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[ { "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[[12, 1, 9, 5],\n [-1, 12, -9, 0],\n [-2, -3, -2, -8],\n [10, -7, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
79
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[[-10, -10, -6, 2],\n [-5, -12, -4, 0],\n [2, 10, 7, -6],\n [-3, -12, 11, 0]]\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 value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[4, 2, 8, 7],\n [0, -4, -10, 3],\n [0, 0, -12, -4],\n [0, 0, 0, -10]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 10, -9, 9],\n [0, 1, 5, 2],\n [0, 0, -7, 4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -4, 10, -1],\n [0, -3, -10, 1],\n [0, 0, -3, 10],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
493
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, 10, -4, -7],\n [0, -2, 2, 10],\n [0, 0, -4, -11],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-53
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[[-3, 10, -2, -2],\n [-8, -7, 1, 3],\n [-12, -5, -12, 11],\n [0, 0, -10, 0]]\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 value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -10, 2, -10],\n [0, -4, -11, 5],\n [0, 0, -2, 0],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
132
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, 0, 2, -6],\n [0, 9, 1, 4],\n [2, 1, -4, -2],\n [-6, 4, -2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
108
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -9, -2, -12],\n [0, -11, 9, -1],\n [0, 0, -7, -7],\n [0, 0, 0, -7]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 10, -1, 4],\n [0, 8, -8, -6],\n [0, 0, -12, 9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
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[[10, 9, 7, -10],\n [-8, 11, 11, 8],\n [-11, 3, 6, 5],\n [4, 10, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
137
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, -7, 7, -2],\n [0, 8, -1, 9],\n [0, 0, 3, 5],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
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, -10, 10],\n [0, 9, -11, 1],\n [0, 0, -3, -5],\n [0, 0, 0, 9]]\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[[-7, -3, -7, -7],\n [-3, 3, 2, 4],\n [-7, 2, -3, 6],\n [-7, 4, 6, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, 3, -1, -1],\n [0, -6, 8, 2],\n [0, 0, -10, 0],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[5, 6, 9, 12],\n [1, 7, -2, 10],\n [2, -2, 1, -10],\n [-1, 9, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-3, -1, 4, -9],\n [6, 0, 4, 11],\n [1, 4, 2, -3],\n [4, -10, -4, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
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[[-11, 7, 9, 0],\n [0, -7, -6, 5],\n [0, 0, 6, 11],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
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, -8, -9, 0],\n [-8, 11, 1, -4],\n [-9, 1, -4, -2],\n [0, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, -7, 7, 11],\n [2, -7, -8, 6],\n [7, -6, 3, -4],\n [-10, 8, 2, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
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, 3],\n [0, 11, 7, -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" } ]
310
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, 4, 7, 10],\n [0, 10, 5, -12],\n [0, 0, 12, 4],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 6, -11, 3],\n [-2, -11, 3, -1],\n [2, 10, 7, 4],\n [8, 7, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-185
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 10, 8, -7],\n [1, 2, 3, 12],\n [3, -10, -11, 4],\n [7, 11, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
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, 10, 0, 6],\n [10, 12, -7, 4],\n [0, -7, 8, 4],\n [6, 4, 4, 3]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 11, 3, -7],\n [-12, -12, 1, 12],\n [9, -1, -9, 5],\n [2, -10, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[-8, 7, 9, -10],\n [0, 2, 9, -12],\n [0, 0, -10, -8],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\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 value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 1, -4, 6],\n [1, -7, 6, -2],\n [-4, 6, -11, 7],\n [6, -2, 7, -11]]\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 absolute values of all entries rounded to the nearest integer?\n[[-11, -11, -8, 2],\n [0, 7, 1, -2],\n [0, 0, 8, 11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
171
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, 10, 2, 3],\n [10, 4, 2, -4],\n [2, 2, 12, 6],\n [3, -4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-288
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, -7, 11, 0],\n [9, 10, 9, -2],\n [-5, -11, 10, -2],\n [-9, -11, -2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
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, 11, 11, -3],\n [-2, -10, -4, 11],\n [9, 9, -6, 0],\n [6, -3, 7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
65
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, 5, -8, -10],\n [5, 5, 8, -4],\n [-8, 8, 4, 10],\n [-10, -4, 10, 3]]\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 at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[-11, 2, 9, 4],\n [0, 7, -6, -6],\n [0, 0, 2, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 5, 0, -2],\n [5, 1, -1, 11],\n [0, -1, 0, -8],\n [-2, 11, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
276
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, -11, -12, -2],\n [-9, -8, 10, 8],\n [7, 5, 0, -3],\n [11, -11, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-2, -4, 1, -1],\n [-4, -5, 1, 2],\n [1, 1, 8, -6],\n [-1, 2, -6, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[0, -4, -6, 3],\n [-9, -11, 4, 11],\n [4, -9, -6, -3],\n [-9, -3, -2, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
61
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, 8, 6, -11],\n [2, -6, 4, 1],\n [4, 8, 3, 2],\n [2, 5, 9, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-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[[6, -1, -12, 11],\n [0, -7, -1, 5],\n [0, 0, 2, 2],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, 0, 2, -3],\n [-9, -9, 9, 12],\n [-2, -2, -8, -6],\n [-2, 2, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, 7, -11, 2],\n [0, -8, -9, 9],\n [0, 0, -8, 9],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, -4, 6, -3],\n [-4, -3, -1, 4],\n [6, -1, 12, 0],\n [-3, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
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[[-7, -4, 5, -9],\n [0, -11, 9, 9],\n [0, 0, -2, -5],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-3, 6, -3, -6],\n [6, -11, 6, -7],\n [-3, 6, 7, 5],\n [-6, -7, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
MATH
[ { "content": "Find the value at position (2, 3) of the inverse of matrix 1/96 * A where A =\n[[1, 0, -5, 0],\n [0, -3, -8, 2],\n [-5, -8, -2, -1],\n [0, 2, -1, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, -8, -4, -2],\n [-8, -1, 5, -12],\n [-4, 5, 4, -1],\n [-2, -12, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-112
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-7, 7, 5, 8],\n [0, -6, -10, -5],\n [0, 0, -4, 2],\n [0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
293
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, -5, 10, -3],\n [-5, -2, 11, 12],\n [3, 9, -10, 4],\n [11, -7, 10, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
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, -10, -10, -11],\n [9, -4, 7, 4],\n [-8, 12, -1, -7],\n [3, 7, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
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, 1, -11, 8],\n [-9, 3, -5, -10],\n [-6, -6, -1, -5],\n [1, 0, -6, -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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -11, -9, 3],\n [-1, 1, 8, -2],\n [10, 9, 12, 6],\n [-12, 0, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-4, 6, 1, -3],\n [0, -5, -9, -10],\n [0, 0, -6, 10],\n [0, 0, 0, -3]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, 7, 4, 5],\n [-7, -1, 6, 4],\n [-1, 1, -10, 2],\n [5, 11, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -4, -6, 3],\n [-4, 1, 2, -10],\n [-6, 2, 10, -4],\n [3, -10, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
107
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 1, -6, 2],\n [1, 0, 12, 2],\n [-6, 12, 12, 12],\n [2, 2, 12, 0]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -12, 1, -9],\n [0, 10, 11, 11],\n [7, -11, -12, 10],\n [0, -5, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-545
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, 11, -7, -10],\n [8, 10, 5, -2],\n [-12, 8, 4, 3],\n [1, -2, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
258
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, 0, -6, -2],\n [0, -7, -10, 5],\n [-6, -10, -9, -4],\n [-2, 5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-1, -6, -4, 2],\n [-6, 7, 0, -4],\n [-4, 0, 11, -6],\n [2, -4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-15
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[[-3, -1, 2, 4],\n [0, 7, -7, 2],\n [0, 0, -10, -7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-41
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[[5, -6, -11, 6],\n [0, 9, 9, -12],\n [0, 0, -4, -1],\n [0, 0, 0, 9]]\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[[12, -1, 8, 7],\n [-7, -12, 5, 12],\n [-3, -1, 12, -3],\n [-9, 12, 3, 1]]\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 at position (1, 3) rounded to the nearest integer?\n[[5, -9, -7, -9],\n [0, 2, 0, 3],\n [0, 0, -7, -12],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-19
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, 4, -7, -8],\n [0, -4, 10, 11],\n [0, 0, -5, -10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
195
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[[-10, -3, -2, 2],\n [-3, -11, 2, -4],\n [-2, 2, 12, -6],\n [2, -4, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
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[[-1, -3, -6, 5],\n [0, -6, 12, 11],\n [0, 0, 9, -11],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-299
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, -4, -6, -12],\n [0, 10, -1, -9],\n [0, 0, -4, -3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-158
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-9, -11, 0, 8],\n [3, -2, -5, 0],\n [1, 3, -3, -4],\n [11, -9, -4, -9]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, 9, 0, -2],\n [0, 11, 3, 7],\n [-4, -6, -9, 4],\n [3, 5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
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, -4, -6, -3],\n [0, -10, 11, -12],\n [0, 0, 9, -10],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-15
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, -8, -5, -3],\n [0, -7, -12, -2],\n [0, 0, 4, 5],\n [0, 0, 0, 7]]\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[[7, -7, -4, -11],\n [0, -5, 4, 7],\n [0, 0, 1, -5],\n [0, 0, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
99
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, 2, 8],\n [2, -2, -6, -6],\n [2, -6, -12, -6],\n [8, -6, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-257
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 6, 2, 2],\n [6, -6, -6, -2],\n [2, -6, 12, 0],\n [2, -2, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
MATH
[ { "content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[9, -4, 3, -5],\n [-4, 10, -8, 4],\n [3, -8, -6, -8],\n [-5, 4, -8, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, 6, -2, 6],\n [6, 7, 0, -7],\n [-2, 0, -11, -4],\n [6, -7, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
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[[-11, -11, 7, 7],\n [0, 2, -11, 0],\n [0, 0, 3, -8],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-244
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, -12, 1, 4],\n [0, -2, 1, -4],\n [0, 0, 9, -7],\n [0, 0, 0, 4]]\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[[-9, -12, 1, -4],\n [0, -2, 12, 7],\n [0, 0, 1, 6],\n [0, 0, 0, 5]]\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 (1, 3) of the inverse. Round your answer to the nearest integer:\n[[-11, 9, -12, 12],\n [-6, 6, 3, -3],\n [-7, 1, 0, -10],\n [2, -9, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3
MATH
[ { "content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -7, -2, -4],\n [-7, -2, 6, 2],\n [-2, 6, -4, 0],\n [-4, 2, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1288
MATH
[ { "content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[5, -4, 4, -4],\n [-4, -10, 4, 2],\n [4, 4, -10, -8],\n [-4, 2, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-51
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[4, -5, 0, 10],\n [0, 11, 9, -2],\n [0, 0, -2, 9],\n [0, 0, 0, -6]]\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 absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 6, 2, -5],\n [-7, 12, -11, -1],\n [-7, 10, -6, -3],\n [3, 9, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
509
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, 11, 6, -9],\n [0, 8, 11, 6],\n [0, 0, 12, -6],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
299
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, -10, -6, -8],\n [0, -5, 1, 8],\n [0, -5, 0, 9],\n [-8, -4, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
64
MATH
[ { "content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[-12, 7, -6, 7],\n [-2, -7, -11, 5],\n [-5, -5, -3, -4],\n [-5, 6, -11, -1]]\nRound your answer to the nearest integer.\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 value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -10, 8, 6],\n [-1, 10, 10, -9],\n [-5, 10, -12, -11],\n [5, 6, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[7, -6, -2, 9],\n [0, 1, 7, -6],\n [0, 0, 1, -4],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-501
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[[5, -7, -10, 11],\n [0, -7, 3, 11],\n [0, 0, 4, 7],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 4, 2, 4],\n [4, 9, -4, 0],\n [2, -4, 5, 0],\n [4, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
131
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, 11, 1, -6],\n [0, 12, -9, -3],\n [0, 0, 9, 2],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 4, 0, -8],\n [4, 6, -2, 0],\n [0, -2, 4, 8],\n [-8, 0, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
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, 12, -8, 0],\n [12, 1, 2, -8],\n [-8, 2, -6, 2],\n [0, -8, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-61
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-4, 0, 3, -1],\n [0, 9, -4, 5],\n [3, -4, -3, 6],\n [-1, 5, 6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
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, -12, 6, -1],\n [7, -3, 4, 12],\n [9, 12, 6, -10],\n [0, 12, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[12, 5, 2, 0],\n [5, 4, 8, 4],\n [2, 8, -11, -2],\n [0, 4, -2, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
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, 10, -2],\n [0, -6, 1, 4],\n [10, 1, -9, 4],\n [-2, 4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
73
MATH