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[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[7, 1, 3, -1],\n [-2, 1, -4, 12],\n [-3, 8, 8, 0],\n [2, -3, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-21
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, -8, 4, 6],\n [-8, -6, 2, 4],\n [4, 2, 0, -3],\n [6, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2437
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[[-5, 4, -12, 1],\n [0, -7, 6, -12],\n [0, 0, 8, 3],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-58
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[3, 5, -3, -10],\n [-9, -5, -5, -2],\n [12, -5, -2, -5],\n [-2, 12, 2, 5]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 5, 3, 10],\n [-2, 9, 11, 0],\n [-10, 8, -7, 4],\n [10, -2, 9, 12]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 0, -3, 8],\n [0, -5, -1, 4],\n [-3, -1, 8, 0],\n [8, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
121
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[[-6, 8, -2, -3],\n [0, -4, 8, -3],\n [0, 0, 5, 9],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
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[[-6, 4, 4, 2],\n [4, -12, -1, 0],\n [4, -1, -1, 0],\n [2, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
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[[11, 6, 0, -8],\n [0, -4, 10, -8],\n [0, 0, -11, 8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-78
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[[-1, 2, 7, -6],\n [0, 12, 8, 1],\n [0, 0, 4, -6],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-76
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, 3, -7, -2],\n [3, -4, -11, 1],\n [-7, -11, 6, -4],\n [-2, 1, -4, 7]]\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[[6, -5, 0, 4],\n [4, -1, 12, 10],\n [11, -8, -12, 4],\n [-2, 9, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[-12, 2, -2, 4],\n [2, 0, -9, 4],\n [-2, -9, 12, 0],\n [4, 4, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12
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, -6, -3, -6],\n [0, -7, 11, -1],\n [0, 0, -2, 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" } ]
-99
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[[-1, -9, -3, -1],\n [-3, 11, 11, 8],\n [-1, -10, 5, 1],\n [1, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[11, 7, 5, -8],\n [0, 11, 4, -3],\n [1, -3, 1, -4],\n [5, 10, 1, -10]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, 3, -12, -9],\n [3, -10, 6, 2],\n [-12, 6, 7, -4],\n [-9, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
142
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[[10, 0, 0, 0],\n [0, -3, -6, 4],\n [0, -6, -11, 6],\n [0, 4, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
337
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[[-6, 4, 2, -5],\n [4, 2, -3, -1],\n [2, -3, 1, 3],\n [-5, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[3, -10, -1, 12],\n [9, 6, -2, 6],\n [0, -7, 2, -10],\n [-5, 4, 2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, -11, 2, -11],\n [0, -8, 6, -9],\n [0, 0, -11, 6],\n [0, 0, 0, 12]]\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[[-9, 5, 2, -8],\n [1, -4, 11, 5],\n [-6, -9, -3, 5],\n [10, 7, -3, 6]]\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[[0, 1, -2, -10],\n [3, -10, -11, 12],\n [-1, 0, 6, -12],\n [11, 0, -3, 5]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, 2, 7, 1],\n [2, 12, -8, 2],\n [7, -8, -10, -2],\n [1, 2, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
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[[-9, -10, -1, -3],\n [0, -5, -10, -7],\n [0, 0, 11, -9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-37
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, 3, -12, -5],\n [9, -4, 5, 0],\n [8, -7, 4, -2],\n [8, 11, -7, -11]]\nRound your answer to the nearest integer.\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 2, 8, 2],\n [8, 6, -8, 4],\n [12, 5, 4, 9],\n [0, -9, -10, 5]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -4, 5, 3],\n [0, -9, 2, 2],\n [0, 0, -4, 12],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-67
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, -3, -12, -11],\n [0, 2, 5, 5],\n [0, 0, 3, 9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
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[[12, -10, 10, 9],\n [0, 10, 6, 11],\n [0, 0, 9, -5],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
231
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, 4, 10, -8],\n [0, -3, 9, 7],\n [0, 0, -9, 11],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-61
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[[10, -7, 12, -7],\n [-9, 12, 2, -10],\n [7, -11, 4, -2],\n [6, 7, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
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[[1, 8, 5, -1],\n [0, -1, 6, 8],\n [0, 0, 5, -9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4272
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, 11, -11, -12],\n [0, 11, -1, -3],\n [0, 0, 3, 8],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
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[[-1, -10, -12, -11],\n [0, -9, -5, 9],\n [0, 0, 9, 0],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-144
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, 0, 4, -6],\n [0, 11, 6, -3],\n [4, 6, -6, -4],\n [-6, -3, -4, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-73
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[[3, -8, 3, 0],\n [-8, 2, 6, 4],\n [3, 6, 7, 5],\n [0, 4, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
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[[6, 8, -3, -11],\n [0, 7, -7, -11],\n [0, 0, -6, 6],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
62
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[[6, -3, -5, 1],\n [0, -2, 10, 8],\n [0, 0, -4, 11],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
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[[2, 11, 8, -9],\n [-3, -2, 10, -8],\n [-4, 7, -1, -6],\n [-10, 9, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
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[[4, -2, -8, 11],\n [0, 1, 3, 0],\n [0, 0, -6, -2],\n [0, 0, 0, -3]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -4, -3, 3],\n [0, 12, -8, -10],\n [0, 0, -4, 10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-232
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 4) of the inverse. Round your answer to the nearest integer:\n[[-2, -9, -2, 5],\n [3, 4, -8, -8],\n [-11, -6, 0, -11],\n [11, 7, 7, 4]]\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[[5, -4, -10, -8],\n [3, 4, -8, 6],\n [-1, 4, -9, 2],\n [-2, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, -2, -1, -10],\n [-6, -10, 2, 0],\n [9, 11, 10, 2],\n [2, 5, -9, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
127
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[[10, 3, -12, 12],\n [0, -9, 2, -1],\n [0, 0, 8, 9],\n [0, 0, 0, -8]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 4, -5, 8],\n [4, -2, 6, 8],\n [-5, 6, -4, 2],\n [8, 8, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
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[[12, -8, -8, 1],\n [0, 5, 1, -9],\n [0, 0, 11, -12],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-52
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, -4, -3, 3],\n [0, 2, -1, 6],\n [0, 0, 10, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
701
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, 6, 7, -10],\n [-2, 9, 3, 3],\n [-9, 9, -2, -9],\n [-6, 11, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
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[[-9, 1, 12, -11],\n [0, 2, -4, 4],\n [0, 0, -12, -4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-256
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[[-8, 11, 2, -12],\n [-11, 8, -1, 12],\n [-3, -9, -6, 8],\n [4, -6, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
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, -5, 10, 8],\n [0, -2, -5, -10],\n [0, 0, 9, 10],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
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[[6, 5, 4, -2],\n [5, 5, 2, 0],\n [4, 2, 4, -2],\n [-2, 0, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1653
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, -12, 4, 2],\n [0, -2, -8, -10],\n [0, 0, 1, 6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2522
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, 6, 0, 7],\n [0, -2, -5, 2],\n [0, 0, -2, -1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-163
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[[-5, -2, -8, 0],\n [0, 11, 2, 12],\n [0, 0, -9, 3],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
142
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 2, -7, 0],\n [2, -1, -4, -1],\n [-7, -4, -1, 0],\n [0, -1, 0, 12]]\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 absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 11, -10, -6],\n [-3, -2, 3, 6],\n [2, -10, -5, 11],\n [12, 1, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
73
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, -1, 0, -2],\n [-1, -9, 0, -2],\n [0, 0, 11, 4],\n [-2, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
256
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, -5, 8, -3],\n [-5, 1, -1, -4],\n [8, -1, 3, 2],\n [-3, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
498
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[[-6, 0, -4, -8],\n [0, -9, -1, -1],\n [-4, -1, -8, 0],\n [-8, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-15
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 0, -5, 9],\n [0, 3, -4, -12],\n [0, 0, 10, 6],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
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, -11, -4, 5],\n [0, -3, -12, 12],\n [0, 0, -1, 12],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3528
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, -5, -4, -8],\n [0, 8, -2, -6],\n [0, 0, -8, 12],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
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[[1, -9, -5, 0],\n [-9, 3, -4, -2],\n [-5, -4, 9, 0],\n [0, -2, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
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, -6, 6, 3],\n [0, -11, 1, -11],\n [0, 0, 4, -2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-89
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, 6, -8, -4],\n [6, -11, 3, 0],\n [-8, 3, -4, -2],\n [-4, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
269
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, 8, 0, 8],\n [0, 2, -4, -2],\n [0, 0, -2, -2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[-5, -3, -2, 6],\n [-3, 1, -4, -6],\n [-2, -4, -3, -3],\n [6, -6, -3, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
MATH
[ { "content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[7, -6, 4, -2],\n [-6, -7, -12, 3],\n [4, -12, -11, -2],\n [-2, 3, -2, 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 trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, -5, -2, 7],\n [11, 8, -2, 3],\n [8, -9, 1, -5],\n [-6, -12, -10, 2]]\nRound your answer to the nearest integer.\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[[7, 11, -7, -8],\n [-10, -2, -2, 1],\n [3, 3, -3, -3],\n [11, 1, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-82
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 4) rounded to the nearest integer?\n[[2, 3, -9, -8],\n [0, 7, 9, -4],\n [0, 0, 12, 1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
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[[-10, -2, -6, -10],\n [-2, -10, 2, -6],\n [-6, 2, -6, -6],\n [-10, -6, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12
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, -5, 10, -10],\n [0, -1, -8, 11],\n [0, 0, 2, -8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3184
MATH
[ { "content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[8, 0, 0, 6],\n [0, 8, -10, 12],\n [0, 0, -1, -4],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-208
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[[11, 0, 0, -1],\n [0, -9, 3, -4],\n [0, 3, 5, -1],\n [-1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[8, 11, -7, -8],\n [-9, 2, -2, 1],\n [10, -7, -5, 5],\n [-3, 4, -8, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
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[[-3, 4, 4, 0],\n [4, -1, 1, -11],\n [4, 1, 6, 0],\n [0, -11, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[7, -10, -4, 2],\n [0, -7, 0, 7],\n [0, 0, 3, 5],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
131
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[[-10, 1, -8, -5],\n [2, 8, 1, 2],\n [-5, 12, -3, -9],\n [1, -7, -7, -7]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 8, 12, -4],\n [0, 11, 0, 3],\n [0, 0, -3, -5],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
47
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, 0, 3, -10],\n [0, 6, -3, 3],\n [0, 0, 2, -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" } ]
33
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, -2, 2, -6],\n [-2, -9, -11, -4],\n [2, -11, -10, -8],\n [-6, -4, -8, 10]]\nRound your answer to the nearest integer.\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[0, 2, -5, 7],\n [2, -4, -1, 0],\n [-5, -1, -10, -8],\n [7, 0, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-38
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[[7, -7, 12, 4],\n [0, -12, -9, -9],\n [0, 0, -9, 3],\n [0, 0, 0, -10]]\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, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -11, 11, -4],\n [0, 6, -1, 2],\n [0, 0, 6, 8],\n [0, 0, 0, 3]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, 1, -2, -7],\n [0, 6, 9, 1],\n [0, 0, -1, -9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-427
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, -6, -5, 0],\n [-2, 12, -2, -3],\n [7, -6, 7, -11],\n [1, -10, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
229
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, 12, -5, -12],\n [0, -1, -4, 9],\n [-8, -2, 6, -8],\n [6, 9, -1, 7]]\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 absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -6, 6, -2],\n [-6, 8, 2, -1],\n [6, 2, 4, -3],\n [-2, -1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
691
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[11, -8, 6, 4],\n [-8, -8, 4, -2],\n [6, 4, 3, -1],\n [4, -2, -1, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
83
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[[11, -7, 7, 2],\n [0, -9, -4, 1],\n [0, 0, -12, 2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
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, 9, 9],\n [0, -8, -7, -11],\n [0, 0, -7, 6],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
203
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[[9, 0, 10, 12],\n [11, 2, -10, 5],\n [1, 3, -9, 3],\n [5, -6, -11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
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[[0, 0, 0, 8],\n [0, -2, 0, -3],\n [0, 0, -4, 4],\n [8, -3, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
158
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[1, 8, 4, -6],\n [8, 4, 0, -8],\n [4, 0, 1, 0],\n [-6, -8, 0, -7]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -5, 2, 2],\n [-5, 0, 2, 0],\n [2, 2, -5, -11],\n [2, 0, -11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
106
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[[-2, 3, 5, 10],\n [0, 6, 11, 7],\n [0, 0, 9, 8],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
MATH