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[ { "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[[8, 11, 10, -7],\n [-11, 11, 11, -4],\n [6, 9, -3, -11],\n [10, 4, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
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[[7, -3, 5, -4],\n [-2, -7, 11, 11],\n [5, 0, -8, 8],\n [-1, -6, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-20
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, -7, -3, 10],\n [-2, -6, -11, -9],\n [-4, 5, -11, 11],\n [-12, 1, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
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, -7, 4, -2],\n [0, 3, 3, 1],\n [0, 0, -9, -1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
108
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[[-3, 3, -1, 4],\n [-6, 8, 9, -5],\n [-7, -4, 11, -2],\n [3, 2, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-75
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, -8, -8, -7],\n [6, -7, 8, -4],\n [9, 7, -4, -7],\n [5, 7, -5, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
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[[11, 2, 0, 1],\n [2, -1, -8, 0],\n [0, -8, -12, -6],\n [1, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
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, 3, -10, 10],\n [0, 4, 3, 6],\n [0, 0, 2, 5],\n [0, 0, 0, -10]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 2, -8, -6],\n [2, -10, 6, 6],\n [-8, 6, 12, -2],\n [-6, 6, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-20
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[[8, 4, 11, -7],\n [0, -7, -3, 4],\n [0, 0, -2, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
236
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, -9, 4, -4],\n [-10, 1, 10, 9],\n [-10, -3, -8, -3],\n [-12, 8, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-107
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, -2, 5, 2],\n [-2, -10, -10, 9],\n [5, -10, 1, 6],\n [2, 9, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
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, 9, -10, -6],\n [0, 10, 0, -7],\n [0, 0, 4, -8],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
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[[2, -7, -6, -11],\n [0, -7, 3, 0],\n [0, 0, -8, -8],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
222
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, 1, 9, 2],\n [-3, 3, 9, 10],\n [11, 8, -8, -7],\n [2, 10, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
285
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[[-2, 4, 4, -7],\n [4, 0, -7, -4],\n [-3, 9, -11, -6],\n [6, 8, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, -6, 10, -3],\n [0, 5, -12, 11],\n [0, 0, 7, -4],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
111
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[[7, 4, 4, 1],\n [0, 1, 11, -1],\n [0, 0, -11, -5],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
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[[-3, 1, 6, -8],\n [-7, 0, -4, 12],\n [10, -8, 0, -6],\n [8, -8, -5, -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 all entries rounded to the nearest integer?\n[[-1, -2, 10, 7],\n [-2, -3, 0, -2],\n [10, 0, -11, -2],\n [7, -2, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
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[[2, 7, -8, -7],\n [-11, 7, -11, 6],\n [-2, 2, 0, 7],\n [-7, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1588
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[[-4, 9, 8, 8],\n [0, -2, 10, -9],\n [0, 0, 5, -12],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2209
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -6, -8, 5],\n [0, 2, 11, -2],\n [0, 0, 4, -7],\n [0, 0, 0, -8]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 0, -1, -12],\n [-6, -11, 9, -7],\n [10, -7, 10, -4],\n [10, -1, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[7, -1, 9, -11],\n [-2, 6, 8, 3],\n [8, -7, -3, -2],\n [-12, -12, -9, 4]]\nRound your answer to the nearest integer.\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 value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-10, 4, -7, -12],\n [0, -4, 3, -1],\n [0, 0, -2, 1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-36
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, 0, 4, 2],\n [0, -4, -1, 2],\n [4, -1, -8, -1],\n [2, 2, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-126
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[12, 7, -3, -6],\n [0, -11, 2, -4],\n [0, 0, -10, -5],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
66
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, -12, -2, -1],\n [0, 7, -2, -2],\n [0, 0, 2, -2],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
172
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[[3, -8, -4, -10],\n [0, 5, -8, -1],\n [0, 0, 6, -6],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
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[[-2, 2, 0, 8],\n [0, -4, 3, 10],\n [0, 0, 1, 12],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
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[[-9, -1, 6, 1],\n [-1, 3, -1, 2],\n [6, -1, -7, 0],\n [1, 2, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[6, 7, -6, -3],\n [0, 4, 6, -9],\n [0, 0, -11, -2],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -4, -11, -2],\n [0, 12, -1, -5],\n [0, 0, 6, -11],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
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[[5, -4, -4, -5],\n [-4, 3, 6, 0],\n [-4, 6, -12, 3],\n [-5, 0, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-165
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, -4, 6, -1],\n [-4, 2, 8, 0],\n [6, 8, -1, 6],\n [-1, 0, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1355
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[7, 2, -9, 4],\n [-1, 8, -3, -9],\n [7, -2, -6, -8],\n [-7, 2, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-12, 3, -10, 11],\n [-7, 11, -12, -8],\n [-1, -8, -3, 7],\n [8, 6, 8, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-17
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-10, -10, -7, 2],\n [-1, 2, -6, 9],\n [-1, 11, -2, -5],\n [-8, 7, -1, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
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[[-3, -6, 10, -3],\n [-6, 10, 5, -2],\n [10, 5, 11, 8],\n [-3, -2, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
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[[-12, 0, 8, -9],\n [2, 1, -3, 6],\n [-7, 8, -11, -8],\n [0, -12, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[1, 12, 2, -2],\n [12, -3, 2, 4],\n [2, 2, 10, -2],\n [-2, 4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
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[[-7, -4, -7, 1],\n [-12, 7, -10, 3],\n [2, -9, -9, 12],\n [1, 0, 9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
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[[-3, 8, 2, 8],\n [8, 3, 4, 0],\n [2, 4, -4, 6],\n [8, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1041
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[[1, 5, -8, 6],\n [0, -5, 9, 12],\n [0, 0, 10, -10],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-152
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[[-3, 9, 11, -10],\n [0, 1, 11, 4],\n [0, 0, 4, 10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-928
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[[0, 0, 6, -4],\n [0, 12, -5, -2],\n [6, -5, 6, 4],\n [-4, -2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-106
MATH
[ { "content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[1, -10, -9, 2],\n [-7, -2, 8, 3],\n [-5, -6, 8, -8],\n [1, -5, -2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-27
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, 12, -12],\n [11, 0, 3, -4],\n [-8, -1, -7, 1],\n [-11, -1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-129
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-2, -2, 2, 4],\n [-2, -4, -2, -2],\n [2, -2, -7, 7],\n [4, -2, 7, -4]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 6, 7, 1],\n [10, 11, 5, 4],\n [11, -11, -1, -6],\n [-1, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
231
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, 9, -12, -3],\n [0, -5, -9, -12],\n [0, 0, -8, 7],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
59
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[[-5, 1, 2, 3],\n [1, -1, 0, -4],\n [2, 0, -2, 6],\n [3, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-140
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[[-8, 10, 2, 9],\n [0, -3, 8, 5],\n [0, 0, 1, 1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
624
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[[-3, -3, -1, 1],\n [0, 8, -9, -3],\n [-9, -2, 8, 11],\n [3, -12, 7, 2]]\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 value at position (3, 3) rounded to the nearest integer?\n[[2, 1, 1, -5],\n [1, 5, 0, 4],\n [1, 0, 8, -1],\n [-5, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
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[[-7, 4, 2, -8],\n [4, 10, -4, 2],\n [2, -4, 0, 2],\n [-8, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1283
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[[9, -2, 9, 2],\n [11, 11, 6, -12],\n [-11, 3, 0, -4],\n [-3, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1212
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[[1, 11, -6, -8],\n [0, -9, 5, 3],\n [0, 0, -9, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
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[[3, 4, 6, -9],\n [0, 7, -6, -3],\n [0, 0, 10, -9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, -7, 10, -3],\n [-7, -3, 6, 6],\n [9, 1, -2, -4],\n [4, 8, -11, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
595
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[2, 1, 10, -7],\n [0, -7, -6, 5],\n [0, 0, -11, 10],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
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, -7, -4, 5],\n [4, 8, -6, 6],\n [0, 12, 7, -3],\n [1, -7, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
117
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, 11, 12, -9],\n [6, -10, 2, -10],\n [12, 4, -5, 6],\n [-5, -8, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-38
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, 10, 9, 7],\n [7, 4, -2, 10],\n [-4, 5, 10, 10],\n [4, 10, 11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
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, -7, 5, 8],\n [6, 5, -7, 9],\n [-8, 12, 9, -8],\n [-8, 0, 6, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-34
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[0, -12, -6, 1],\n [-11, 5, -11, -5],\n [-10, 3, -12, 8],\n [-1, -1, -1, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-734
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[[4, 11, 3, 9],\n [-7, 11, -10, 0],\n [-10, 12, -10, 9],\n [1, 2, -7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
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[[-7, 11, -12, 6],\n [0, 9, -2, 4],\n [0, 0, 8, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[-11, 12, -12, 12],\n [-12, 4, 6, -10],\n [-5, -7, -5, -8],\n [3, -9, -5, 6]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, 6, -4, -4],\n [6, -7, -3, 1],\n [-4, -3, -9, -4],\n [-4, 1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
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, -7, -2, 1],\n [0, 9, 8, 11],\n [0, 0, 2, 3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
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, -3, 10, -7],\n [5, -1, 9, 2],\n [11, 12, 5, 11],\n [2, 12, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-43
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[[10, 4, -12, 7],\n [0, 12, -1, 12],\n [0, 0, -9, -6],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
163
MATH
[ { "content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[-6, -6, -12, 1],\n [12, 11, -3, 11],\n [-12, -7, 9, 0],\n [-12, -9, 10, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
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[[-4, -8, 7, 4],\n [-8, 4, 3, -6],\n [7, 3, 11, 6],\n [4, -6, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, 5, -2, 4],\n [0, -10, 2, -1],\n [0, 0, 2, -12],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
931
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, -2, 1, 4],\n [-2, 9, 10, 4],\n [1, 10, -5, -2],\n [4, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
99
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[[4, -2, 8, -1],\n [-2, -7, 7, 4],\n [8, 7, -9, -2],\n [-1, 4, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-64
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[[-7, -7, -12, -1],\n [0, -8, -8, -7],\n [0, 0, -4, -11],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-63
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, 6, 1, 2],\n [-8, 7, 3, -5],\n [-8, 5, 3, -10],\n [11, -12, 12, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
62
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, 10, 0, -12],\n [10, -11, 2, -2],\n [0, 2, 10, -5],\n [-12, -2, -5, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
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, 1, 5, -10],\n [0, 6, 9, 8],\n [0, 0, 9, -6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
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[[12, -2, -2, -9],\n [6, 11, -7, 4],\n [-3, -3, 5, 7],\n [3, 4, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-33
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[10, -5, -1, 0],\n [-5, -9, -4, 3],\n [-1, -4, 11, 1],\n [0, 3, 1, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
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[[9, -5, -12, 5],\n [0, 1, 7, 6],\n [0, 0, 2, -2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
587
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[6, 10, 4, 2],\n [0, -11, 1, 8],\n [0, 0, -9, -10],\n [0, 0, 0, -5]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 10, 2, -2],\n [10, -6, 1, -7],\n [2, 1, -8, -2],\n [-2, -7, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-216
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[9, -12, -5, 3],\n [4, 11, -3, 2],\n [6, -3, -1, -5],\n [-2, 9, -10, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
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[[11, 4, -5, -4],\n [4, -4, 0, 0],\n [-5, 0, 2, -4],\n [-4, 0, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
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[[11, -6, -5, 1],\n [12, -11, 11, 3],\n [-11, -10, -9, 4],\n [6, 8, -12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
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, 0, 4, -8],\n [0, -8, 6, 8],\n [4, 6, 9, -4],\n [-8, 8, -4, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
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[[0, -6, -10, 1],\n [-6, 4, 2, 0],\n [-10, 2, -8, 0],\n [1, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-69
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, -4, -1, -3],\n [-11, 9, 10, -2],\n [-7, -8, -12, 6],\n [-9, 4, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
497
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 2, 0, -5],\n [2, 4, 2, 2],\n [0, 2, 7, -10],\n [-5, 2, -10, -12]]\nRound your answer to the nearest integer.\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[[-8, 4, 10, 2],\n [0, -3, 11, -6],\n [0, 0, -1, 8],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2624
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[[-8, 5, 8, -9],\n [0, 2, 2, 0],\n [0, 0, -2, -3],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-54
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[[9, 10, 2, 4],\n [10, 10, 0, 2],\n [2, 0, 6, -8],\n [4, 2, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[6, 5, 7, 8],\n [0, 3, 10, 12],\n [0, 0, -9, 6],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\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 (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -2, 0, -5],\n [-2, 10, -9, 4],\n [0, -9, -8, 2],\n [-5, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH