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[ { "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[[6, -8, -4, 0],\n [-8, -3, -6, -10],\n [-4, -6, -10, 4],\n [0, -10, 4, -9]]\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 (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-1, -2, 5, 6],\n [-2, -2, -4, -4],\n [5, -4, 0, -2],\n [6, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 2, -8, 5],\n [2, -9, 4, -12],\n [-8, 4, 12, -4],\n [5, -12, -4, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, -1, 2, 4],\n [-10, -1, -10, -4],\n [2, -3, 10, -6],\n [11, 1, -8, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
137
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, -11, 1, 3],\n [-11, 5, -7, 0],\n [1, -7, 7, 4],\n [3, 0, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[2, 12, -2, -12],\n [0, 12, -9, 12],\n [0, 0, -6, 8],\n [0, 0, 0, 12]]\nRound your answer to the nearest integer.\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[[7, 12, 6, 12],\n [0, -11, 5, -3],\n [0, 0, -10, -12],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 3, 7, 6],\n [1, 0, 6, 4],\n [-2, 6, -11, -10],\n [3, 12, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
285
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, -8, -1, -1],\n [-8, 12, 4, 0],\n [-1, 4, -11, 2],\n [-1, 0, 2, 0]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 12, 8, 3],\n [0, 7, 10, -6],\n [0, 0, 12, 6],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
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, 0, 6, -2],\n [0, 4, -8, 6],\n [6, -8, 4, 7],\n [-2, 6, 7, 8]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-11, 2, 12, -4],\n [0, 9, -6, -7],\n [0, 0, -12, -3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
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, 8, 2, -6],\n [8, -3, 0, 2],\n [2, 0, -6, -4],\n [-6, 2, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-22
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[0, -11, 4, -5],\n [-9, 0, 12, 7],\n [0, 7, -10, -9],\n [1, -9, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 2, 0, -4],\n [2, 5, 6, 7],\n [0, 6, -8, -5],\n [-4, 7, -5, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
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, -5, -6, 12],\n [-11, 8, -10, 11],\n [-6, -1, 0, 8],\n [-6, 1, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
169
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, 4, 2, 0],\n [4, 6, 2, 0],\n [2, 2, -9, 8],\n [0, 0, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
203
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, 4, 3, -4],\n [0, -11, 5, -7],\n [0, 0, -6, 1],\n [0, 0, 0, -12]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, -1, 9, 6],\n [-12, 8, -4, 5],\n [-5, -4, 9, -8],\n [9, 7, 12, 8]]\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[[5, 3, 11, 11],\n [-11, -8, 8, 5],\n [8, 8, -7, 9],\n [-8, 12, 11, -12]]\nRound your answer to the nearest integer.\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 sum of all entries rounded to the nearest integer?\n[[-10, 2, -10, -9],\n [0, -9, -12, -9],\n [0, 0, -11, 5],\n [0, 0, 0, -5]]\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 at position (2, 1) rounded to the nearest integer?\n[[10, 10, -6, 0],\n [10, 8, 0, -6],\n [-6, 0, -1, 0],\n [0, -6, 0, 4]]\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[[-7, -8, 4, 8],\n [9, 10, 6, -8],\n [-2, -1, 0, 7],\n [-12, 9, 10, 1]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 7, 4, 1],\n [7, 9, -2, -4],\n [4, -2, -12, 8],\n [1, -4, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, -5, -4, -3],\n [-10, -4, 11, 11],\n [-8, 0, -3, -5],\n [12, -10, -9, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
179
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[[10, -4, -1, 10],\n [0, -5, -9, 1],\n [0, 0, 5, 8],\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -3, -12, 2],\n [0, -12, -3, 9],\n [0, 0, 4, 9],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
691
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, 4, -7],\n [7, -8, -10, -8],\n [-7, 8, 9, -4],\n [-2, -5, -2, -4]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, 8, 12, -7],\n [12, -10, -10, -6],\n [3, 0, 4, 1],\n [-1, -3, -8, -1]]\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 9, -11, 1],\n [0, -11, -9, 8],\n [-5, 3, 12, 3],\n [-4, 11, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
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, -10, -5, 2],\n [-6, 8, 0, 5],\n [-2, 3, 9, -5],\n [-2, -8, 12, -4]]\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 value at position (4, 1) rounded to the nearest integer?\n[[3, 10, -1, -10],\n [0, -2, 3, 10],\n [0, 0, -8, -6],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[0, -4, -8, 6],\n [-4, 10, 2, 2],\n [-8, 2, 8, -8],\n [6, 2, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
189
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, -9, -9, -8],\n [0, -7, -5, -11],\n [0, 0, 5, 2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
165
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -3, 6, -8],\n [-11, -9, -10, -4],\n [9, 10, -2, 5],\n [12, 11, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
129
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 10, -1, 3],\n [10, 6, 0, -2],\n [-1, 0, 8, 1],\n [3, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
147
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[[-6, 3, -12, 8],\n [4, 3, 11, 0],\n [-7, -9, 8, 11],\n [-10, -10, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[-11, -11, 7, -2],\n [0, -1, 3, -9],\n [0, 0, -2, -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" } ]
0
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 3, -8, 3],\n [0, 3, -11, 12],\n [0, 0, -5, 12],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-150
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 5, -11, -6],\n [0, 3, 4, -1],\n [0, 0, 10, 10],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
66
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[[0, -10, 12, -6],\n [11, -9, 7, -1],\n [-9, 1, 10, 4],\n [12, 6, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
207
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, -9, 6, -2],\n [12, -3, 12, 8],\n [-8, 6, 5, 4],\n [-6, 0, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, -3, 11, -7],\n [0, 10, -3, 6],\n [-10, -10, 1, 2],\n [-2, 1, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
135
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, -8, 6, 10],\n [2, -10, -5, 1],\n [-8, -3, -6, 8],\n [-4, -12, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 3, -12, 4],\n [-1, 8, 2, 9],\n [8, -9, -8, -6],\n [4, -1, 1, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
97
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, 9, 8, -11],\n [0, -9, -12, -4],\n [0, 0, -7, 5],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
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, 6, 0, -11],\n [9, -6, -2, 5],\n [-6, -4, -6, 3],\n [12, -12, -7, -8]]\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[[-4, 0, -10, -1],\n [0, -12, 4, -1],\n [-10, 4, 2, 6],\n [-1, -1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 2, 8, 6],\n [2, -5, -12, -4],\n [8, -12, -5, 8],\n [6, -4, 8, -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 value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[4, -8, -12, 9],\n [-6, 1, 3, -10],\n [2, 12, 2, 1],\n [2, -3, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2
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, -9, -1, 5],\n [8, -11, -5, 5],\n [-2, -8, -5, 12],\n [3, -9, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-20
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -9, -11, 7],\n [0, -5, -12, 1],\n [0, 0, 6, 2],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[4, -7, -9, -12],\n [0, 12, 10, -1],\n [0, 0, 2, 11],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -1, -9, -8],\n [0, -4, -12, -5],\n [0, 0, 12, -5],\n [0, 0, 0, -8]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, -8, -8, 0],\n [-8, 8, 0, 2],\n [-8, 0, 5, 7],\n [0, 2, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
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, 0, 2, 6],\n [0, -12, 0, 3],\n [2, 0, -4, 4],\n [6, 3, 4, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 3, -4, -2],\n [3, 0, -10, 2],\n [-4, -10, 7, 2],\n [-2, 2, 2, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-85
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, 4, -8, 8],\n [4, -7, 2, -6],\n [-8, 2, 9, 8],\n [8, -6, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, -2, -2, -8],\n [-8, 11, 8, -10],\n [-9, 3, 12, -3],\n [-5, 9, 4, -9]]\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 absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, -9, 4, 8],\n [-1, 3, 0, 0],\n [9, 9, 1, 0],\n [7, -6, -4, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
510
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, -3, 4, -1],\n [-4, -3, -7, 3],\n [10, 11, -7, -2],\n [9, -3, 4, 3]]\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 value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -6, -4, -3],\n [-6, -5, 0, 0],\n [-4, 0, 8, -2],\n [-3, 0, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[12, -6, 1, 2],\n [-6, -7, -2, 2],\n [1, -2, -1, 8],\n [2, 2, 8, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, 12, -4, -9],\n [0, -6, -11, -8],\n [0, 0, 8, 3],\n [0, 0, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
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, -11, -3, 1],\n [0, 11, 3, 6],\n [0, 0, 10, -12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -10, -2, 1],\n [-10, 10, -9, -4],\n [12, 8, -2, -10],\n [-7, -11, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -8, 11, 5],\n [12, 9, -6, -1],\n [6, -3, 12, -9],\n [-8, 4, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[5, 7, -9, -7],\n [12, 7, -4, -9],\n [7, 10, 8, -6],\n [-7, 1, -7, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-25
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[[-6, 10, -11, -9],\n [8, -8, -3, 8],\n [-6, 8, 11, 9],\n [6, 1, 8, -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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -10, 6, -1],\n [0, 3, 10, -9],\n [0, 0, -6, 0],\n [0, 0, 0, -4]]\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[[4, -2, 1, 11],\n [0, -12, -11, 11],\n [0, 0, -12, 1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
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[[8, 11, 12, -5],\n [0, 2, 4, 12],\n [0, 0, 1, 7],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, -10, 3, 7],\n [-2, 1, -2, 6],\n [4, -2, 5, -3],\n [-2, 1, -11, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
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, 0, -2, 8],\n [0, -4, 8, -10],\n [-2, 8, 5, -8],\n [8, -10, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-27
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[7, -4, -10, -3],\n [8, -8, -9, 8],\n [-12, 1, 7, -9],\n [-9, -12, 6, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 2, -5, -7],\n [0, 11, 4, -12],\n [0, 0, -7, -9],\n [0, 0, 0, -5]]\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[[4, 11, -7, -12],\n [0, 10, 3, -7],\n [-2, 5, 4, -9],\n [8, -7, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-17
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, -12, 5, -2],\n [0, -2, 2, 6],\n [0, 0, 3, -5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 2, 2, -12],\n [2, -10, 2, -4],\n [2, 2, 6, 2],\n [-12, -4, 2, 10]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 0, -5, -4],\n [0, -3, 8, 5],\n [-5, 8, 1, -2],\n [-4, 5, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-33
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, -10, -8],\n [-10, 0, -2, 0],\n [10, 8, 10, -12],\n [7, 7, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63
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, -7],\n [0, 4, 6, -2],\n [0, 0, 11, -2],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
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[[0, 8, -8, 0],\n [8, 7, 10, 6],\n [-8, 10, -4, 3],\n [0, 6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
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, -2, 6, -2],\n [-2, 7, 8, 3],\n [6, 8, 12, -11],\n [-2, 3, -11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[4, -3, -2, 12],\n [0, -6, 11, 6],\n [0, 0, 10, -3],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
141
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, -1, -8, 2],\n [-3, -6, 7, 1],\n [2, 11, 0, 6],\n [8, 1, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
292
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, 1, -3, -4],\n [0, 7, 9, -7],\n [0, 0, 4, 6],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
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, -6, 5],\n [0, -3, -8, 12],\n [0, 0, -11, 7],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
427
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, 7, -10, -10],\n [0, 2, 7, 3],\n [0, 0, 1, -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" } ]
-336
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[7, 10, 1, 10],\n [0, -6, 11, 12],\n [0, 0, -5, 10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[-6, -5, 8, -8],\n [4, -2, -2, 0],\n [3, 1, 11, -10],\n [11, -5, -8, 4]]\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 value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -10, -6, -2],\n [-10, -11, 1, -2],\n [-6, 1, 6, -11],\n [-2, -2, -11, 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 (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-12, -12, -2, -10],\n [0, -7, -9, 4],\n [0, 0, -7, 2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -4, -6, 4],\n [-4, 0, -8, -2],\n [-6, -8, 6, 5],\n [4, -2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-49
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, 6, -1, 4],\n [6, 5, -4, -6],\n [-1, -4, 2, 2],\n [4, -6, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-652
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, -2, -12, 7],\n [0, 11, -1, 0],\n [0, 0, -1, 3],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-202
MATH
[ { "content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[8, -4, 10, -2],\n [0, 6, -5, 0],\n [0, 0, 12, -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" } ]
0
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[[7, 9, 11, 3],\n [-9, -10, -1, 12],\n [3, -1, -8, 9],\n [7, -12, 9, 4]]\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[[-4, -5, 0, -8],\n [0, 10, 3, 6],\n [0, 0, -8, 7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-39
MATH
[ { "content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[7, 3, -6, 4],\n [3, -6, 0, 2],\n [-6, 0, 3, 11],\n [4, 2, 11, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH