, 11, 24, -8, -8, 17, -14],\n [11, 22, -26, -16, 0, 10, 12, -26, -12, -9, 16, -2],\n [-26, -8, 7, -17, -15, 12, 18, -25, 5, 24, -1, -7],\n [-21, -20, -25, -10, -1, 4, 7, -9, 14, 16, -13, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
507
|
math
|
train
| 425,069 |
math_arithmetic_matrix_svd_level_7_7_838
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -26, -7, -25, 16, 19, 10, -26, -17, 23, 24, -22],\n [14, 18, -14, -23, -3, 21, 0, 9, 16, 9, -25, 5],\n [-10, -15, -15, -6, -19, -5, -17, -7, 1, 24, -2, 22],\n [1, -23, 18, -1, -14, -8, 7, 18, -11, 18, -23, -7],\n [14, -1, 17, 11, 3, -21, 11, -14, 9, -10, 0, 8],\n [13, 6, 26, -9, -7, 24, 6, 4, 10, -8, 6, -10],\n [6, 9, -22, 13, 20, 18, 0, -20, -13, -23, 23, -9],\n [7, 22, -11, 0, 11, -7, 19, -8, -26, 17, -4, 21],\n [-18, 1, -7, -11, -14, 6, -24, -12, -11, 3, -2, -13],\n [-26, 6, 10, 2, 10, -19, -26, -3, 23, -26, 19, 16],\n [-17, -9, -6, -17, -5, 24, 18, -18, -18, 13, 18, 12],\n [-6, 4, -25, 24, 26, -3, 6, -16, -26, 22, 24, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
math
|
train
| 425,070 |
math_arithmetic_matrix_svd_level_7_7_839
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-18, -6, 20, -5, 2, 13, -24, 22, -2, -9, -16, 3],\n [-2, -16, 7, -3, 21, 5, -24, 18, -2, 18, -7, -7],\n [24, -10, -7, -9, -13, 7, -11, 5, -19, 15, -11, 12],\n [11, -23, 8, 1, 16, 15, -13, -22, -25, 18, 23, -3],\n [-24, -4, -16, 11, 8, -26, -21, -21, 13, -1, 8, -14],\n [-2, -5, -10, -13, -24, -23, 8, 20, 1, 16, -25, 18],\n [21, 11, 20, -23, 20, 22, -15, 7, 10, 17, 14, 3],\n [-6, 1, 15, 23, -22, 6, 7, 5, 0, -24, 13, 17],\n [15, 24, 17, -23, 9, 9, 14, 25, -24, 23, -26, 12],\n [13, 12, 0, 17, -24, 9, 10, 3, -26, -17, -24, 11],\n [-24, 10, 25, 7, 25, -7, -16, -8, 0, -3, -21, -26],\n [-8, 25, -17, 17, 5, 21, 10, 9, -25, 10, -13, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
math
|
train
| 425,071 |
math_arithmetic_matrix_svd_level_7_7_840
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-14, 23, -10, 0, 2, -14, 22, -2, -3, 21, 9, -4],\n [-1, 21, 9, -21, -11, -17, 12, 0, -25, -17, 21, -19],\n [-18, -14, 25, -19, 0, 19, 15, -6, 14, 7, 2, 3],\n [17, -11, -26, 18, 20, 2, 15, 3, -5, -12, -7, 11],\n [-4, 4, -10, 8, -25, 20, 26, 4, -1, 4, -19, -11],\n [-15, 26, -8, 17, -14, -26, -14, -23, 24, 18, 21, 4],\n [-19, 0, -19, 24, -3, -5, 13, 2, -18, -10, -26, 17],\n [5, -7, -26, -2, 14, 0, -4, -9, 25, 4, 1, 25],\n [15, -6, -15, 10, -3, 24, 12, 22, 6, 24, -10, 6],\n [-11, 24, 0, 14, 26, 1, 9, -20, 7, 19, -26, -23],\n [-1, -7, 24, -14, 8, -17, -19, -9, -10, -22, 3, 4],\n [12, 25, -3, -10, 26, 7, 16, 8, -12, -16, 7, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
math
|
train
| 425,072 |
math_arithmetic_matrix_svd_level_7_7_841
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-12, 9, 10, -4, 12, -1, 7, -16, -15, -19, 19, -19],\n [14, -22, 18, -17, -24, 16, 10, -5, -2, -23, 10, -19],\n [3, -18, -12, -26, 24, 17, -14, -23, -11, 17, 20, -26],\n [-13, 0, -1, 20, 5, 13, -25, -11, 1, 22, -1, -16],\n [-4, 3, 25, 4, -25, -7, 2, -17, -9, 4, -23, 0],\n [-9, 17, 4, -20, -8, 12, -25, -13, 9, 16, 19, 1],\n [11, -24, 2, 0, 21, 25, 21, -24, 21, 3, -9, -19],\n [-17, -5, -3, -24, -13, 20, -3, 0, 7, 4, 21, 0],\n [18, 2, 2, 20, 19, 23, 21, -15, -13, 0, 20, -25],\n [10, 18, -9, -14, -18, 2, -17, -7, 10, 2, -21, 14],\n [-1, -5, 16, 20, 11, -1, -10, -26, 4, -18, -1, 23],\n [26, -21, 19, -25, 15, 0, -26, 3, -9, 7, -6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
math
|
train
| 425,073 |
math_arithmetic_matrix_svd_level_7_7_842
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[20, 5, 16, 7, 20, 26, -13, -22, 9, 5, -18, 18],\n [8, -2, -16, 19, 14, -14, 3, 7, 5, 3, -9, 12],\n [-24, -20, 12, 7, -19, 16, 21, 5, 13, -13, -22, -20],\n [-17, -7, -6, 1, 2, -21, 11, 15, 14, -24, 10, -10],\n [6, -17, 10, 6, 1, -4, 15, 19, 21, 23, 24, 19],\n [-17, -19, -11, 16, 5, 22, 18, -2, 10, -12, -11, 15],\n [-10, 0, 20, -1, -19, 14, 14, -16, 0, -18, -16, -20],\n [1, 3, 9, 24, -18, 8, 24, -14, 21, -23, -17, -1],\n [-24, 23, 26, 16, -10, 22, 0, -5, 17, 9, -19, 6],\n [-1, 4, 26, -16, 2, 2, 11, 10, -12, 24, -12, -20],\n [22, 26, 2, 6, 19, 24, -11, 7, -6, -20, 17, 2],\n [-18, 22, -20, -13, 3, -3, 24, 7, -19, -26, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
math
|
train
| 425,074 |
math_arithmetic_matrix_svd_level_7_7_843
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[4, -12, -12, 24, 7, -22, -5, -15, 18, 4, 2, -5],\n [21, -19, 10, 1, -6, -16, -16, -4, 15, -14, 16, 0],\n [-4, 24, 6, 26, -1, 16, 9, 6, 26, 11, -11, -17],\n [16, 21, 14, 17, 25, -10, 25, 16, -4, -26, 2, -2],\n [-21, -17, 13, -13, -4, -8, 26, 4, 12, 12, 11, -8],\n [16, -26, 11, -14, 23, 7, -10, 5, 22, 7, 6, 17],\n [1, 17, 2, 10, -3, 21, -11, -14, -1, -20, 17, -13],\n [25, 5, 14, -16, 5, -16, -7, 25, 7, 20, 23, -5],\n [-4, 2, -15, 12, 4, 2, 4, -15, 8, 15, 14, 0],\n [-12, 3, -20, 9, 19, -3, -9, -3, 5, -15, 1, -16],\n [-24, 10, -24, 2, 5, 11, 4, -26, 10, -6, 19, 14],\n [15, -7, -16, -17, -24, 21, -13, 18, 18, 4, 8, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
math
|
train
| 425,075 |
math_arithmetic_matrix_svd_level_7_7_844
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-18, -21, 2, 25, 19, 26, 25, -5, 22, 19, -24, -25],\n [1, 10, -22, -18, 5, -10, -16, 11, 8, 20, -9, 9],\n [-8, -2, 19, 13, 4, -4, 24, -13, 0, 8, -14, 9],\n [-3, 6, 22, -20, -18, 23, -6, 5, -25, 17, -2, -26],\n [-16, -11, -4, -12, 0, -11, 19, 6, 12, -19, 21, -26],\n [-8, -1, 10, 26, 20, -24, -3, -5, -26, 12, -18, 6],\n [-4, 7, 22, 22, 8, 22, -17, 5, -25, -20, -3, -24],\n [-15, 12, 15, 9, 0, -26, 19, 9, 5, 0, 17, 4],\n [6, 19, 5, -23, 26, -2, 12, 2, -18, -13, 23, -22],\n [25, -10, 5, -21, -22, 2, 1, -17, -4, 22, 26, -8],\n [-23, 19, 5, -7, 19, 1, 9, -4, -24, -3, -25, -9],\n [22, 5, 21, 19, 21, 21, 3, 11, 0, 11, 11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
math
|
train
| 425,076 |
math_arithmetic_matrix_svd_level_7_7_845
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, 25, -26, 23, 13, -19, -10, -26, -13, 16, 17, -14],\n [3, -14, -24, -5, 8, -13, 13, 18, -5, 6, -15, -3],\n [-22, -18, -25, 4, 19, 2, 2, 9, 3, -5, -6, 14],\n [22, -15, -20, -2, -19, 6, -11, 13, 18, 24, 18, -17],\n [-15, -5, -20, 18, -6, 13, 11, -5, -18, -7, -14, 24],\n [-3, 3, 14, 25, 23, -9, -2, 26, -7, -16, 13, 7],\n [-4, -1, -4, 22, 15, 20, 6, -2, 7, -1, 12, -22],\n [2, 3, 18, 0, 10, 26, -2, 16, -17, 17, 7, -15],\n [2, 12, -8, -8, 2, -25, -1, 18, 10, 21, 24, 7],\n [3, -15, -7, 6, -18, -25, 1, 7, -6, -8, -13, -10],\n [-22, -6, -5, 13, -7, 1, 5, 18, -8, 1, -4, 6],\n [-9, 8, 19, 10, 15, 9, 17, -8, -1, 9, 16, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
502
|
math
|
train
| 425,077 |
math_arithmetic_matrix_svd_level_7_7_846
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-20, -4, -22, 26, -4, 9, 5, -12, 0, -10, -7, -11],\n [21, 15, 1, 4, -11, -13, 20, -17, -25, 6, 14, -5],\n [-25, -20, 25, 14, 18, 17, 3, 11, 12, -8, 20, 11],\n [-10, 10, -17, -12, -22, 23, 11, 16, 8, -23, 8, -26],\n [-10, -6, 19, -5, -22, 19, 9, 11, -18, -7, 19, 15],\n [18, -13, -7, -1, -23, 24, 12, -7, 15, 25, -16, -20],\n [17, 4, 23, -19, -4, 21, -12, -26, 20, -17, 14, -3],\n [-12, 22, 21, -6, -5, -3, -17, -4, -11, -22, 6, 9],\n [-2, 13, -1, -25, 7, 4, 13, 17, 18, -8, 10, -9],\n [23, -24, -20, -4, 10, -26, 23, -20, -5, -24, -8, 3],\n [-18, 8, 8, -14, -1, 18, 24, 1, -2, 12, -24, -16],\n [3, 26, 6, 7, 14, -24, -22, 4, -23, -19, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
math
|
train
| 425,078 |
math_arithmetic_matrix_svd_level_7_7_847
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[11, -3, 4, 22, 25, 22, 19, -2, 11, 5, 22, -1],\n [9, 0, -4, -7, 19, 0, 26, -10, -13, -24, 13, 0],\n [18, -13, 1, 17, -2, 13, -16, 25, -15, 6, -7, 7],\n [-4, -8, 9, 17, -26, -17, -26, -22, -5, 16, -25, -18],\n [17, -20, 21, -6, -20, -18, 13, -18, 24, 22, -15, 17],\n [9, -18, -17, 22, -17, 17, -10, 11, -23, -11, 22, 21],\n [9, 0, -21, 13, -18, 5, 11, 3, -13, 18, 23, 2],\n [1, -5, 4, -10, -10, 22, -12, 20, 5, 1, -16, 12],\n [-10, -15, 24, 24, 12, 25, -18, -2, -1, -23, -8, -14],\n [2, 20, -18, 15, 13, -20, -20, -6, -18, 23, 18, 0],\n [21, -6, -22, -22, -19, -12, -14, 6, 17, 20, 5, 9],\n [22, 26, -4, 7, -9, -15, -4, -25, 17, 0, 23, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
math
|
train
| 425,079 |
math_arithmetic_matrix_svd_level_7_7_848
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[21, -5, -22, -10, 16, -20, -9, -25, 4, 1, -24, -18],\n [6, 1, 1, -9, -12, -16, -2, -22, 14, 19, 0, -15],\n [-17, -18, 26, -25, -18, 20, 24, -11, -26, -6, 23, 10],\n [12, -26, 22, 20, 13, -13, 13, 21, 17, 5, -3, 12],\n [10, 6, 3, -1, 16, 17, -13, -15, 17, -24, -20, -6],\n [0, -17, -17, 9, -10, 15, 7, -9, -1, -25, -18, 18],\n [-22, -1, 25, 14, -12, -2, -1, 1, -4, -6, -5, -8],\n [23, -17, 15, 9, 4, 4, 8, 25, -16, -10, 6, -5],\n [16, -1, 9, 21, -25, 5, -24, 11, 23, -4, 23, -26],\n [-22, 17, 10, -26, -9, 25, -22, -9, 8, 5, -1, 6],\n [15, -3, 0, -8, -9, -12, 0, -16, -3, -24, 12, -20],\n [-15, 6, -5, 8, -13, -1, -8, -6, 14, 18, 4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
524
|
math
|
train
| 425,080 |
math_arithmetic_matrix_svd_level_7_7_849
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, -10, 5, 24, -23, -17, 3, 10, 24, -18, -1, -5],\n [-6, 21, -4, -15, 4, -10, 13, 18, -6, 20, 14, 6],\n [-12, 5, 8, -12, 2, -16, 2, 14, 24, -5, -1, -9],\n [-2, -6, -3, 23, 1, 26, -24, -14, 11, -21, -16, -4],\n [-18, 22, -10, -18, -8, 8, 5, 1, 1, 19, -12, -8],\n [6, -4, 1, -23, 20, 20, 4, 8, -22, 6, 21, 5],\n [21, 21, -12, 10, 7, 13, 20, -18, 14, 8, 20, -3],\n [-9, -10, -26, -16, 6, -21, 2, 17, -7, -9, -13, 18],\n [16, -7, -9, 26, 0, -9, -10, -2, -22, -21, 13, 9],\n [6, -12, 12, -11, 11, 12, -3, -6, 11, -14, 2, 7],\n [-22, -24, -6, -18, -24, 17, 3, -24, 22, 20, 22, 12],\n [14, 23, 7, -10, 26, -13, 22, -16, -26, -26, 25, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
math
|
train
| 425,081 |
math_arithmetic_matrix_svd_level_7_7_850
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-25, -15, 18, 15, -25, -4, 7, -10, 14, -13, -16, -7],\n [17, -20, -26, 21, -12, 18, 11, 7, -18, -26, -18, 15],\n [-25, -5, -2, 24, -13, 8, -11, -8, 14, 4, -25, 5],\n [9, -16, -19, 21, -22, 7, 5, 20, -21, -19, 7, -23],\n [9, 17, -2, -1, 6, -18, 20, -19, -10, -12, 15, -14],\n [16, 21, 20, 23, 17, -24, 26, -15, 2, -26, 5, 10],\n [-7, -19, 10, 4, 4, -2, 23, 13, 18, 22, -19, 3],\n [3, 0, 8, 23, 17, -14, -6, -18, -3, 21, 6, -26],\n [-19, -24, -13, -13, 22, 6, -23, 11, -2, 20, 26, -14],\n [14, 26, 12, -2, 11, -18, 11, 16, 11, 8, 26, 2],\n [23, -13, 11, 7, -2, 15, 1, 24, 3, 12, 10, 20],\n [15, -25, -6, 7, -8, 13, 11, 4, -1, -15, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
97
|
math
|
train
| 425,082 |
math_arithmetic_matrix_svd_level_7_7_851
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[21, 4, 21, -12, -17, 9, 13, -1, -18, 26, -10, -21],\n [-5, -11, -5, 26, 12, 25, -23, -23, -18, -13, 15, 24],\n [-1, -24, 5, -16, 24, -24, -14, 17, -14, -3, -7, -17],\n [-4, 25, 15, 6, 8, -13, 26, -11, 3, -8, 6, 14],\n [-25, 23, 11, 22, -19, -7, -24, -6, -26, -6, 23, -19],\n [-25, -4, 14, 26, -16, -11, -18, 22, 5, 20, 12, 9],\n [-4, 20, 22, 3, -17, 4, 17, -1, 21, 12, 15, 3],\n [-25, 2, 5, 17, 24, 11, -6, 0, 25, -3, 7, -4],\n [25, -13, 12, -22, 26, -18, 18, 20, 10, -19, -20, 3],\n [-15, -7, 2, -15, -7, -5, 19, -4, 21, 18, -1, 18],\n [20, 16, 1, 13, -18, -22, -25, 15, 1, -14, -12, 26],\n [-13, 16, 19, 12, -13, -24, -17, 26, 11, -21, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
math
|
train
| 425,083 |
math_arithmetic_matrix_svd_level_7_7_852
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[21, 16, -7, 22, 17, -24, -23, -16, 14, 4, 2, 11],\n [-7, -3, -4, -5, -5, 14, -7, 19, 11, 21, 23, 14],\n [-20, -3, 23, 17, 10, 19, -2, -13, 2, -24, 12, 2],\n [-11, -6, -5, -6, -5, -18, -4, 22, -18, 23, 19, 5],\n [9, 20, 9, -22, -1, -23, -3, 14, 16, -13, 0, -15],\n [-9, 17, -18, -25, 24, 11, 5, -14, 20, -3, -25, 21],\n [11, 19, -8, 20, -9, 17, -25, -1, 25, -3, 21, 0],\n [26, 25, 2, 20, -19, 26, 4, 7, -13, -23, 16, 22],\n [2, 12, 6, -6, 14, 22, -26, 0, -25, 24, 16, -17],\n [-17, 3, -26, 4, 8, 21, 2, -14, -18, 13, 16, 14],\n [-16, -3, -2, -14, -13, 14, -24, -21, 19, -14, -26, 2],\n [-13, -15, -1, -4, -24, -13, 7, -4, -17, -23, 12, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
83
|
math
|
train
| 425,084 |
math_arithmetic_matrix_svd_level_7_7_853
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-17, -3, 7, -3, -2, 25, -12, -15, -26, 15, -18, -13],\n [14, 4, -3, 26, 25, -17, 15, 16, -9, -24, -15, 8],\n [17, -4, -5, -16, 19, 22, -4, -15, 2, -2, -3, 26],\n [-23, 10, 2, -24, 4, -2, 20, 10, -4, 22, -5, 2],\n [9, 24, -14, -24, 19, -5, 22, 26, 9, -17, -18, -8],\n [-19, 6, -7, 3, 8, 4, -8, 23, 19, -13, -17, -24],\n [7, 24, 1, -8, 12, -1, -23, -15, -1, -20, -24, -1],\n [-25, -15, 5, 24, 11, -16, 5, 18, -12, -21, -1, -19],\n [-19, 11, -19, -10, 12, -8, -24, 14, 22, -18, 26, 19],\n [6, 5, 5, -21, 22, 22, 26, 2, 10, -10, 23, -8],\n [4, -8, -4, 23, 20, 8, -13, -26, 22, 6, 22, 9],\n [-26, -7, -5, 8, -24, -15, 16, 10, -14, -15, -25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
| 425,085 |
math_arithmetic_matrix_svd_level_7_7_854
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-26, 14, 8, -3, 25, 11, -1, -16, 25, 25, 16, -12],\n [-21, 13, -18, 23, -21, -10, -4, 4, -11, 24, -5, -11],\n [18, -15, -18, -21, -23, 11, -10, -17, 13, 8, 20, -6],\n [26, -8, 0, -16, -21, 14, 16, 1, -24, 14, 18, -3],\n [10, -14, -12, -18, 12, 8, 18, -9, 16, 26, -24, 1],\n [-11, 15, 14, 20, 16, -4, 5, -17, 11, 11, -14, -12],\n [1, -14, 8, -25, -26, 14, 5, 3, -5, -23, 26, 19],\n [-3, -13, -10, -13, 13, 12, 14, 25, 0, -6, 13, 8],\n [-1, 4, 6, 22, -16, -11, -21, 7, 14, 5, -6, 2],\n [-16, -22, 0, 1, 4, 23, -16, -14, 16, -21, 0, 3],\n [26, 21, -8, -13, -18, 18, 1, 1, 19, -2, -1, -23],\n [-24, 7, -6, -10, 11, 7, 17, -15, -2, -6, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
522
|
math
|
train
| 425,086 |
math_arithmetic_matrix_svd_level_7_7_855
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-21, -7, 26, -7, 5, 4, -7, 24, 3, -24, -7, -19],\n [-6, 21, -4, -26, -25, -17, 10, 3, 24, 17, -3, 5],\n [23, 3, 11, -13, -24, -2, 18, -20, -10, 14, 0, 11],\n [11, -4, 5, -25, -16, 7, 25, 20, 7, -20, -17, -2],\n [-25, 22, 3, -10, 2, -9, 19, 8, -10, 20, -5, 24],\n [-2, -7, -11, -2, -12, 10, -12, -12, -9, 10, -26, 6],\n [-24, 22, -5, -6, 19, 14, 0, -23, 24, 8, -26, -23],\n [-3, 19, 2, -5, -4, -6, -13, -19, -11, 8, -3, -1],\n [-20, -2, 11, 18, -1, -1, 3, -25, 16, 26, -18, 12],\n [17, -16, -12, -15, 8, 23, 13, 20, -11, 22, 5, -9],\n [26, 18, -6, -11, -20, -22, 17, 14, 6, 4, -6, -24],\n [-17, -16, -5, -10, 23, -2, 14, 1, 23, -7, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
math
|
train
| 425,087 |
math_arithmetic_matrix_svd_level_7_7_856
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, -17, 24, 6, 14, -7, 21, -13, -19, -19, 11, 1],\n [-17, 13, -13, 24, -13, -21, 7, -10, -6, 12, 1, 11],\n [-12, 9, 9, -18, 17, 8, 18, -9, -10, -9, -23, 21],\n [-7, -14, -16, 24, 16, 6, 1, -19, 16, -7, -9, -20],\n [17, 6, 24, -16, 26, 3, 8, 18, -7, 10, -17, 3],\n [-9, -2, 5, 12, 7, 17, 12, 4, 1, -1, 17, -23],\n [16, -7, -19, -25, 23, 23, 0, 7, 9, -6, -19, -4],\n [16, -19, -22, 13, -26, -6, 17, 16, -17, -25, -6, -14],\n [17, 23, 1, 3, -9, 15, -25, -8, -6, -1, 19, -2],\n [-8, -2, 14, -7, -21, -9, 22, -9, -7, 12, 7, -17],\n [6, 24, -8, -25, 20, 22, -24, 3, 12, -8, -6, 17],\n [-13, 4, -6, -10, 26, 24, -3, 10, 13, 14, 7, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
507
|
math
|
train
| 425,088 |
math_arithmetic_matrix_svd_level_7_7_857
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-7, -11, 22, 15, -15, 14, -3, -14, 7, 0, 11, -6],\n [26, -24, 22, -13, 16, 11, 10, 14, 15, 17, 3, 18],\n [-17, -26, 12, 1, 18, -8, 3, -7, 25, -7, -4, 4],\n [5, 20, 25, -1, -13, -21, 6, -19, -23, -14, 8, 2],\n [-2, 7, -16, 11, 2, 18, -5, 7, 19, -16, 1, -19],\n [-3, -17, -12, 18, 12, 12, -6, 9, 9, 23, 21, -7],\n [-14, -25, 20, 0, -20, 14, -1, 3, -8, 13, -6, -1],\n [-17, 9, 17, 0, -19, -1, -26, -4, -18, 4, -20, -18],\n [-20, 1, 7, 26, 25, -11, -17, -3, -17, 19, 2, -2],\n [14, 3, 24, -8, 26, 4, 3, 7, 1, 25, -8, -16],\n [1, -21, -10, 10, 0, 16, 9, -26, -11, -23, 20, -4],\n [5, -24, 17, -6, -3, -12, -16, -24, -8, 16, -19, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
math
|
train
| 425,089 |
math_arithmetic_matrix_svd_level_7_7_858
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, 7, 17, 13, 11, -1, -24, 5, 16, 21, 16, -17],\n [-17, 22, -16, -13, 4, -18, 21, -21, 22, 8, 7, 16],\n [-9, -4, 3, -24, -12, 10, 16, -24, -12, -24, 2, 4],\n [-20, -20, -16, 21, 1, 9, 16, 19, 13, -2, -10, 23],\n [11, -6, 25, -7, -17, -21, -15, -10, 18, 6, 9, 21],\n [-8, -22, 18, 15, 2, 10, 21, 3, -26, -15, -12, -22],\n [11, -16, -7, 2, -13, -1, 7, -17, 0, 17, 14, 14],\n [-2, -17, 12, 5, 7, -4, 6, 5, -5, -5, 26, -4],\n [-8, -4, -5, 3, -8, -5, -26, 7, -1, -23, 21, 18],\n [-15, 1, 10, -24, 1, 2, -7, -25, 10, -26, 19, 20],\n [9, 17, 15, -9, -18, 10, -2, 14, -8, -2, 25, 22],\n [-12, 19, 23, -1, 19, -7, -24, -2, -6, 7, 25, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
525
|
math
|
train
| 425,090 |
math_arithmetic_matrix_svd_level_7_7_859
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[11, -3, 14, -2, -26, 2, 5, 20, -26, 8, -11, 5],\n [20, -12, -22, -17, -5, 16, -19, -12, -7, -2, -15, -1],\n [-23, -1, -17, 21, -12, -22, 5, 5, -5, -5, -15, -16],\n [-3, 16, 18, 14, -11, -11, -26, 24, -4, 1, 5, 24],\n [26, 9, 10, -24, 24, -14, 1, 1, 18, -3, 24, -14],\n [-3, -22, -10, 23, -15, 22, -9, 6, 4, 7, 3, 18],\n [5, -17, 4, 8, -12, 0, 0, -26, -15, -23, -4, 7],\n [25, -4, 24, -8, -7, -7, 2, -14, 1, -3, -5, -5],\n [13, -16, -19, 5, -3, -15, 22, 13, -6, -24, 12, 18],\n [-9, 15, -21, 9, 18, -12, 22, 18, -12, 11, 24, 17],\n [25, 25, -3, -20, -18, -16, -11, -20, -2, -13, -26, -7],\n [1, 22, 11, 7, -18, 21, -7, 16, 25, 11, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
527
|
math
|
train
| 425,091 |
math_arithmetic_matrix_svd_level_7_7_860
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-5, -14, 17, 20, -2, -5, 11, 25, -7, 5, -11, 26],\n [-7, 14, -5, 15, 11, 18, 10, -12, -15, -18, 10, 17],\n [-12, 17, -5, -15, 0, -8, 20, -2, -17, 8, 17, -15],\n [23, -19, -16, 12, -8, -4, -3, -12, -7, -2, -13, -17],\n [21, 23, 2, 20, 22, 22, -15, 6, -4, -13, -4, 22],\n [26, 10, -5, 2, 9, -25, -7, -22, 0, -24, -9, -14],\n [-5, -14, -15, 5, 9, -20, -21, 13, 10, -21, -2, 0],\n [-22, -8, -18, 23, 13, -26, 19, -18, 12, -17, 22, 16],\n [22, -13, 19, 13, -2, 23, -8, 23, -10, -9, 19, 13],\n [23, -18, -26, -21, 11, 11, 12, -10, -18, -16, 26, -9],\n [18, 19, 10, -20, 8, 17, -20, 12, -16, -17, 7, -3],\n [-15, -18, -5, 11, 19, 5, -19, 21, -6, -11, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
math
|
train
| 425,092 |
math_arithmetic_matrix_svd_level_7_7_861
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 24, 12, -21, -23, -4, -18, 9, -16, 8, -15, 8],\n [-20, 2, -6, -24, -3, 3, 0, 2, 3, 9, -4, 10],\n [-1, 23, 9, 1, 10, 24, -23, 2, 17, -13, 17, 18],\n [10, 6, 24, 4, -13, -2, -18, -2, 14, 19, -2, 3],\n [-7, -4, -26, -12, -6, 3, -16, 23, -1, 25, 3, -18],\n [-22, 20, 20, 7, 6, 7, -26, 24, -12, 4, -15, -20],\n [18, 6, 15, 5, 24, -22, 11, -22, -10, -20, -2, -2],\n [-24, 25, 9, 1, -4, -19, 4, -6, 18, 8, 14, 14],\n [15, 23, 2, -24, 17, -2, -25, 17, 14, 7, -12, 12],\n [12, 13, 20, -15, 25, 25, -3, -21, -21, 21, 10, -1],\n [-24, 5, 19, -9, 1, 6, -10, 5, -15, 10, -6, -25],\n [-1, 12, -10, 25, 9, 7, -8, 5, 23, -5, 23, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
math
|
train
| 425,093 |
math_arithmetic_matrix_svd_level_7_7_862
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[12, -9, 24, -3, -26, 14, -25, 13, -3, 13, 25, -25],\n [0, -25, -4, 6, 7, 5, -24, 0, -15, -19, -7, 25],\n [-10, 18, 6, -16, -18, 7, 17, 16, -20, -11, 0, -12],\n [-3, 10, 22, 13, -8, 26, -4, 12, 4, 3, -20, 18],\n [23, 23, -24, 11, 21, 3, -17, 7, -14, 12, -14, -2],\n [14, 7, 13, 13, 13, 7, -12, -24, 25, 19, -5, 7],\n [-22, 14, -5, 2, -19, 7, -23, 25, -2, 23, -4, -2],\n [7, 17, -21, 7, -6, 17, 3, -24, -12, -6, -8, -8],\n [22, 19, 7, -13, -23, 4, 19, -16, 17, 18, -16, 22],\n [-23, -11, 11, -21, -9, 26, -2, -3, 25, 12, 20, -18],\n [10, 7, 7, 13, 13, 10, 1, 23, 21, -16, -13, -1],\n [-19, 1, -7, -2, -17, -16, -1, -4, -8, -9, 23, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
math
|
train
| 425,094 |
math_arithmetic_matrix_svd_level_7_7_863
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[12, 13, -12, -11, -7, -8, -16, -20, -8, -3, 4, 25],\n [21, -19, 23, -3, -19, -14, -17, -8, 23, -4, 15, 6],\n [3, 3, 2, 10, 8, -18, -19, 21, -2, 15, 24, 19],\n [10, 11, -19, -1, -16, 13, -4, 5, 18, -26, 22, 21],\n [-18, 13, 1, 6, 5, -19, 10, -9, -20, -9, 21, -15],\n [-23, -14, -16, -11, 17, -13, -11, 25, 26, -5, -9, 13],\n [-2, 8, -20, -7, 0, 2, -17, -16, -7, 6, 16, 10],\n [-14, -11, -16, -22, 11, -24, -25, 26, 11, -17, -21, -6],\n [4, 7, 22, 5, 2, -26, 6, 11, -10, 7, 22, -11],\n [-20, 9, -14, -7, -23, -22, -11, -18, 16, -15, -13, -12],\n [-22, 15, -9, -19, -19, -2, -23, 24, -1, -16, -21, 6],\n [-5, 2, -22, -26, -5, 8, 4, -24, -24, -20, -26, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
533
|
math
|
train
| 425,095 |
math_arithmetic_matrix_svd_level_7_7_864
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-3, 25, 10, 3, 5, 5, -6, 21, -11, -23, -10, -14],\n [8, 13, 7, -16, 9, -2, 13, 3, -14, -3, 9, 7],\n [-19, -9, -20, 22, 19, -5, -20, -14, -25, 17, -25, 2],\n [0, 13, -9, -25, 26, -23, 22, 19, -19, 9, 21, -18],\n [-9, 23, -5, 18, -16, 0, 5, -25, -25, 3, -5, -5],\n [-3, 0, -16, -14, 0, -12, 21, 21, 22, -10, 12, -18],\n [-4, -23, -12, 16, 4, -21, -1, -26, -5, 3, -5, 6],\n [-22, 9, 19, -17, -26, 26, -15, 22, -24, -17, -26, -8],\n [-9, 18, 25, 4, 22, -5, -23, 14, -17, -17, -12, -22],\n [23, 16, 18, -10, -9, 21, 23, -22, -19, 19, 0, -2],\n [25, -1, 18, -4, 14, -4, 2, 6, -9, -20, 5, 14],\n [-20, -19, 23, -6, 15, -10, 24, 6, 3, -25, 19, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
math
|
train
| 425,096 |
math_arithmetic_matrix_svd_level_7_7_865
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-5, 5, 22, -2, 22, -19, 6, 2, -10, 13, 18, -25],\n [22, 12, 21, 22, 4, -23, 15, -1, -18, 4, -17, 24],\n [-21, 17, -1, -16, -12, -7, -13, 17, 24, -6, 17, 0],\n [3, -20, 10, -12, -11, 16, -7, 22, 11, -7, -5, -21],\n [17, 25, 13, -7, -22, 26, -16, -25, 3, -19, 13, -19],\n [-10, 12, 8, 3, -26, -22, -11, 9, -12, 22, -10, -14],\n [-3, 16, 21, -23, 20, 17, 19, -14, -18, -1, 20, -11],\n [15, 10, 16, -21, -16, -25, 3, -8, -4, 20, -15, 12],\n [-21, 16, 9, 19, 15, -12, 9, -14, -19, -2, -3, 4],\n [13, -14, 2, 5, 16, 10, -9, -1, -9, 7, 4, -12],\n [10, -7, 1, -23, -19, -9, 5, 26, -4, -12, 17, -20],\n [21, 4, 5, 13, -13, -8, 23, 13, -11, -18, -26, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
math
|
train
| 425,097 |
math_arithmetic_matrix_svd_level_7_7_866
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-19, 12, 5, -19, -14, -24, -25, 18, 1, -23, -4, 7],\n [-20, 3, -18, -8, -18, -4, -16, -14, 2, 4, -19, 19],\n [-8, -22, 21, 0, 12, -13, -5, -5, -22, 25, -11, 12],\n [-1, 26, -11, -15, -11, 22, 13, -15, 5, -22, 9, 1],\n [24, 17, -23, 12, 12, 2, -8, -2, 8, -3, -8, -4],\n [4, -8, 5, -14, 19, -9, -20, 18, -3, 19, -10, -12],\n [-18, 7, 8, -19, 23, -16, -3, 15, 3, -6, 16, 8],\n [-15, -18, -15, 1, 2, 19, 18, 13, 8, 2, 24, -21],\n [-11, 19, 1, -26, 2, 25, 13, -21, 0, 10, -5, -20],\n [-26, -14, 21, 24, 17, -13, -12, -15, 22, 14, -23, 23],\n [17, 16, -6, -25, 25, -6, -13, 17, -25, -16, 10, -13],\n [20, -7, 8, 0, 22, -21, -20, 18, -26, -14, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
| 425,098 |
math_arithmetic_matrix_svd_level_7_7_867
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[11, 9, 11, -26, -26, -8, 24, 3, -14, -20, 16, -7],\n [17, -18, -14, 12, -7, -2, -22, 21, 25, 23, -2, -15],\n [-1, -5, -26, -19, 9, 22, -24, -5, 23, 13, -6, -6],\n [4, -26, 14, 0, -25, 2, 15, 19, -26, 15, -19, 8],\n [18, 8, -20, -4, -4, 16, 19, 12, -8, -12, -19, 6],\n [8, 13, -14, 23, 4, -20, -7, 11, -19, 9, -13, 3],\n [24, -18, -14, -15, -25, 11, -6, 2, -7, 23, -18, -12],\n [26, 6, 26, -20, -24, -4, -5, 12, -14, -18, 7, -15],\n [7, 18, 6, 23, 8, 1, 12, -24, 20, -15, 16, -14],\n [-24, -9, 20, -1, -17, 25, -23, 10, -15, 26, 24, -11],\n [-10, 13, 4, -1, -25, 2, 3, 21, 20, -16, 10, 7],\n [-20, 12, 2, 6, 22, 0, -11, -10, -16, -13, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
math
|
train
| 425,099 |
math_arithmetic_matrix_svd_level_7_7_868
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, 25, -2, 13, 17, 16, -15, 20, 26, -23, 15, 21],\n [14, 22, 0, 18, -19, -19, 2, -24, -6, 4, -14, 4],\n [-10, 21, 5, -3, -25, 15, -24, -1, -25, 6, 7, -1],\n [7, 11, -13, 4, -7, -17, -7, 6, 18, 21, -25, 19],\n [24, -15, -11, -18, -16, -6, -15, -23, -1, -8, 15, 20],\n [-10, 17, -26, 21, -19, 3, 24, 14, -3, 16, -10, 3],\n [14, 25, 16, -18, -25, -1, 5, 0, 14, -16, -26, 25],\n [10, -9, -19, 0, -9, -18, -25, -10, -16, 19, -21, -22],\n [-15, 17, 15, 8, 24, -3, 3, 25, -10, 20, 9, -21],\n [5, 7, 17, -11, -20, 5, -10, 5, -13, -1, -18, -14],\n [23, -2, -15, 18, -11, 22, 3, 25, -6, -3, 16, -22],\n [20, 6, 22, 4, 23, -18, 22, 8, -19, -16, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
math
|
train
| 425,100 |
math_arithmetic_matrix_svd_level_7_7_869
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-7, 0, -13, -5, 22, -20, -16, -10, -14, 24, -10, -16],\n [-23, -11, 4, -6, 6, -14, 22, 2, -12, -17, 6, -12],\n [16, -14, 8, -6, 3, 21, 19, 16, 15, 18, -20, 22],\n [-3, -11, -22, -21, -25, -24, 26, -17, -3, 21, 6, -7],\n [26, -5, 5, 3, -24, -23, 24, -23, 12, 4, -18, 3],\n [26, 2, -2, 25, 12, 8, -2, 10, 9, -16, -1, 15],\n [19, -2, -6, 22, -25, -17, 12, 8, 6, 14, 4, -23],\n [-24, -22, -10, 22, -14, -26, 18, 12, 17, -4, 14, 26],\n [23, -2, 25, 26, 4, -14, -26, 7, 2, 4, -19, -25],\n [-15, 6, 3, 14, 0, -2, 11, 23, 6, 11, 25, -11],\n [5, -3, -25, -25, -7, 0, -5, 12, 21, -8, -20, -24],\n [23, 7, 14, -4, -22, 16, -24, -3, 0, 7, 24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
math
|
train
| 425,101 |
math_arithmetic_matrix_svd_level_7_7_870
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-6, -15, 5, 20, 22, -5, 7, -4, -26, -23, -10, -1],\n [4, 12, 10, 13, 6, 1, -17, 9, 19, -18, -1, 22],\n [19, 24, 7, -13, 14, -1, 10, 4, 20, 11, 21, 16],\n [1, 14, 17, 13, -10, -15, 0, -26, 13, 6, -14, -22],\n [25, 10, 13, 16, 1, -3, -7, 13, 15, 10, -7, -4],\n [-24, -22, -12, 19, 26, -22, 7, 12, 12, 19, -4, 20],\n [-10, -18, -23, 3, 21, -13, 3, 4, -26, 0, -25, 18],\n [13, 14, -17, -3, -7, 15, -11, 14, 11, 17, 22, 15],\n [16, 14, -9, 8, 3, 10, -22, 10, -16, -23, 10, 24],\n [-16, -15, 22, 20, 1, -1, 7, -26, -21, 6, 20, -3],\n [7, -19, -11, -11, -11, 25, 24, 7, -7, -13, -1, -25],\n [-8, -25, 23, -1, -2, 22, -8, 19, 22, 21, 24, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
| 425,102 |
math_arithmetic_matrix_svd_level_7_7_871
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -15, -6, 9, 13, 1, 6, 19, -18, -9, -3, 5],\n [-4, -15, 7, -1, -21, -22, -4, 23, 19, -12, 5, -14],\n [14, 1, 24, 6, -19, -11, 12, 5, -11, 18, -14, -7],\n [-8, -16, 0, -11, -18, -14, -8, 3, 15, 12, -10, 3],\n [2, 15, -25, 23, 21, -24, -7, -26, -22, 6, 12, -4],\n [-9, -23, 14, 6, -1, -5, 3, -1, -26, -21, -10, 4],\n [21, 24, -23, -17, 21, 26, 12, 7, -5, 25, -5, -20],\n [12, 10, -12, -8, -17, 10, 10, 23, -23, 19, 23, 14],\n [-2, 1, 22, 17, -9, 21, 8, -8, 15, 26, -7, 12],\n [6, -26, 20, -26, 14, 19, 18, -8, 21, 22, -18, -13],\n [-24, 3, 14, 25, -26, -22, -4, -21, -7, 19, 15, -19],\n [4, -12, -1, 6, 21, 25, 12, 5, -26, -22, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
math
|
train
| 425,103 |
math_arithmetic_matrix_svd_level_7_7_872
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[15, 26, -22, -19, -21, -17, 19, 13, 11, 14, 20, -11],\n [1, -26, 19, 25, -9, 12, 17, 15, 20, 12, 10, -16],\n [-24, 2, -23, 4, -16, 3, -12, -12, 5, 2, 22, 16],\n [1, -6, 11, 12, -16, 5, 0, -3, 10, -26, 5, 26],\n [-26, 18, 7, -9, 2, -21, 4, -13, -16, -22, -5, 24],\n [-14, -15, 14, -23, 11, -23, 3, -26, 22, 4, 22, 15],\n [23, -4, -13, 8, -10, 5, 9, -4, 7, 20, 11, 14],\n [12, -5, 15, -25, -7, -13, 11, 10, 10, 25, -15, 1],\n [-19, 2, -6, 12, 21, -9, 21, -8, -17, -18, -4, 3],\n [-5, 2, -21, 23, 8, -13, -22, 19, -9, 8, 3, -20],\n [7, 11, 15, 26, -8, 18, -16, 14, -10, -16, 18, 1],\n [-24, -17, -3, 6, -1, -22, -3, 17, -1, -20, -15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
math
|
train
| 425,104 |
math_arithmetic_matrix_svd_level_7_7_873
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[17, 9, -10, -11, 4, -9, 5, -25, 22, -17, 21, 12],\n [-13, 25, 20, -17, 1, -3, 13, 7, 22, 14, -18, 20],\n [2, 18, 14, 9, -18, 14, 20, -16, -6, -14, 22, -3],\n [-26, 8, 8, -6, 20, -22, -6, -23, 6, 9, -19, 2],\n [26, -20, -26, -22, -14, -1, -15, -19, 26, 22, 7, -5],\n [23, -18, -18, 18, -9, -10, -20, 12, 24, 7, -11, 1],\n [-2, -5, 7, -12, -11, -11, 11, -5, 2, 5, 16, -3],\n [14, 23, -4, 11, -4, -2, -1, 9, 23, 7, -14, 6],\n [14, 19, -23, 26, 9, -7, 2, -12, -12, -14, -13, -5],\n [-26, -26, 4, 6, 20, -26, 11, -3, 12, -5, -4, -25],\n [-5, -18, -23, 23, -2, -12, -3, 13, -20, -19, 0, 0],\n [18, 8, 11, 3, 12, 2, -22, -9, -12, -1, -25, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
math
|
train
| 425,105 |
math_arithmetic_matrix_svd_level_7_7_874
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-2, -2, 5, -5, 25, -17, 9, -15, -6, -12, -16, 19],\n [-20, -3, 3, -13, 13, 19, -21, 23, 19, -19, 9, -15],\n [-22, -14, -8, -5, -15, 5, 23, 11, 11, -10, -1, -11],\n [-15, 10, 19, -11, -22, -19, -20, 0, -1, -14, 8, 19],\n [-10, -20, -18, 15, -17, 18, 15, 11, 26, -13, 10, -14],\n [-19, 14, 25, -17, 6, 10, -7, -23, -26, 24, -8, -3],\n [20, -16, -5, 10, -24, -10, 21, 13, -7, 8, 17, 13],\n [-12, -16, -14, -1, -4, 13, -14, 21, 23, -11, 18, -13],\n [13, 25, 7, 25, 13, 2, 1, 0, 11, -14, -24, 12],\n [11, -22, -11, 4, -5, -24, -22, -24, -12, 7, -12, 0],\n [-14, 7, -9, -17, 5, -23, -25, 3, 25, 4, 19, -24],\n [17, -22, 7, -13, 10, -20, -12, -8, -8, -10, 21, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
math
|
train
| 425,106 |
math_arithmetic_matrix_svd_level_7_7_875
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-14, -6, 16, -26, -9, -3, 3, -20, 0, 25, 0, -24],\n [25, 26, -11, -23, 18, -26, 6, 17, 18, -1, 12, -24],\n [-23, 6, 23, -22, 2, 25, -16, -24, -9, 3, -10, 19],\n [3, 3, 6, -10, 12, -11, 6, 20, -25, -25, -3, -22],\n [9, -24, 13, 5, -13, 11, 16, -22, 10, 19, -1, -10],\n [-8, -16, -20, -14, 24, -2, 23, 21, -15, 4, 1, -12],\n [6, -16, 12, 5, -11, -18, 25, 14, -15, -8, -13, -15],\n [-3, -18, -6, -15, 18, 10, -22, -18, 24, -7, -21, 13],\n [23, -14, -11, -7, -22, 16, -10, -17, 3, -20, -16, -19],\n [24, 10, 4, 21, -26, -2, 1, -4, 24, 2, -5, -17],\n [19, -10, -14, -11, 24, -15, 21, 22, -12, 12, -8, -6],\n [5, -22, 20, -12, 5, -26, -12, 8, -7, 4, -7, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
98
|
math
|
train
| 425,107 |
math_arithmetic_matrix_svd_level_7_7_876
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-3, 13, 25, -17, -13, 8, 2, -18, 25, -17, 26, -25],\n [-4, -9, -26, -16, 10, 9, 6, 9, -3, -2, -4, -5],\n [6, 20, -8, 7, -4, 19, -1, -5, -24, -23, 6, -16],\n [-7, 23, 5, 26, 21, -12, -2, -10, -5, 7, 6, -2],\n [-13, 19, 23, 3, -5, -5, -8, 11, -23, -19, 18, 25],\n [12, -17, 23, 1, -6, -26, 10, 7, -16, -11, 12, -13],\n [-26, 4, 17, 16, 22, -15, 0, -10, 23, -11, -26, 3],\n [10, -4, 0, 10, -11, -3, 1, 3, -1, -3, 4, -2],\n [24, -25, -20, 21, -4, 2, 8, 3, 2, 4, 23, 15],\n [-25, 24, -12, -11, -19, 1, 13, -10, 26, -13, -6, 23],\n [0, -6, 5, -11, 1, 11, 2, 22, 24, 9, -3, -6],\n [12, 23, -19, 1, -9, -8, -8, 11, 17, -1, -21, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
519
|
math
|
train
| 425,108 |
math_arithmetic_matrix_svd_level_7_7_877
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[22, -1, 1, 17, 5, 7, 18, 10, -2, -5, 4, -21],\n [4, -26, 13, -18, -15, -6, 15, -24, 15, 19, -22, 10],\n [-14, 2, 1, 22, -2, -17, 7, -12, 3, -14, 10, 22],\n [-22, -13, -17, 20, 7, 4, 24, -22, -21, -14, 13, -14],\n [19, 21, 6, 10, -4, -6, -19, 7, 26, 4, 4, -7],\n [8, -25, -3, -16, -23, -1, -13, 19, 15, -7, 9, -2],\n [12, -17, 8, -22, -23, 22, -7, -4, 16, -22, 2, 17],\n [2, 19, 5, -5, 18, 16, 17, -20, 6, -5, 14, 1],\n [-6, 24, 9, -23, 16, -21, -8, 24, 26, -16, 23, -10],\n [19, -9, 19, -14, 14, 24, -16, 24, 0, 22, -11, 23],\n [-12, -13, -12, -9, -15, -1, 15, 13, -9, -1, 19, -9],\n [-26, -11, 10, -6, -19, 25, -25, -8, 2, 3, -24, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
math
|
train
| 425,109 |
math_arithmetic_matrix_svd_level_7_7_878
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[8, -9, -1, -2, -19, -9, -3, -22, -1, -17, -16, -23],\n [-17, 10, -15, -17, -15, -22, 16, 0, 6, 5, -22, -4],\n [-3, 19, -25, 3, -17, -26, -14, 9, -24, 17, 17, -11],\n [-13, 13, 18, 21, 20, 19, -22, -2, 11, 2, -10, -18],\n [-9, -15, 18, 22, 12, 1, 26, 5, -7, 13, -26, -15],\n [-5, 24, -19, -15, 11, 26, -3, 11, 12, 14, 1, -15],\n [4, 11, 11, 1, -18, -5, -20, -23, 2, 26, 18, -17],\n [15, -6, -23, -3, -6, -9, -1, -19, -4, 20, -18, -2],\n [9, 5, -20, 6, 4, -10, 8, -5, 2, 26, 24, -9],\n [20, -17, -12, -20, 11, -13, -1, -9, -9, -21, 18, 16],\n [-2, 14, -15, 24, 3, -8, -6, -11, 8, -20, 15, -8],\n [11, -1, 14, -9, -15, -22, -1, -22, 11, -9, -21, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
527
|
math
|
train
| 425,110 |
math_arithmetic_matrix_svd_level_7_7_879
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-16, -11, -1, 12, 22, -9, 9, 10, -1, 6, -26, 0],\n [10, -5, -8, -14, 10, 23, -24, 0, 8, -18, -7, -1],\n [19, 8, -6, 5, -5, -13, 2, 4, -10, -4, 9, -2],\n [-9, -11, -25, -1, 7, -15, 21, -17, 2, -25, -11, 9],\n [15, 22, 9, -5, -21, 8, 14, 10, 4, 14, 18, -25],\n [8, 1, -20, -6, 17, -2, -9, 14, 18, 16, -14, -19],\n [26, 20, -13, -10, -14, -16, -17, -10, 2, 17, -25, -26],\n [20, 0, -8, -9, 8, -18, -2, -5, -14, 16, 2, 24],\n [-5, -11, -8, -19, -15, 26, -25, -22, -13, -11, 24, 7],\n [15, -17, -19, 17, -2, 24, 0, -17, 9, 12, -20, -12],\n [23, -14, 6, 8, -25, 13, -16, -6, -13, -2, -4, 17],\n [-26, -21, 9, 22, -9, 22, 15, 10, -22, 25, -26, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
math
|
train
| 425,111 |
math_arithmetic_matrix_svd_level_7_7_880
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, 21, -13, 1, 4, -4, 15, 4, -20, -7, -7, 4],\n [-18, -16, -21, 16, 19, -9, 2, -26, 17, 6, -24, 11],\n [18, 10, 14, -11, 11, 8, -1, 9, -6, 9, -8, -18],\n [0, 4, -12, 5, 2, -18, 17, 10, -10, 22, -13, 12],\n [24, 13, -21, 11, 5, -21, 24, 24, 26, 5, 22, 7],\n [7, -15, -18, -22, -10, 1, 23, -5, -21, 23, 5, -8],\n [25, 21, 18, -10, -17, -12, 23, 12, 11, 21, -6, 13],\n [-24, 3, -12, 0, 4, -11, 1, 18, 13, 10, 16, -18],\n [-18, -15, 1, -20, 8, 9, 20, 11, -26, 7, -5, 3],\n [-7, 24, -19, 18, -20, -25, 3, -15, 9, 15, 11, 0],\n [7, 11, -16, -7, 3, 16, 5, -1, -4, 14, -3, -25],\n [14, 5, 26, 21, -12, -21, -11, -16, 18, 19, -18, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
526
|
math
|
train
| 425,112 |
math_arithmetic_matrix_svd_level_7_7_881
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-20, 25, 25, 3, -5, -23, -22, -5, -23, 13, -23, 16],\n [18, -12, -11, 15, -7, -17, 6, 4, 11, 17, -26, -2],\n [10, -9, -2, -12, -23, 8, -23, 15, -7, -15, 3, 14],\n [-5, 9, 7, 0, -2, 12, -15, -15, -6, 23, 6, -20],\n [-8, -3, 18, -7, -22, 3, 24, -20, -7, 20, -10, 26],\n [7, -20, -16, -9, 3, -7, -25, -20, 0, -12, -8, 7],\n [-25, 1, -25, -16, -21, -4, 19, -17, 6, -8, -16, -3],\n [1, 18, -15, 1, -22, -8, -19, 17, 10, 1, 17, 16],\n [-22, -19, 21, -3, -7, 8, -21, -22, -17, 26, 1, -15],\n [26, -12, -24, -4, 26, 25, 9, -20, -26, -19, 0, 22],\n [-5, 25, 4, 16, 12, -16, 16, -6, 26, -12, 1, 11],\n [-4, 0, -8, 18, -11, -15, 24, -4, 24, -20, 23, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
564
|
math
|
train
| 425,113 |
math_arithmetic_matrix_svd_level_7_7_882
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[19, 3, -11, 23, 5, 14, -6, -23, -20, 0, 16, -21],\n [-7, 17, 17, -15, -13, 15, 7, 25, 17, -10, 13, -7],\n [-25, -6, -15, -14, -26, -9, -13, 4, -3, -15, 25, -2],\n [9, -13, -9, -3, -1, 3, -23, 13, 2, -9, -23, 6],\n [11, 18, -25, 24, -15, -5, -1, -13, -18, -17, -20, 14],\n [20, -7, -12, 16, 23, 7, 25, 24, -3, -25, -7, -14],\n [-2, 9, -24, 20, -15, 6, 1, -16, -10, 13, -13, 4],\n [-22, 20, -25, 12, -14, -7, -16, -13, 15, -23, 25, 20],\n [-24, -16, 25, 23, -2, -4, -10, 26, 4, -13, 20, -9],\n [-24, 18, 8, 12, -8, -4, 4, -3, 23, -10, 0, -18],\n [5, -13, -5, 13, -13, 10, 25, -13, 1, 17, 13, 6],\n [21, -5, 13, 10, 8, 18, 1, 10, -24, -5, 19, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
544
|
math
|
train
| 425,114 |
math_arithmetic_matrix_svd_level_7_7_883
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[26, 12, -4, -21, -13, -5, 9, -7, 24, 15, -4, -14],\n [17, 19, 18, 24, -18, 21, 14, -21, 19, 1, -20, -8],\n [4, 8, 2, 20, 17, 6, 16, -5, -24, 22, -14, 13],\n [-14, 13, 13, -14, -15, -22, -14, -15, 24, -17, -12, -25],\n [11, -11, 6, 7, -2, 20, -1, 21, 13, -13, 15, -12],\n [8, 11, 4, 7, -18, -20, 24, 11, -26, -4, -13, -2],\n [26, -19, 13, -21, -12, 24, -7, -10, 5, -21, 12, 1],\n [-17, -18, 10, 7, -14, -16, -16, 3, 1, -4, -12, 19],\n [26, -16, -14, 1, 23, -20, 4, 22, 16, -5, 11, -13],\n [-21, 19, 4, 24, -24, -10, -7, -20, -10, 15, 23, -1],\n [23, 26, 0, -14, 13, -22, -26, -10, 10, -11, -9, 1],\n [-24, -9, 14, 26, 3, 5, -13, -10, -8, 20, -19, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
570
|
math
|
train
| 425,115 |
math_arithmetic_matrix_svd_level_7_7_884
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 2, 20, 22, -16, -15, -13, -20, -24, 5, -16, -25],\n [-10, 15, -4, 6, -5, 18, -13, 22, 15, -7, 20, 26],\n [-10, 18, -19, -20, 22, 10, 9, 22, -23, 3, 25, 25],\n [-6, 16, 15, 0, -24, 4, -11, -14, -20, -16, 24, 26],\n [7, 15, -16, 5, 18, 25, 6, 2, 23, 4, 0, 12],\n [12, -25, -19, 16, 22, 20, -15, -7, 13, -22, 13, -14],\n [19, 19, -26, 6, -18, 12, 14, 7, -19, 6, 9, -15],\n [9, -8, 12, -6, 6, 16, -23, -23, 17, 22, -16, -1],\n [-22, 3, -25, -3, 14, -11, -9, -15, -1, -15, -1, -23],\n [23, 0, 26, -4, -6, 21, 10, 7, 18, -16, -24, -21],\n [-13, -21, -14, 2, 6, -10, -16, -25, 7, 4, -11, 17],\n [14, 10, -5, 19, 8, -20, 23, 26, -12, -23, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
97
|
math
|
train
| 425,116 |
math_arithmetic_matrix_svd_level_7_7_885
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, 23, -11, -26, 7, 7, -11, 5, 13, 6, -12, -10],\n [-10, 8, 26, 2, -15, 10, -14, -6, 12, -26, 22, -14],\n [16, 22, -3, -3, -14, 9, -22, -13, -11, -21, -25, 18],\n [23, -23, -11, 9, 21, -6, -10, -24, -3, -21, -8, 7],\n [-5, 19, -24, 12, -4, -16, 5, 20, 3, 23, 9, -24],\n [21, 13, 13, 9, -11, 5, 9, 11, -5, 11, 23, -15],\n [13, -13, -20, -25, 13, -16, 22, -17, 12, -21, -18, -8],\n [-2, -22, -22, -24, -23, -15, -1, -21, 26, -17, 0, 13],\n [-4, 22, 11, 3, 10, 15, -2, 17, -13, -24, 25, -23],\n [9, -2, -19, -2, 9, 3, 24, -12, 18, 10, 20, 23],\n [-22, -9, 5, 15, 23, -20, 15, -23, 14, 18, 4, -11],\n [18, -24, 20, 22, -24, -24, 2, -8, -23, 8, 26, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
math
|
train
| 425,117 |
math_arithmetic_matrix_svd_level_7_7_886
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[24, -1, 11, 22, -23, 22, 7, 24, -6, 14, -2, -24],\n [18, -9, -2, 5, -7, -12, -25, 26, 3, -15, 12, 16],\n [20, -20, -5, -19, -4, -4, -15, -21, -13, 1, -22, -23],\n [-2, 0, -23, 2, 14, 20, 23, 0, -20, 5, -7, 21],\n [16, 9, 3, 2, 1, 13, -24, 0, -6, 10, 8, -7],\n [-18, 8, -17, 22, 26, -6, 16, 14, 16, -3, 12, -26],\n [19, 16, 4, 19, -4, -9, 0, 14, 17, 19, -15, 8],\n [14, -11, -6, 0, 9, 26, -14, 23, -19, -19, -11, -4],\n [18, 7, -3, -6, -14, 23, 24, -23, 2, -23, -6, 7],\n [-18, -2, 14, -6, -23, -11, -2, 13, -20, 18, -22, 13],\n [-6, 7, 21, -5, 0, 23, -17, 14, -12, -24, 20, -14],\n [-1, -26, 20, -18, 12, -1, -9, -19, -12, 19, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
542
|
math
|
train
| 425,118 |
math_arithmetic_matrix_svd_level_7_7_887
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[19, -23, -6, -11, 19, -2, -4, -10, 5, 21, -25, -26],\n [20, -18, 18, -1, 22, 8, -21, 14, -18, -7, 22, -1],\n [14, 7, 20, -17, 15, 3, -23, 12, 7, -18, -22, 15],\n [-18, -2, 13, -24, -2, 24, -9, 19, -16, -4, 7, 26],\n [7, 20, -3, 23, 21, -25, -14, -7, -20, -18, 24, 7],\n [-26, 26, -19, 24, 26, 14, -26, -2, 22, 2, 25, -10],\n [-20, 8, -11, -6, -25, -1, -22, -22, -18, 20, 26, 21],\n [-9, -8, -21, 0, 22, 4, -6, -13, -11, -25, -9, -9],\n [8, -13, -9, -8, -2, 8, -20, -24, 11, -15, -11, -7],\n [-22, 4, -3, 16, 18, 17, -3, -11, 20, 12, 1, -22],\n [-14, -12, 14, 22, -23, -13, 0, -17, -4, 10, 1, 17],\n [-14, 9, 5, 18, 10, -26, -23, -26, -9, -14, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
math
|
train
| 425,119 |
math_arithmetic_matrix_svd_level_7_7_888
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-12, 14, 14, -17, 26, 8, -23, -22, 17, 11, 11, -3],\n [-3, 13, -8, -7, 25, 1, 16, -16, -4, -12, -6, 9],\n [-14, 5, -17, 19, 10, 5, 22, -7, 12, 20, 24, -11],\n [12, -22, -10, 9, 21, -1, 24, -23, 11, 19, -1, -7],\n [-14, 19, -20, -3, -24, -24, 23, -11, 4, 6, -13, 23],\n [25, 21, -2, 24, -25, 14, -14, -9, -7, -25, -20, -14],\n [-19, -24, -13, -4, -19, 6, 0, -16, 6, -16, 11, 16],\n [-9, 1, 14, -1, 3, 18, -17, 15, -24, 5, 9, -17],\n [-6, 24, 23, -20, 26, -2, 7, -2, -18, -19, 26, 8],\n [17, 1, -17, -13, 2, -26, -8, -13, -7, 11, 21, 9],\n [14, -19, 11, 15, -3, -20, 16, -22, -13, -18, -7, 25],\n [-1, -2, 25, -7, -21, -20, 9, 22, 9, -7, 19, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
math
|
train
| 425,120 |
math_arithmetic_matrix_svd_level_7_7_889
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-19, 0, -22, 4, 19, 14, -6, 25, -24, -1, -10, 3],\n [-4, -2, 23, -23, 14, -16, 14, 11, -9, 6, 9, 11],\n [-9, 22, -11, -5, -6, 23, 17, 4, 4, 0, 25, 14],\n [23, 10, -24, 4, 7, -1, -3, -17, 2, 11, -14, 10],\n [12, 24, -21, -13, 3, 12, 22, -23, 18, 1, 12, -17],\n [-1, 7, 2, -19, 12, -9, -18, -5, -9, 10, 20, 6],\n [21, 18, 21, -25, -1, -10, -23, -18, 25, -17, 22, -22],\n [11, 22, 13, 22, -5, 14, -8, 10, 6, 22, 23, -21],\n [-4, -13, 4, 26, 6, -10, -26, -15, -24, 18, 9, -3],\n [14, 21, -13, 10, 1, 0, -7, -12, 15, -2, 17, -21],\n [24, 19, -13, 12, 15, 3, 20, 20, 23, 1, 4, -18],\n [21, -25, 26, 20, 18, -26, -25, 21, 1, 9, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
math
|
train
| 425,121 |
math_arithmetic_matrix_svd_level_7_7_890
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[6, 3, 11, -2, 21, -11, 11, 20, 12, -20, 17, 6],\n [7, -10, 22, 13, -23, -14, -1, -14, 5, 16, -15, -13],\n [-6, 6, 14, -24, -20, -12, -20, 16, 21, -1, -1, -15],\n [25, 13, 18, -25, 13, -12, 17, 4, 10, 7, -15, -21],\n [13, 5, 9, -17, -11, -2, 3, 13, 2, 21, -4, 12],\n [17, -20, 22, 20, -13, 10, -25, 10, -22, 11, 19, -5],\n [-21, 18, -20, 23, 9, -22, -1, 1, 20, -4, -25, 13],\n [23, -6, -25, -25, -9, 12, 0, 19, -22, -18, -13, -23],\n [-26, 13, -5, -12, -2, 24, 5, 4, 15, -4, -10, 7],\n [-22, 20, 15, 3, 23, 18, 26, 3, -13, -2, -24, 11],\n [-7, -4, -4, -6, 17, -22, 25, -18, 12, -5, -8, -22],\n [-23, -6, -9, -22, 12, -14, -1, -11, -16, -24, -23, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
math
|
train
| 425,122 |
math_arithmetic_matrix_svd_level_7_7_891
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-18, 3, 24, 18, -15, 22, -14, -6, 16, 15, -6, 0],\n [-22, -10, -6, -26, -11, 13, -5, -4, -7, 22, -19, 19],\n [22, 14, 11, 26, 3, -25, 5, -8, -14, 15, -3, -17],\n [20, -22, 0, 25, -2, -20, 18, 0, 25, -6, 16, 1],\n [-6, 7, -6, 20, 0, -12, 24, -22, -10, -19, 21, 20],\n [-3, -9, 23, 20, 15, -22, -11, -6, -15, -10, 17, 6],\n [-16, 13, 10, 13, -16, 1, 16, 3, 19, -13, 24, 16],\n [-6, 5, 0, 7, -19, 16, 6, 10, -6, 20, 24, 2],\n [-11, -23, 17, -2, -22, -8, 16, 12, -21, 3, 1, -14],\n [20, -24, 8, -23, -17, 24, -21, -26, -26, -20, -11, -3],\n [-23, -11, -20, 23, -2, -12, -18, -16, -20, 26, 12, -4],\n [-24, -20, -24, -15, -24, -20, -4, 11, -12, -4, 15, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
579
|
math
|
train
| 425,123 |
math_arithmetic_matrix_svd_level_7_7_892
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[14, 22, 26, 2, -8, -3, -4, 1, -10, -18, 26, -10],\n [-26, 13, 24, -18, 13, -21, -12, 20, -21, 26, 20, -9],\n [-3, 11, 23, 23, 3, -8, 1, -4, -3, 25, 0, -14],\n [-16, -12, 3, -21, -2, 4, -16, -23, -12, 21, -3, -13],\n [-3, -4, -22, 20, -1, 3, 15, 11, 21, 21, 24, -24],\n [25, -9, -5, 24, 1, 3, -25, -18, -26, 9, -6, 1],\n [9, 5, -21, -4, -21, -5, 4, -8, -19, -19, -7, -3],\n [-14, 14, 26, 24, -20, 25, -19, 0, 16, -24, -10, -22],\n [11, 20, -18, 24, -21, -19, 17, -1, 21, -7, -1, -24],\n [21, -2, -12, -16, 5, 5, -21, -25, -4, 2, -20, 3],\n [-11, -26, -14, 9, -26, -5, 10, 2, -11, 24, 17, -18],\n [-2, 11, -5, 14, -25, -26, -17, 8, -3, 23, -3, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
math
|
train
| 425,124 |
math_arithmetic_matrix_svd_level_7_7_893
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[20, 19, -17, 11, -7, 25, -15, -4, -4, -18, -23, 2],\n [0, 2, -23, -25, -20, 16, 21, 15, 20, 7, -15, 0],\n [-5, -12, 16, -17, 8, 13, 26, -7, 5, -7, -22, 2],\n [0, -1, -16, 2, 17, -7, 16, -21, -19, 18, 20, -25],\n [0, 11, -7, 3, 2, -25, -12, 6, -16, 13, -3, 14],\n [-12, -22, -18, -23, 0, 15, -23, 10, 24, 26, -14, -6],\n [-16, -15, -13, 18, 9, -14, -22, -6, -18, 6, 17, -10],\n [0, -26, 24, -22, -15, -2, -2, -15, -16, 3, 21, 0],\n [-10, 3, -24, -16, 22, 6, 20, -18, -9, -26, -21, 7],\n [-22, -24, -1, 10, 13, -21, -16, -16, 16, 13, 11, -11],\n [-7, -7, -1, 8, 13, 18, 15, -2, 3, 13, -2, -17],\n [18, 8, 0, -23, -11, 2, 8, -6, 14, 4, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
96
|
math
|
train
| 425,125 |
math_arithmetic_matrix_svd_level_7_7_894
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[11, 5, -23, -13, -26, 13, -8, 21, 5, -19, -22, -19],\n [22, -21, 8, 26, 25, -16, -14, -2, 24, 2, -7, 8],\n [-1, 24, -7, 12, 16, 14, 20, 17, 17, -21, -10, 23],\n [0, 14, 16, -8, 15, 5, 16, -4, 11, 14, 4, -11],\n [-24, -11, 23, 24, -11, -23, -22, 1, -4, 15, -8, -2],\n [-8, -24, -19, -1, 4, -8, -10, -26, 26, -14, 16, -15],\n [5, -3, 7, -3, 15, -18, 21, -23, 21, -2, 9, -3],\n [-4, 12, -12, -2, 16, -17, -17, -21, 25, -22, 2, -7],\n [-26, -5, 20, -4, -1, -13, 9, -15, -12, 22, -11, -12],\n [-19, 17, 23, -13, -25, -15, -3, -25, -9, -23, 1, -2],\n [14, 13, -20, 18, -15, 17, 18, -8, -23, -25, -3, 18],\n [-16, -3, 12, -18, -20, 2, 8, -3, -24, -26, 6, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
547
|
math
|
train
| 425,126 |
math_arithmetic_matrix_svd_level_7_7_895
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[19, 7, 16, -17, -12, -16, 13, 6, 5, 11, -7, 5],\n [-19, 24, 26, -10, 19, 9, -25, 21, 25, 7, -16, -13],\n [-9, -17, -4, -3, 17, -16, 14, 1, 0, 21, -19, 10],\n [20, 20, 22, -25, 18, 16, -26, 14, -23, 21, 21, -24],\n [-1, 23, -20, -5, -17, -17, 12, -26, 22, 25, 10, -16],\n [7, -17, -13, 11, -25, 12, -17, 5, 2, 23, -26, 17],\n [-23, 6, 19, -3, 14, -5, -17, 17, -1, -13, -15, -7],\n [7, 8, 18, -5, 11, -10, 1, -4, -11, -4, 10, 23],\n [9, -4, 4, -12, -14, -13, -5, -18, -19, -13, 26, -20],\n [-24, 9, -4, -10, 14, -2, -4, -16, 5, 26, -26, 0],\n [17, 1, 12, -1, -18, 3, -24, 16, 4, 26, -17, 24],\n [5, -26, 19, -19, 12, -17, -3, 17, -8, 26, -20, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
97
|
math
|
train
| 425,127 |
math_arithmetic_matrix_svd_level_7_7_896
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[5, -8, 12, 2, -11, 12, 17, -24, -22, -21, -10, -10],\n [9, 15, 5, 13, -13, 5, 16, 11, -14, 20, -4, -15],\n [-5, 3, 26, -5, -17, -15, 9, 1, -4, -3, 1, -19],\n [-7, -24, -20, -4, 8, 6, 24, 19, 8, -5, 7, 9],\n [10, 11, -1, 14, -17, 10, 23, -20, 15, -16, -10, -19],\n [-20, 19, 16, -19, 6, -21, 19, -22, -11, 18, 21, -13],\n [7, 23, 7, -2, -5, -24, 14, -9, -7, -14, 15, 7],\n [-6, 2, 24, -18, 13, -5, 4, 18, 4, -21, 14, 19],\n [-25, -20, -15, 16, 24, -8, 20, -7, -14, 20, -6, 10],\n [-1, 6, 21, -5, -16, -12, 18, 20, -9, 4, 20, 7],\n [2, 14, -10, -9, 5, -17, -18, 25, 25, 0, -1, -6],\n [2, -7, -18, -23, -12, 25, -4, 15, 15, -11, -26, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
math
|
train
| 425,128 |
math_arithmetic_matrix_svd_level_7_7_897
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -23, 1, 13, 22, 8, 8, 17, 13, -6, 10, 0],\n [20, 13, -14, -21, 4, -4, 15, 6, -18, -22, 17, 18],\n [11, 21, 17, -23, 5, -24, 7, 15, -15, 9, 20, 19],\n [5, 4, -14, 22, -5, 0, -22, 15, 15, -1, 22, -8],\n [-4, 17, 1, -25, -24, 20, -14, 9, -6, 19, 18, 12],\n [-13, 11, 1, -22, 18, 11, -10, 13, 12, 19, 8, -9],\n [-6, -2, 4, -12, 20, -8, 24, -14, 5, 4, -13, -2],\n [-8, -4, -8, -10, 17, -11, 5, 4, 24, 26, 18, -17],\n [-19, 22, 18, -25, -2, 0, 17, -3, 23, 24, -3, 21],\n [-7, 5, 7, 2, 25, 11, -13, -3, 8, 26, -8, -19],\n [-19, -21, 15, -16, 22, 16, 24, -14, 0, -3, 1, -24],\n [-21, -25, 6, -11, 0, 14, -6, -26, -9, 22, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
508
|
math
|
train
| 425,129 |
math_arithmetic_matrix_svd_level_7_7_898
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-9, -13, 22, -1, -21, -16, -25, -2, -24, 13, 3, -18],\n [3, 15, -6, -5, 18, -15, 15, 26, 3, 19, -21, 0],\n [7, -12, 3, -12, 9, 16, 2, -20, -12, 25, 24, 2],\n [-13, -17, -3, 11, -25, -20, 26, 8, 1, 13, 23, -1],\n [5, -12, 16, -5, -4, -17, -2, 26, 0, 22, -1, -9],\n [-26, -25, 5, 10, 4, 15, -15, -14, 21, 2, -24, -23],\n [-11, -17, -13, 26, 24, 10, -8, 16, 22, 3, 12, -23],\n [20, 9, 21, 5, 0, -4, -8, 7, -16, -8, -4, 19],\n [17, 24, 15, 13, 22, -19, -18, -13, 20, 21, 13, 8],\n [7, -26, 5, -19, -4, 5, 11, 16, 8, 19, -5, 10],\n [0, -6, 25, 2, -14, 26, 10, 10, 15, 18, 15, 13],\n [7, 7, 24, -17, -12, 0, -11, 15, 15, -1, 25, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
math
|
train
| 425,130 |
math_arithmetic_matrix_svd_level_7_7_899
|
arithmetic_matrix_svd7
|
expert (level 6,7)
| 7 |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[24, -23, 7, 14, -16, -24, 12, -2, -2, 11, -26, -15],\n [-9, 14, 10, -14, -9, -12, 20, -21, 12, -14, -15, -17],\n [-1, 0, -5, 6, 16, -11, -26, 23, 16, 14, 19, 16],\n [-26, -16, 14, -5, 2, 7, 15, -24, 4, -14, -16, 23],\n [19, 10, -19, -17, 11, -12, -19, 3, 9, 3, 4, 14],\n [-22, -8, 22, 7, -14, 22, -2, -13, -16, 3, -20, -25],\n [8, 16, -24, 6, 24, 19, 5, -10, 24, 24, 1, -6],\n [24, -8, 6, -16, 6, -4, -20, -19, 3, -20, 20, 21],\n [-5, 0, 13, 15, 9, 18, 9, -8, 0, -21, -11, -3],\n [-3, 3, 12, 18, 8, 26, 23, 22, 8, -7, 9, -16],\n [23, -8, 13, 18, -2, 23, -5, -26, -7, 22, 8, -4],\n [-3, 12, -4, 11, 20, -20, 12, 17, -18, 2, 14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
math
|
train
| 425,131 |
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