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[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-12, 5, -1, 6],\n [5, -7, 0, -4],\n [-1, 0, 0, 0],\n [6, -4, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
883
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[-10, -7, -1, -4],\n [0, 4, -11, -9],\n [-4, 0, 12, -9],\n [-1, 7, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-4, 7, 9, 6],\n [7, 2, -5, -2],\n [9, -5, 6, 2],\n [6, -2, 2, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -2, 12, 6],\n [-9, 10, 3, 1],\n [7, -6, 10, -9],\n [-3, 8, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
865
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 0, 8, 10],\n [0, -6, 8, 10],\n [8, 8, 7, 4],\n [10, 10, 4, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 8, 6, 7],\n [8, -5, 0, 2],\n [6, 0, 7, -4],\n [7, 2, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-43
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, -10, -3, 0],\n [-5, 3, 2, -11],\n [5, 10, -10, -5],\n [-4, 0, 3, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -10, 2, -1],\n [0, 1, -8, -6],\n [0, 0, 1, -6],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-358
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[0, 6, -7, -7],\n [-6, -7, -12, 11],\n [-11, -7, 5, 0],\n [-8, -2, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -5, 5, 5],\n [-7, 8, -11, -3],\n [-5, -5, 0, -11],\n [-6, -11, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, 7, 9, -6],\n [9, -7, 0, 2],\n [-6, -6, 9, 10],\n [0, -3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -5, -5, 6],\n [-3, 1, 2, 0],\n [3, -12, 0, -4],\n [9, -7, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 12, 4, 3],\n [0, 5, 12, 8],\n [0, 0, -8, -9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -12, 2, -2],\n [-12, 7, 7, -1],\n [2, 7, -3, -4],\n [-2, -1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[4, -10, 5, 5],\n [-7, -11, -4, 12],\n [5, 0, -6, 6],\n [-9, 4, 12, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 0, -10, -7],\n [0, -9, -8, -4],\n [-10, -8, 11, 6],\n [-7, -4, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-50
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[-1, 0, -4, -2],\n [0, 2, -2, 7],\n [-4, -2, -2, -1],\n [-2, 7, -1, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -12, -3, -6],\n [-7, 3, 12, 11],\n [2, -2, -8, 8],\n [-10, -2, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[-2, 6, -2, 0],\n [6, 12, 2, -8],\n [-2, 2, 2, 6],\n [0, -8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 2, 2, 4],\n [2, 2, -10, 5],\n [2, -10, 8, 6],\n [4, 5, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -4, 3, 10],\n [10, -5, 0, -9],\n [-8, -7, 11, -6],\n [-5, 6, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-61
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[10, -11, 2, 5],\n [4, 2, -8, -12],\n [-11, -8, -12, -9],\n [-2, 5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, -6, 4, -1],\n [-6, 10, 2, 2],\n [4, 2, 12, -8],\n [-1, 2, -8, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-171
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[10, 0, -10, 4],\n [-3, -12, 4, 6],\n [10, -4, 1, 5],\n [4, 8, 12, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[-3, 2, 4, 8],\n [2, -11, -1, -2],\n [4, -1, -4, 11],\n [8, -2, 11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -3, -9, -1],\n [0, -11, 11, 11],\n [0, 0, -10, -8],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
117
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 9, 5, -5],\n [0, 10, 12, 11],\n [-9, -9, -10, 1],\n [10, -2, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
638
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[7, -4, -2, -2],\n [-4, 10, 7, 4],\n [-2, 7, 7, -8],\n [-2, 4, -8, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, 0, -8, 1],\n [0, 8, -3, -4],\n [-8, -3, -7, -1],\n [1, -4, -1, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 11, 5, -1],\n [4, 4, 0, 6],\n [5, 8, 5, 8],\n [1, -6, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
290
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[1, 6, 5, 6],\n [0, -8, 5, 10],\n [0, 0, 3, 0],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, -5, -4, 4],\n [-5, -7, 5, -3],\n [-4, 5, 4, -3],\n [4, -3, -3, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
122
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 0, -2, -5],\n [12, 1, 0, 5],\n [-6, 12, -4, 1],\n [7, -2, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, -5, -7, 4],\n [11, 9, 8, -3],\n [0, -12, 4, -9],\n [-8, -1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[12, 11, -4, 11],\n [8, 8, -6, 11],\n [-5, 5, 6, -3],\n [-1, -7, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
143
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-9, 6, 8, -12],\n [0, -11, -12, 0],\n [0, 0, -8, -9],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 0, -6, -12],\n [0, -8, 2, 12],\n [0, 0, -8, -8],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
234
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-7, -3, -2, -9],\n [0, 7, 8, 11],\n [0, 0, 7, -3],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-25
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 11, 2, -2],\n [11, 3, -8, -1],\n [2, -8, 8, 4],\n [-2, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
65
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-7, -2, 9, 4],\n [11, 12, -10, 10],\n [12, 4, -7, -8],\n [5, 7, 4, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, 11, 12, -3],\n [-8, -2, 7, 1],\n [6, -8, -11, 5],\n [11, -7, 12, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
102
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[12, 10, 6, -5],\n [10, 11, 0, 6],\n [6, 0, -8, 0],\n [-5, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-1, 5, -7, -7],\n [0, -2, -5, 0],\n [0, 0, -6, 2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[1, -4, 1, 3],\n [-4, -12, 6, 10],\n [1, 6, 2, 1],\n [3, 10, 1, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
79
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, 2, 0, -8],\n [2, -12, 10, 0],\n [0, 10, 11, 4],\n [-8, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
631
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 0, -3, -6],\n [0, 10, 0, -2],\n [-3, 0, -11, 6],\n [-6, -2, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
151
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 1, 8, 3],\n [8, 10, 1, 10],\n [-4, -7, 6, -4],\n [-1, -5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 3, 8, 1],\n [3, 12, 12, 3],\n [8, 12, 3, -2],\n [1, 3, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
855
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 10, 8, 2],\n [0, -12, -12, -10],\n [0, 0, 2, 11],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-2, 12, 3, 1],\n [12, 6, -8, 2],\n [3, -8, 9, 1],\n [1, 2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -4, 6, -2],\n [-4, 2, -2, 2],\n [6, -2, 0, 2],\n [-2, 2, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[7, 8, -3, -3],\n [5, 9, 5, -5],\n [-2, 6, -7, -4],\n [12, -2, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, 9, -9, -8],\n [0, 10, 9, -10],\n [0, 0, -9, 12],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[-7, -8, -4, -6],\n [-8, 9, 0, 0],\n [-4, 0, 9, 4],\n [-6, 0, 4, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-74
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[12, -1, 9, -2],\n [5, -7, 10, 7],\n [-7, 9, -5, -9],\n [-10, 0, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 10, 12, -8],\n [0, -8, -10, 11],\n [0, 0, -9, -10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-163
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 0, -2, 2],\n [0, -6, -6, 6],\n [-2, -6, -11, 6],\n [2, 6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -6, 5, -3],\n [5, -6, 11, -10],\n [0, -1, -2, 9],\n [1, 0, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-70
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, -11, -12, 11],\n [0, -5, 5, 12],\n [0, 0, 3, -1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-148
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[-9, -11, 0, 7],\n [-6, 1, 11, 5],\n [-9, 12, -1, -9],\n [-5, -6, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[12, 8, -8, -6],\n [8, -8, -2, -8],\n [-8, -2, -3, 8],\n [-6, -8, 8, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, -5, -11, 11],\n [-3, -12, 3, 0],\n [-11, -10, 12, 2],\n [0, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
334
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-1, -4, 9, -8],\n [0, 10, 8, -9],\n [0, 0, -2, 10],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, 8, 6, 9],\n [8, 7, -5, -1],\n [6, -5, 10, -2],\n [9, -1, -2, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[12, 11, 10, -11],\n [7, -4, 6, -5],\n [11, -4, -6, 10],\n [10, -11, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
218
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-7, 3, -7, 7],\n [0, -3, -5, -9],\n [0, 0, -8, -6],\n [-3, -4, 8, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
258
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-3, -6, -5, 2],\n [0, 5, -5, 12],\n [0, 0, -6, -10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 5, 2, 6],\n [0, -4, 1, 12],\n [0, 0, 7, -8],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, 8, -4, 0],\n [8, -2, 1, -4],\n [-4, 1, 0, -2],\n [0, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-119
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 10, -8, 6],\n [4, -1, 9, 1],\n [5, 8, -9, -12],\n [8, -10, -8, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[8, 4, -2, -11],\n [0, -1, -7, 10],\n [0, 0, -8, -2],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -8, 0, 12],\n [0, -10, 9, -1],\n [0, 0, 8, -7],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -12, -2, -2],\n [-2, 5, 7, 11],\n [10, 7, 9, -7],\n [8, 8, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 2, 0, 6],\n [2, -11, -3, -2],\n [0, -3, -11, -3],\n [6, -2, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, -5, -5, -12],\n [-5, 9, 11, -1],\n [-4, -11, -5, 6],\n [-11, -7, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, 4, -7, 1],\n [0, 8, 6, -9],\n [0, 0, 1, -8],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -2, -5, -2],\n [-2, -8, 4, -1],\n [-5, 4, -12, -2],\n [-2, -1, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
549
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 2, 6, 3],\n [-8, -7, 2, -1],\n [-8, -12, -6, 2],\n [2, 8, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-52
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 4, -11, 1],\n [0, 4, -3, 4],\n [0, 0, -8, -12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 2, 4, 2],\n [2, -9, -4, 1],\n [4, -4, -1, 4],\n [2, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
505
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, -6, -6, -3],\n [0, 2, 3, 0],\n [0, 0, -1, 12],\n [0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
875
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -2, -10, -2],\n [-2, -11, 0, 0],\n [-10, 0, -4, 2],\n [-2, 0, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[10, 2, -10, -2],\n [2, 8, 7, -3],\n [-10, 7, 7, -1],\n [-2, -3, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 11, 5, 7],\n [0, 10, -1, 4],\n [0, 0, 9, 0],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-2, 1, 9, -2],\n [0, -3, 2, 7],\n [0, 0, -6, 0],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-77
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 10, -2, -1],\n [-12, -3, 12, -6],\n [0, -1, -4, 12],\n [0, 6, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-9, -4, 12, -10],\n [-9, 9, 7, -3],\n [-2, 9, -4, -2],\n [-2, -1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-155
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, -2, -2, 1],\n [-2, -11, -2, 0],\n [-2, -2, 8, -2],\n [1, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, 8, -4, 2],\n [8, -11, -7, -2],\n [-4, -7, -2, -4],\n [2, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-37
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 0, 8, -4],\n [0, 3, 2, 0],\n [8, 2, -6, -12],\n [-4, 0, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, -4, -3, -6],\n [-5, 10, -10, -1],\n [-3, -1, -11, 12],\n [-10, 9, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3886
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -2, 6, 11],\n [0, -5, 6, 0],\n [0, 0, -9, -10],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-68
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[8, 4, -6, 0],\n [4, 1, 6, 2],\n [-6, 6, 1, -2],\n [0, 2, -2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-123
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, -6, 3, 4],\n [-6, 1, 5, -2],\n [3, 5, 10, -5],\n [4, -2, -5, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 8, -8, -5],\n [-10, 10, 9, 4],\n [2, -3, -8, -10],\n [-4, 11, 5, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[6, -7, -9, -1],\n [0, 10, 5, -5],\n [0, 0, 8, 1],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 3, -6, -7],\n [3, 3, 1, -8],\n [11, -12, -8, 4],\n [12, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, 3, -9, 4],\n [0, -6, -6, -6],\n [0, 0, -4, 12],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-6, -9, -11, 9],\n [0, -8, 2, -10],\n [0, 0, -1, -7],\n [0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-172
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[6, -2, -7, 7],\n [3, 8, -9, 0],\n [9, 4, -8, -8],\n [12, 3, 3, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH