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[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -1, -5, 2],\n [-1, -3, -6, -8],\n [-5, -6, -12, 2],\n [2, -8, 2, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
107
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[[1, 6, 2, 0],\n [6, -5, 6, 4],\n [2, 6, 11, -2],\n [0, 4, -2, -6]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -9, 0, -3],\n [0, 4, -4, 1],\n [0, 0, 11, 4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
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, -11, 9, 7],\n [0, 4, -6, 12],\n [0, 0, 11, 2],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
871
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, -2, -9, 1],\n [0, 5, 7, -9],\n [4, 7, 9, -1],\n [6, -2, -11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
270
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, 0, 0],\n [0, 6, -3, 4],\n [0, -3, 9, 6],\n [0, 4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-96
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, 3, 10, 12],\n [-8, -4, 2, 8],\n [4, -10, 12, 0],\n [-7, -8, 0, 12]]\nRound your answer to the nearest integer.\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 sum of all entries rounded to the nearest integer?\n[[-5, 10, -10, 0],\n [10, 2, -7, -11],\n [-10, -7, -8, 7],\n [0, -11, 7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-62
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 0, 2, 4],\n [0, 9, 2, 2],\n [2, 2, -8, -2],\n [4, 2, -2, -1]]\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 value at position (3, 3) rounded to the nearest integer?\n[[9, 6, -8, 3],\n [6, 4, -2, -2],\n [-8, -2, 0, -1],\n [3, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-22
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 1, -3, -6],\n [0, -1, 6, 5],\n [0, 0, 6, 3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[3, -10, -10, 12],\n [-2, -12, 1, 2],\n [-6, 6, 2, 2],\n [12, 9, -8, 5]]\nRound your answer to the nearest integer.\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 10, 3, 2],\n [10, 0, -6, 4],\n [3, -6, 2, -5],\n [2, 4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
478
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, 1, 8, -10],\n [1, -4, -11, -10],\n [8, -11, 2, 2],\n [-10, -10, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[6, 9, -4, -7],\n [1, 12, 3, 7],\n [-2, -2, 10, -10],\n [3, -8, -7, -1]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -6, -1, 9],\n [12, 1, 11, 7],\n [9, -3, 7, 11],\n [-3, 6, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
239
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[8, 10, 9, -10],\n [-7, -1, -9, 7],\n [-6, -5, 10, -8],\n [-6, -11, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
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, 7],\n [5, -2, 8, -4],\n [0, 8, 4, -8],\n [7, -4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-12, -4, 12, -2],\n [-4, 5, -1, 6],\n [12, -1, 6, -2],\n [-2, 6, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
619
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[[7, -2, -1, 8],\n [5, -7, -1, -11],\n [-2, 6, -8, 7],\n [2, 8, -5, -7]]\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 (1, 3) rounded to the nearest integer?\n[[-5, 4, 2, 11],\n [2, 12, -10, -7],\n [12, -4, -7, -7],\n [-6, -2, -6, -7]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, -10, 3, 8],\n [-6, -7, 5, 1],\n [-6, -12, -4, 10],\n [8, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-45
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, -2, -6, 12],\n [0, -11, -10, -2],\n [0, 0, -4, -3],\n [0, 0, 0, 11]]\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 value at position (3, 1) rounded to the nearest integer?\n[[8, -7, 12, 1],\n [0, -1, 8, 6],\n [0, 0, -8, -1],\n [0, 0, 0, 1]]\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[[9, -2, 6, 10],\n [0, 9, -7, 6],\n [0, 0, -4, 6],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[-6, -5, 8, 1],\n [0, 6, -3, -7],\n [0, 0, 4, 8],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 6, -1, 0],\n [11, 8, 9, 7],\n [-8, -10, 0, 7],\n [-10, -12, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
64
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[[-7, 5, 3, 6],\n [4, 3, -11, -5],\n [7, 0, 0, -3],\n [5, 0, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[10, -2, -4, 1],\n [-2, -4, 6, 3],\n [-4, 6, -7, -4],\n [1, 3, -4, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
381
MATH
[ { "content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[8, 1, -2, -10],\n [7, 8, -11, -3],\n [9, 2, 1, 7],\n [7, 5, 11, -1]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 2, 4, 2],\n [2, -6, -8, -3],\n [4, -8, -2, 8],\n [2, -3, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
124
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[2, -8, -6, 8],\n [5, 2, -4, -9],\n [5, -11, -9, 6],\n [7, -2, 3, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
319
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-12, 5, 4, 9],\n [0, -6, -8, -5],\n [0, 0, -12, 10],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-27
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -6, 12, 3],\n [9, 0, -11, 10],\n [-10, 11, -8, 11],\n [-7, 8, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
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, -5, 5, -4],\n [-5, 9, -3, 5],\n [5, -3, 0, 0],\n [-4, 5, 0, 9]]\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 6, 3, -3],\n [0, 5, -4, -9],\n [0, 0, 12, -11],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
190
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, 9, 3],\n [0, 3, -3, 2],\n [0, 0, 2, 10],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
563
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, -3, 1, -4],\n [-3, -1, -3, 3],\n [1, -3, -11, 0],\n [-4, 3, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
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, -10, -5],\n [0, -12, -12, -11],\n [0, 0, -7, -8],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-4, 12, 11, 10],\n [0, 11, -7, 6],\n [0, 0, 6, 7],\n [0, 0, 0, 12]]\nRound your answer to the nearest integer.\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 value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -6, 3, -7],\n [0, 10, 4, -7],\n [0, 0, 10, 7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-4
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[7, 0, -10, -8],\n [0, 8, -10, 3],\n [0, 0, 9, 3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[2, -10, -10, -3],\n [-11, -12, -1, -5],\n [10, -2, -5, -6],\n [-3, -2, -4, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-19
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-6, -6, -10, -2],\n [1, 8, 11, 5],\n [1, 3, -9, -1],\n [-10, 5, -2, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
59
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, -4, -2, -4],\n [-4, 9, 0, -2],\n [-2, 0, 3, 3],\n [-4, -2, 3, 10]]\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[[11, 7, 3, -12],\n [-8, 8, -2, -8],\n [-10, -6, 5, -1],\n [-2, 8, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4781
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, 4, 0, 8],\n [4, 6, 0, -4],\n [0, 0, 4, 6],\n [8, -4, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
202
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, 11, 5, -9],\n [0, 11, 9, -8],\n [0, 0, 1, 6],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
682
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[[-7, -8, 0, -8],\n [-8, -8, 6, 4],\n [0, 6, -3, 0],\n [-8, 4, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-4
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[0, 5, 11, -5],\n [-4, 11, -5, 11],\n [3, -6, -8, 3],\n [2, -1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -12, -2, 0],\n [-12, -4, -5, -5],\n [-2, -5, 6, 8],\n [0, -5, 8, 6]]\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[[9, 6, -2, -2],\n [6, -7, -4, -4],\n [-2, -4, 0, -1],\n [-2, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-495
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 7, 2, 9],\n [0, 10, -2, -6],\n [0, 0, -9, 11],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-83
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-1, 8, 5, 1],\n [0, -10, -5, 4],\n [0, 0, -8, -6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-127
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, -2, -5, 4],\n [0, -12, 3, -12],\n [0, 0, -1, -8],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -5, 5, 9],\n [3, 6, -5, 6],\n [-11, -2, 8, -9],\n [7, -10, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
455
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, -10, 7, 0],\n [0, 6, -10, -11],\n [-3, -5, 4, -1],\n [-1, -12, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, -1, 6, -7],\n [0, -2, 5, -3],\n [0, 0, -10, 9],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-36
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[[-10, -7, -5, 6],\n [0, -6, 6, -12],\n [0, 0, -9, 10],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
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[[-6, 0, -6, -1],\n [0, 4, -3, -9],\n [0, 0, -7, 9],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
309
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, 3, 0, -4],\n [0, 5, -10, 5],\n [0, 0, -11, 4],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[11, 1, 8, 10],\n [4, -11, 9, 7],\n [1, -4, 4, -3],\n [5, 12, -9, 3]]\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 value at position (4, 3) rounded to the nearest integer?\n[[-9, 5, 3, -6],\n [0, 9, 11, 0],\n [9, 11, -7, 6],\n [0, 3, 8, 2]]\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[[5, 8, -1, -5],\n [8, 3, -8, 8],\n [-1, -8, -11, 5],\n [-5, 8, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, 1, 12, -5],\n [0, 8, 9, -3],\n [0, 0, -1, 10],\n [0, 0, 0, -5]]\nRound your answer to the nearest integer.\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 at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 3, 9, 3],\n [0, 11, 4, -6],\n [0, 0, -2, -11],\n [0, 0, 0, -11]]\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[[-3, -11, 8, 7],\n [6, -7, 5, -2],\n [-6, -9, 4, -12],\n [-10, 2, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[3, -6, -11, 4],\n [-6, 7, -8, 4],\n [-11, -8, -10, -10],\n [4, 4, -10, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 6, -4, -7],\n [6, 1, -9, 3],\n [-4, -9, 0, -2],\n [-7, 3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-60
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, -1, 2, -12],\n [0, 4, -12, 0],\n [0, 0, -7, 11],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
53
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[[-1, -2, -4, -5],\n [0, 1, 8, -1],\n [0, 0, -6, 2],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-192
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, -11, -2, -6],\n [0, -10, 12, 5],\n [0, 0, 10, -4],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-188
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[0, -4, 9, -5],\n [-2, -3, 6, -1],\n [6, -7, 2, 9],\n [-9, -10, 2, -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 value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-8, -1, 3, -4],\n [-1, 2, -6, -2],\n [3, -6, -7, -3],\n [-4, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -5, -11, -6],\n [0, -6, -4, -10],\n [0, 0, -9, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 6, 10, -6],\n [6, -8, 5, -10],\n [10, 5, 12, -8],\n [-6, -10, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, 10, 8, 1],\n [11, -3, -6, -6],\n [10, 2, 6, -10],\n [-3, 6, -2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -2, -5, -7],\n [0, 2, -12, -7],\n [0, 0, 11, -1],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
413
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -7, -6, -5],\n [-7, 0, 8, -9],\n [-6, 8, -9, 0],\n [-5, -9, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
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, -6, 12, 4],\n [0, -1, 0, 12],\n [1, 3, 9, 8],\n [-8, -11, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 7, 0, -10],\n [12, -11, 3, 8],\n [7, 5, -1, 1],\n [4, -11, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, 3, 2, -2],\n [3, -7, 8, 2],\n [2, 8, -11, -1],\n [-2, 2, -1, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
860
MATH
[ { "content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[5, 0, -8, 3],\n [0, -12, -5, -12],\n [0, 0, 2, -12],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "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, 1, 4, 0],\n [1, -11, -1, -6],\n [4, -1, -9, 0],\n [0, -6, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
135
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, 9, -9, -4],\n [0, -6, -10, 1],\n [0, 0, 10, 3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
149
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, 4, 5, 11],\n [-5, -11, 9, -8],\n [0, -8, 3, -12],\n [-2, 0, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
102
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, 3, 11, 3],\n [0, -3, -12, 0],\n [0, 0, 5, 6],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-96
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -7, -6, -1],\n [0, -3, 11, 0],\n [0, 0, -11, -4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-33
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-3, -6, -5, 0],\n [-6, -1, 0, 2],\n [-5, 0, 10, -6],\n [0, 2, -6, 0]]\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 at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 0, 2, 2],\n [0, 6, -6, 0],\n [2, -6, -12, -2],\n [2, 0, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 1, 5, 9],\n [-1, -5, 10, 1],\n [8, -9, 10, -11],\n [-8, -9, 11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[-3, 7, 5, 6],\n [0, 8, -5, -3],\n [0, 0, -11, 0],\n [0, 0, 0, 11]]\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 value at position (2, 2) rounded to the nearest integer?\n[[9, -2, -11, 3],\n [-10, 9, -11, 3],\n [3, 9, -8, -5],\n [-8, 5, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -2, 8, 6],\n [10, -11, -8, -11],\n [11, 8, 6, -5],\n [1, 4, -10, 8]]\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, 2) rounded to the nearest integer?\n[[10, 7, 12, 0],\n [-2, 11, 1, -10],\n [-6, -2, 1, 9],\n [3, 1, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-4
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 10, -10, -9],\n [0, -5, 11, 1],\n [0, 0, 11, 2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-48
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-11, -2, 9, 8],\n [9, -10, 1, 2],\n [-6, -1, -10, 12],\n [-2, 5, -5, -10]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 4, -6, -6],\n [4, -8, 2, 0],\n [-6, 2, 11, 5],\n [-6, 0, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
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, -3, 8],\n [-9, -6, 10, 1],\n [1, 6, 0, -7],\n [-4, 6, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-103
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, -4, -4, 0],\n [9, -6, 9, -4],\n [-12, -8, 6, 3],\n [-6, 3, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
190
MATH