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[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, 8, -4, -3],\n [8, -5, 7, -3],\n [-4, 7, 12, 3],\n [-3, -3, 3, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
47
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, 9, 6, -10],\n [9, 4, -2, -4],\n [6, -2, 4, -7],\n [-10, -4, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[8, 0, 2, 4],\n [0, -10, -8, -12],\n [0, 0, -4, -10],\n [0, 0, 0, 12]]\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 sum of all entries rounded to the nearest integer?\n[[8, 0, -4, -4],\n [0, -2, -2, 3],\n [-4, -2, 6, -1],\n [-4, 3, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
229
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[9, -1, -7, 10],\n [-1, 9, 10, -2],\n [-7, 10, 10, 0],\n [10, -2, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
442
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[3, -1, 4, 4],\n [-1, -12, -1, -7],\n [4, -1, 10, -7],\n [4, -7, -7, 12]]\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 sum of all entries rounded to the nearest integer?\n[[-2, 0, -4, -1],\n [0, -1, 2, 2],\n [-4, 2, 9, 0],\n [-1, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-70
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, -7, -7, -11],\n [0, 4, -4, 7],\n [0, 0, -3, -10],\n [0, 0, 0, -4]]\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 value at position (1, 1) rounded to the nearest integer?\n[[-2, 2, -9, 3],\n [2, -5, 0, -4],\n [-9, 0, 3, 10],\n [3, -4, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-703
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 4) rounded to the nearest integer?\n[[-7, 0, 8, -11],\n [0, -1, -8, -9],\n [0, 0, -1, 0],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 5, -1, 5],\n [0, -6, 6, 4],\n [0, 0, -8, 2],\n [0, 0, 0, -7]]\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 all entries rounded to the nearest integer?\n[[10, 1, -7, 8],\n [-9, 10, -4, 5],\n [9, -8, -5, 2],\n [-3, 2, -5, -3]]\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[[7, 3, 8, 10],\n [0, -5, 6, -12],\n [0, 0, 7, -6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
175
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, -6, 8, -4],\n [-6, -12, 2, 8],\n [8, 2, 8, -8],\n [-4, 8, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
618
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[1, -6, -12, -6],\n [0, 7, -4, -5],\n [0, 0, -7, 9],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[5, -1, -8, 10],\n [0, -12, 2, 2],\n [0, 0, -9, 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" } ]
97
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[[7, -4, -3, -2],\n [-4, -7, -2, -6],\n [-3, -2, -5, 4],\n [-2, -6, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-55
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, 8, -2, 0],\n [8, 6, -2, -2],\n [-2, -2, 3, 0],\n [0, -2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-9, -6, -7, -3],\n [0, -11, 1, -8],\n [0, 0, -8, 7],\n [0, 0, 0, 7]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -6, -10, -5],\n [-7, -8, -12, 9],\n [11, 1, 8, 3],\n [6, -3, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-2, -5, -5, 1],\n [0, 12, 6, 12],\n [0, 0, -7, -2],\n [0, 0, 0, -5]]\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, -3, 12, -5],\n [-3, 11, 1, 3],\n [12, 1, 3, 1],\n [-5, 3, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
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[[5, 9, 7, 2],\n [9, 5, 6, -2],\n [7, 6, -3, 8],\n [2, -2, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -10, -4, 7],\n [-12, -7, 10, -9],\n [-3, 4, -4, 6],\n [0, 10, 7, 1]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 6, 5, 0],\n [6, -10, 4, -6],\n [5, 4, -7, -1],\n [0, -6, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[5, 1, -6, 0],\n [1, -6, -1, 10],\n [-6, -1, -2, 1],\n [0, 10, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-1, 1, 7, 12],\n [0, -4, -5, 6],\n [0, 0, 11, 1],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-95
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[10, -4, 10, -1],\n [5, 0, 5, 11],\n [-12, 7, 12, 4],\n [8, 8, -11, -8]]\nRound your answer to the nearest integer.\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, -5, -4, -5],\n [0, -12, 11, -8],\n [0, 0, -10, -12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-118
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, 8, -5, 5],\n [6, -1, -5, 7],\n [1, 6, -2, 2],\n [-5, 9, -11, 1]]\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[[3, 3, -11, 8],\n [0, 4, 7, 12],\n [0, 0, -11, -12],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
319
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[[4, -4, 6, 1],\n [-4, 9, -1, -10],\n [6, -1, -7, -2],\n [1, -10, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26
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, -2, -2],\n [-2, -9, 10, -8],\n [-2, 10, -5, 6],\n [-2, -8, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
326
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[-9, -4, 7, 12],\n [9, 5, -6, -10],\n [-12, 4, 6, 8],\n [4, -9, 9, 6]]\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 (1, 3) rounded to the nearest integer?\n[[-2, -10, 0, 0],\n [-10, 10, -7, 6],\n [0, -7, 11, 4],\n [0, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[4, -8, -2, -4],\n [-8, -10, -6, 2],\n [-2, -6, -4, 6],\n [-4, 2, 6, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
118
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, -11, -2, -7],\n [-7, 2, -8, -10],\n [1, 6, -11, 4],\n [-11, -5, -7, -11]]\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[[-2, 0, -1, 8],\n [-2, 11, 12, -6],\n [5, 12, 9, -2],\n [4, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-46
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, -1, 6, 9],\n [4, -12, -9, 2],\n [9, 5, 0, 2],\n [-10, 9, 9, 4]]\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[[-1, 6, 5, 11],\n [11, -2, 0, 6],\n [0, 8, -2, 1],\n [11, 0, -8, 12]]\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[[-4, 4, 10, 2],\n [4, 6, 0, 0],\n [10, 0, -6, 4],\n [2, 0, 4, -11]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, 8, -8, -3],\n [0, 10, -4, 1],\n [0, 0, 4, 1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-3, -12, -5, 2],\n [0, -3, -3, -9],\n [0, 0, 12, -11],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32
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, 2, 2, -1],\n [2, -6, 1, 2],\n [2, 1, 10, -1],\n [-1, 2, -1, 3]]\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[[-4, -7, 5, 4],\n [0, -8, 1, 9],\n [0, 0, -7, -12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
137
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-6, -6, 10, 5],\n [0, 1, 6, 12],\n [0, 0, 3, 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" } ]
-96
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, 2, 0, -2],\n [2, 2, 8, -4],\n [0, 8, 9, 0],\n [-2, -4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 10, 6, 6],\n [0, -6, 5, 9],\n [0, 0, 5, -12],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-115
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[[-11, 3, -8, 6],\n [3, -1, -2, 1],\n [-8, -2, 3, -8],\n [6, 1, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[2, 3, 2, -5],\n [1, -6, 10, 0],\n [10, -7, -12, -7],\n [-5, -1, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[11, 2, 2, 6],\n [2, 6, 7, 0],\n [2, 7, 7, 2],\n [6, 0, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
139
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, -9, -11, 5],\n [2, -6, 2, -2],\n [8, -9, -7, -12],\n [-11, 1, -4, -2]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -2, 2, 6],\n [-2, 0, 2, 3],\n [2, 2, -6, -3],\n [6, 3, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
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, -10, 3, -12],\n [0, 11, 11, 9],\n [0, 0, 6, -8],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
142
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, 0, -10],\n [4, 6, 0, -7],\n [0, 0, 7, -6],\n [-10, -7, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
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, -9, 9, 8],\n [0, 11, -5, 6],\n [0, 0, -4, 5],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-15
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 2, 7, 6],\n [9, 10, -5, -7],\n [-8, -6, -7, -5],\n [3, 8, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-18
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -6, 12, -7],\n [0, 12, 3, 3],\n [0, 0, -7, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
429
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, 4, 1, 4],\n [4, -5, -3, 1],\n [1, -3, -10, -8],\n [4, 1, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
371
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[7, -1, 10, -4],\n [-8, -3, 7, -11],\n [3, -2, 9, -3],\n [-9, -8, -2, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
215
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 8, -2, 11],\n [6, -3, -10, 0],\n [7, 4, 6, 4],\n [-1, 11, 1, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
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, -10, 12, -9],\n [9, 11, -5, 12],\n [-2, 7, 4, 12],\n [-9, 6, -3, 5]]\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 (4, 4) of the inverse. Round your answer to the nearest integer:\n[[9, -5, 3, 4],\n [-9, 7, -1, -11],\n [-5, -7, -5, -9],\n [8, 7, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 1, -1, -5],\n [1, 10, -6, -1],\n [-1, -6, 4, 2],\n [-5, -1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-597
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, -4],\n [0, 7, -12, -11],\n [0, 0, 4, 5],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
79
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 6, 4, -9],\n [6, -4, 2, -6],\n [4, 2, -6, 8],\n [-9, -6, 8, 10]]\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 (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-11, -11, -2, -3],\n [-11, -6, -10, -11],\n [-2, -10, 3, -5],\n [-3, -11, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-4, -9, 5, -6],\n [-3, -9, -2, 6],\n [11, 7, -6, -2],\n [3, 6, -4, 5]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 0, 5, 5],\n [0, 5, -10, 5],\n [0, 0, -6, 5],\n [0, 0, 0, 10]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -2, -3, 0],\n [-2, 7, 4, 4],\n [-3, 4, 0, 4],\n [0, 4, 4, 9]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, -8, 12, -7],\n [0, -7, 0, -1],\n [0, 0, 1, -1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-384
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, -7, 4, -2],\n [-7, 9, -4, -2],\n [4, -4, 5, -12],\n [-2, -2, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-75
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[1, -12, -11, 2],\n [0, 4, -7, 1],\n [0, 0, 3, -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" } ]
2303
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, -4, 2, 6],\n [-4, 12, 2, 0],\n [2, 2, 4, 10],\n [6, 0, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-123
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[[-12, 0, -8, -4],\n [0, -1, 5, -7],\n [0, 0, -3, 6],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, -8, -8, 8],\n [-8, -5, 1, 6],\n [-8, 1, -9, 4],\n [8, 6, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
393
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -5, -6, -3],\n [0, 6, 1, 3],\n [0, 0, -7, -11],\n [0, 0, 0, -4]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 2, 6, 4],\n [2, -4, -6, 0],\n [6, -6, -4, 6],\n [4, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-75
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 0, -4, 0],\n [0, 11, 5, 6],\n [-4, 5, -8, 2],\n [0, 6, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
118
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[[6, -2, 2, -8],\n [-2, 6, 3, -4],\n [2, 3, 12, -6],\n [-8, -4, -6, 2]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, 0, -8, 6],\n [0, -9, 6, 0],\n [-8, 6, 0, 1],\n [6, 0, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26
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, -11, -4, 4],\n [0, -4, 0, 8],\n [0, 0, -8, -4],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-46
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, -4, 12, 10],\n [-12, -9, 12, -6],\n [12, 10, -10, -11],\n [0, 8, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-7, 9, 7, 2],\n [0, 8, 1, -8],\n [0, 0, 11, 10],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
53
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, -10, -1, 11],\n [0, -9, -12, -4],\n [0, 0, -11, 10],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\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 value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[-4, -7, 11, 7],\n [10, -9, -7, 10],\n [7, 1, -11, -2],\n [-8, -10, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
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, -5, 10, 8],\n [-5, 9, -1, 9],\n [10, -1, 6, -7],\n [8, 9, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
227
MATH
[ { "content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[-6, 7, -6, -1],\n [7, -10, 7, 4],\n [-6, 7, 11, -5],\n [-1, 4, -5, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 0, 2, 6],\n [0, -2, 6, 2],\n [2, 6, -8, 2],\n [6, 2, 2, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
271
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, 12, 2, -7],\n [-12, 3, -9, 10],\n [-7, -6, -8, 9],\n [-10, -12, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2052
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, 0, -8, 0],\n [1, -8, 1, 5],\n [-10, 12, -1, 4],\n [9, -5, 1, 6]]\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[[-11, 9, 6, 8],\n [0, -8, -9, 12],\n [0, 0, 8, -2],\n [0, 0, 0, -8]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-1, -6, -3, 2],\n [-6, -11, -6, 4],\n [-3, -6, -12, 4],\n [2, 4, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
137
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, 5, -5],\n [9, 4, -10, -6],\n [6, 9, 2, 5],\n [4, 12, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-227
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[7, -11, 0, -10],\n [6, 11, -5, 3],\n [5, -7, 10, 2],\n [3, 5, -10, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 4, 0, 7],\n [4, -5, -4, 4],\n [0, -4, 11, -2],\n [7, 4, -2, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
122
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, 0, 8, 10],\n [0, -6, -9, -8],\n [8, -9, 1, 0],\n [10, -8, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
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[[5, -6, 5, 3],\n [-6, 0, 0, -3],\n [5, 0, -4, -5],\n [3, -3, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2082
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, -8, -5, -7],\n [0, -9, 11, 3],\n [0, 0, 2, -6],\n [0, 0, 0, -12]]\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 at position (1, 2) rounded to the nearest integer?\n[[-12, -12, -5, 11],\n [0, -11, 10, 4],\n [0, 0, -12, -2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH