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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[[3, 4, -4, -4],\n [4, 8, -6, -2],\n [-4, -6, -9, 8],\n [-4, -2, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-520
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[[-12, -4, 3, 6],\n [2, -2, 9, -4],\n [-12, 10, -1, -12],\n [7, -2, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
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, 3, 3, 11],\n [2, -5, 6, -11],\n [9, 6, 8, -5],\n [-10, -7, 4, 12]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, -1, -1, 7],\n [3, 5, 12, 8],\n [0, -8, 9, -11],\n [11, 2, 7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
254
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[1, -5, -1, -11],\n [0, -9, -3, 11],\n [0, 0, 10, 4],\n [0, 0, 0, -11]]\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[[8, -9, 10, -10],\n [-9, -9, -2, 4],\n [11, -10, -7, -6],\n [-8, 8, 6, -1]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-1, 2, 2, -2],\n [2, 6, -7, -2],\n [2, -7, 12, 1],\n [-2, -2, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[11, 4, 1, 5],\n [8, -4, -9, 6],\n [-3, 3, -1, 3],\n [4, 9, -7, 3]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[2, 9, 3, -11],\n [-8, -4, 4, -4],\n [6, 2, -4, 9],\n [-12, -9, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[4, -5, -1, 12],\n [5, -3, 6, 12],\n [-5, -8, -3, 10],\n [-8, -5, -12, 7]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[8, -2, -1, 11],\n [0, 2, -10, -12],\n [0, 0, -4, 12],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-672
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[[2, -1, -12, -8],\n [-1, 12, 4, 5],\n [12, 8, 10, -2],\n [12, 10, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[-2, 3, -10, 1],\n [0, 4, 1, -1],\n [0, 0, 10, -11],\n [0, 0, 0, 12]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 10, -12, -11],\n [0, 2, 4, -9],\n [0, 0, -4, 4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
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[[-7, 3, 4, -5],\n [10, 0, -8, 7],\n [-9, -2, -7, 4],\n [-3, -2, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
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, 0, 0],\n [-5, -9, -5, 2],\n [0, -5, 10, -2],\n [0, 2, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
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[[-10, 8, -2, 0],\n [8, -6, 4, -1],\n [-2, 4, 0, -2],\n [0, -1, -2, 12]]\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 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, -4, -8],\n [4, 9, -8, 4],\n [-4, -8, -6, 2],\n [-8, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
MATH
[ { "content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[4, -5, -11, -12],\n [0, -9, -1, 8],\n [0, 0, 12, -6],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\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 absolute values of all entries rounded to the nearest integer?\n[[-7, 10, -11, 6],\n [0, -6, -10, 9],\n [0, 0, 3, 9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
670
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[11, 4, 2, -6],\n [0, 8, -11, -11],\n [0, 0, 2, -5],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-9, 12, -5, -1],\n [-6, 11, -7, -11],\n [-9, 12, -4, 0],\n [-3, -11, 1, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
129
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, -6, -4, 4],\n [-6, 5, 1, -8],\n [-1, 3, 3, 6],\n [-7, -3, 8, 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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 10, -6, -5],\n [10, -3, -5, 4],\n [-7, -11, 6, 7],\n [12, -1, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-136
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[[-3, 11, 4, 0],\n [11, -2, 0, 3],\n [4, 0, -4, -2],\n [0, 3, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-18
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[3, 4, 0, -8],\n [4, 4, 8, 0],\n [0, 8, 8, 4],\n [-8, 0, 4, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-21
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-1, 3, 2, 2],\n [3, -12, -12, -4],\n [2, -12, 6, 4],\n [2, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
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, -1, -6, 0],\n [0, -4, 12, -12],\n [4, 10, 3, -9],\n [-8, 10, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, 1, -4, -1],\n [6, -4, -6, 8],\n [11, 4, 2, 1],\n [-9, -3, 3, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
178
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[[8, -1, 9, -7],\n [0, -7, -7, 3],\n [0, 0, 8, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
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, 12, 3, -5],\n [-9, 9, 7, 7],\n [-9, 0, -9, 12],\n [-5, -5, -9, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-35
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[4, -9, 4, 6],\n [0, -10, -12, 6],\n [0, 0, 8, 8],\n [0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-311
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 0, 7, 7],\n [-8, -8, 8, 2],\n [5, -6, 7, 8],\n [11, 1, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-10, 4, 4, 9],\n [4, 2, 4, -6],\n [4, 4, 11, 0],\n [9, -6, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-124
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[[-1, -8, -12, 8],\n [-9, -8, 7, 10],\n [10, 10, -4, -10],\n [-10, -7, 4, 5]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 1, 0, -4],\n [4, 4, -9, 5],\n [-2, -1, 8, 6],\n [2, 3, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
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, 10, 7, -9],\n [0, -9, 12, -10],\n [0, 0, 5, 12],\n [0, 0, 0, 11]]\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 at position (1, 4) rounded to the nearest integer?\n[[2, -7, -8, 12],\n [0, 12, -12, 2],\n [0, 0, 2, -2],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 2, 11, 4],\n [12, 8, 8, -8],\n [-2, 5, -3, 11],\n [-2, 9, 5, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
302
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, -7, 0, 2],\n [-7, 2, -4, 8],\n [0, -4, -8, -6],\n [2, 8, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
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, 6, -2],\n [2, -1, -3, 1],\n [6, -3, 12, -3],\n [-2, 1, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
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[[8, -1, 5, -6],\n [-10, 5, 4, 2],\n [6, 0, -12, -9],\n [-11, 1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[3, 2, -3, -4],\n [2, 11, 0, 4],\n [-3, 0, 5, -9],\n [-4, 4, -9, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[-1, 0, 0, -1],\n [0, -1, -8, -2],\n [0, -8, -11, -8],\n [-1, -2, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-126
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[[1, 7, -8, 3],\n [0, -7, -4, -12],\n [0, 0, 1, -5],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
187
MATH
[ { "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[[2, -2, -2, -4],\n [-2, -8, 4, 7],\n [-2, 4, -5, 2],\n [-4, 7, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-76
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, -7, 2, -11],\n [0, 2, -6, -1],\n [0, 0, -12, 8],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
274
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, -10, 6, -10],\n [0, 9, 9, -9],\n [0, 0, 3, 9],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-145
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[[-7, 12, -7, 12],\n [-10, 2, 8, -1],\n [5, 12, 9, -3],\n [12, 10, 11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
223
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[3, 3, -7, -5],\n [0, 12, 11, 9],\n [0, 0, 12, 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" } ]
40
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, 6, 0, 5],\n [6, -2, 0, 0],\n [0, 0, -1, 2],\n [5, 0, 2, 8]]\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[[1, 2, 4, -3],\n [2, 2, -6, 0],\n [4, -6, 8, -4],\n [-3, 0, -4, 0]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 9, -5, -10],\n [0, -9, -8, -2],\n [11, -11, 10, 5],\n [4, -12, -9, 10]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, -8, 4, 5],\n [-8, -8, -4, 4],\n [4, -4, 5, 10],\n [5, 4, 10, -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 sum of absolute values of all entries rounded to the nearest integer?\n[[6, -12, 0, 6],\n [0, -6, -11, -2],\n [0, 0, 3, 2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
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, -10, -2, 6],\n [-10, -8, 6, -6],\n [-2, 6, -7, -2],\n [6, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
125
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, -7, 11, -1],\n [1, 6, -10, -6],\n [4, 7, 7, 10],\n [-8, 12, -7, 12]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-8, -8, -10, -4],\n [-8, 12, -2, 4],\n [-10, -2, -5, 2],\n [-4, 4, 2, 11]]\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[[-9, -8, 10, 1],\n [2, 9, 7, 4],\n [-4, 4, 11, -2],\n [7, 12, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-114
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[[-3, -6, 3, -9],\n [0, -10, -3, -5],\n [0, 0, -10, -6],\n [0, 0, 0, -8]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 7, 1, 3],\n [0, -3, 6, 9],\n [0, 0, 5, 8],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
311
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, 1, 6, -6],\n [0, -11, 1, 4],\n [0, 0, 9, -6],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
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, 9, -12, -8],\n [0, 10, 0, 7],\n [0, 0, 5, -10],\n [0, 0, 0, 8]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, -2, -8, 7],\n [-2, -10, 2, -8],\n [-8, 2, -6, 2],\n [7, -8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-80
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, 3, 7, -6],\n [3, 6, 2, 2],\n [7, 2, -10, 2],\n [-6, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-76
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, -8, -9, -9],\n [-8, 9, -6, 4],\n [-9, -6, 10, -3],\n [-9, 4, -3, -8]]\nRound your answer to the nearest integer.\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[[10, 4, -8, -2],\n [0, 6, 8, -5],\n [0, 0, -11, -12],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, -4, 0, 7],\n [3, 4, 2, -1],\n [-1, 0, 4, 5],\n [10, 10, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
71
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, 1, 5, 11],\n [0, 6, -12, -9],\n [0, 0, -12, -3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
179
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, -10, -10, 12],\n [0, -6, -7, -10],\n [0, 0, -4, 7],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
47
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, -7, 9, -3],\n [5, -1, -9, -5],\n [-1, -11, -4, -3],\n [-12, -6, 7, -10]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 0, 6, -1],\n [0, -9, 4, 7],\n [6, 4, -5, 4],\n [-1, 7, 4, 12]]\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, -3, 4, -2],\n [-3, -4, 0, -4],\n [4, 0, -4, 0],\n [-2, -4, 0, 4]]\nRound your answer to the nearest integer.\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 absolute values of all entries rounded to the nearest integer?\n[[-9, -2, -4, 0],\n [-2, -11, -4, 3],\n [-4, -4, 0, 2],\n [0, 3, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
151
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, -10, -11, 10],\n [0, 7, -1, 6],\n [0, 0, 8, 6],\n [0, 0, 0, 11]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, -10, -1, -11],\n [0, 9, -10, 3],\n [0, 0, 4, -8],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-87
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-10, 9, 4, 8],\n [9, -4, 6, 4],\n [4, 6, 11, 8],\n [8, 4, 8, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
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[[-4, -7, -12, 11],\n [0, 12, -9, 6],\n [0, 0, 8, 7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
619
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -7, 3, -6],\n [-11, -12, -12, 2],\n [6, 10, -8, 12],\n [-4, -12, 12, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
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[[7, -11, 3, 0],\n [0, 2, -6, -8],\n [0, 0, 11, 4],\n [0, 0, 0, 5]]\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[[6, -10, 4, 5],\n [0, -12, 9, -4],\n [0, 0, -6, -4],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32
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, 1, 1, 2],\n [1, 1, 5, 7],\n [1, 5, 6, 4],\n [2, 7, 4, -11]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 2, 7, 10],\n [2, -7, -4, 2],\n [7, -4, 0, -2],\n [10, 2, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
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, 0, 6, 8],\n [0, 6, -10, -11],\n [0, 0, -5, -2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
198
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, -7, 0, -11],\n [5, -8, 5, 3],\n [10, -9, -10, 10],\n [6, -5, -4, -5]]\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[[2, -8, 4, -1],\n [0, -6, 0, -9],\n [0, 0, 8, 9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
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[[-3, -10, -9, -6],\n [0, 12, 2, 12],\n [0, 0, 6, -8],\n [0, 0, 0, -3]]\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[[2, 4, 8, -5],\n [0, 6, -4, 10],\n [0, 0, 4, -5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
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, -9, 6, -4],\n [0, 10, -12, -7],\n [0, 0, 5, 5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, -10, -11, 1],\n [-10, 2, -3, 6],\n [-11, -3, -5, 2],\n [1, 6, 2, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[5, -1, 3, 7],\n [1, -3, 3, 0],\n [-1, -7, 0, -1],\n [-7, -11, 6, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-22
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, 5, -3, -9],\n [0, -3, 1, -4],\n [0, 0, 8, -5],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-792
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, 0, -9, 0],\n [0, -8, 0, 9],\n [-9, 0, 4, 12],\n [0, 9, 12, -6]]\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[[0, 8, 4, 6],\n [8, -10, 4, -1],\n [4, 4, 2, 0],\n [6, -1, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
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, -6, -8, -8],\n [10, -10, 0, 7],\n [-2, -1, -9, -5],\n [-5, 8, 7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-108
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, 7, -11, -11],\n [0, -3, 6, -12],\n [0, 0, 9, -8],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-498
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[12, 0, -6, -6],\n [-11, -8, 2, 8],\n [9, -9, 0, -1],\n [9, 1, -1, 9]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 4, 0, 0],\n [4, 10, 0, -2],\n [0, 0, 5, -6],\n [0, -2, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
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[[-10, 12, -4, -7],\n [0, 7, 9, 9],\n [0, 0, -1, 8],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4128
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, 1, 9],\n [0, -3, 2, -8],\n [0, 0, 3, -10],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH