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[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[8, -5, -7],\n [-6, 6, -4],\n [4, -4, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
82
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-6, -3, -6],\n [-9, -4, 6],\n [5, -7, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[9, 0, 2],\n [0, 5, 6],\n [0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[-10, 7, 9],\n [-10, 7, -4],\n [-7, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 0, -10],\n [0, 1, 6],\n [-10, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
55
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[0, 2, 4],\n [2, 5, 4],\n [4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-330
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -6, 1],\n [-3, -9, -2],\n [-2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
-20
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 5, 6],\n [0, -8, 5],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your ...
23
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, 6, -4],\n [4, -10, -4],\n [-8, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
MATH
[ { "content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[-7, 2, -4],\n [7, 4, -6],\n [2, -1, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 8, -9],\n [4, -5, -2],\n [-9, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-59
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, -1, 6],\n [-1, 9, 10],\n [6, 10, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-3, -8, 10],\n [-8, 3, 2],\n [10, 2, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[1, -5, -5],\n [0, 10, -10],\n [0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, 0, 4],\n [0, 6, 5],\n [4, 5, -8]]\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 1/60 * A where A =\n[[4, -6, 10],\n [0, 9, 10],\n [0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 0, 0],\n [0, 3, 9],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
58
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 2, -4],\n [0, -9, -7],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
0
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[-9, 1, 2],\n [2, -6, 5],\n [7, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Find the inverse of 1/60 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[[-5, 0, -4],\n [0, 5, -3],\n [-4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
15
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-3, -5, -3],\n [-9, 4, 1],\n [-7, 7, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
61
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, -4, -5],\n [0, -4, 10],\n [-9, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -2, -4],\n [-2, 10, 0],\n [-4, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 5, -7],\n [-10, 2, -7],\n [0, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, 4, 0],\n [4, 6, 2],\n [0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[4, 9, -9],\n [0, 1, 1],\n [0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[0, -2, -6],\n [-2, 8, -4],\n [-6, -4, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -7, 3],\n [0, 5, -8],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, -10, -7],\n [-10, -9, 6],\n [-7, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-22
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-6, -8, -8],\n [0, 1, -8],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-80
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 9, 9],\n [-5, 9, -9],\n [-2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
-5
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, -2, 2],\n [0, 4, 9],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-54
MATH
[ { "content": "Find the inverse of 1/60 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, 3, 0],\n [0, 1, 8],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-1, 8, 8],\n [-6, 3, 1],\n [0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[2, -9, -8],\n [0, -7, 10],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-39
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, -9, -10],\n [-5, 0, -7],\n [4, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1093
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-3, 1, 1],\n [1, -10, 2],\n [1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-54
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, 1, 8],\n [1, 10, 8],\n [-1, 5, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
158
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-3, -4, -9],\n [-1, 8, 0],\n [-9, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[5, -4, -10],\n [-5, 0, 1],\n [3, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -6, 9],\n [0, -9, -5],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -9, -7],\n [0, -6, -9],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-10, 10, -4],\n [0, -9, -4],\n [0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Find the inverse of 1/60 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, -2, -8],\n [6, 8, 5],\n [-10, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 0, 5],\n [0, 2, -2],\n [5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
97
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, -8, 7],\n [-8, -2, -8],\n [7, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the inverse of 1/60 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, 6, 4],\n [6, -1, 2],\n [4, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the inverse of 1/60 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, -8, -6],\n [0, 5, 0],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
273
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-1, 2, 6],\n [0, -2, 7],\n [0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, -5, 2],\n [0, 5, 8],\n [0, 0, -10]]\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 1/60 * A where A =\n[[7, -8, -10],\n [7, 4, -3],\n [-4, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 7, 2],\n [7, -9, -4],\n [2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
21
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -1, -5],\n [-3, 5, -4],\n [4, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
-11
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 1, -10],\n [-2, 5, -6],\n [0, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
15
MATH
[ { "content": "Find the inverse of 1/60 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[[10, -5, -4],\n [-5, -8, 6],\n [-4, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
21
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -4, -9],\n [0, 3, 2],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
-50
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-10, 10, -6],\n [-10, -10, -2],\n [-8, 3, 9]]\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 1/60 * A where A =\n[[-7, 1, 6],\n [-7, 7, 1],\n [-5, 5, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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[[5, -7, 5],\n [0, -3, 4],\n [-5, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-5
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[6, -4, -5],\n [-4, -4, 0],\n [-5, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-4, 0, 0],\n [0, 1, 0],\n [0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Find the inverse of 1/60 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[[0, 7, -1],\n [-3, 3, 5],\n [7, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
14
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-4, 2, -7],\n [8, -3, 2],\n [-1, -7, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the inverse of 1/60 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, 5, 6],\n [0, -10, -10],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[-1, -1, -3],\n [0, -6, 4],\n [0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -2, 1],\n [-2, -7, -7],\n [1, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed...
-22
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 1, -9],\n [0, 7, 10],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your...
-45
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, -6, -5],\n [0, 10, -1],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-3, -4, -2],\n [-4, 0, 2],\n [-2, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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[[-4, -8, 4],\n [-8, 3, 2],\n [4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
-4
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, -4, -2],\n [-4, 10, -3],\n [-2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed...
28
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 6, -4],\n [6, 7, -6],\n [-4, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{You...
69
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, -9, -10],\n [-4, -10, -2],\n [2, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-33
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, -6, 10],\n [0, -7, -1],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-3, -5, -5],\n [-6, 6, 4],\n [-7, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 2, 3],\n [2, -9, -2],\n [3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
-1
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[5, -7, -8],\n [-4, 5, -7],\n [8, -6, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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[[-3, 10, -8],\n [-9, 2, 2],\n [9, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
18
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[4, 9, -3],\n [8, 6, 1],\n [10, 2, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
985
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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[[5, -9, 8],\n [0, 6, 5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your a...
-46
MATH
[ { "content": "Find the inverse of 1/60 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, 6, 1],\n [0, 2, 3],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
248
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[2, -7, 5],\n [7, 8, -7],\n [0, 9, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[5, -5, -3],\n [-5, -8, 7],\n [-3, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-6
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, -4, -2],\n [8, 4, -8],\n [10, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
45
MATH
[ { "content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[8, 0, 5],\n [0, -8, -8],\n [0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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[[-9, -2, 6],\n [-2, -8, 4],\n [6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
-7
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 10, 6],\n [1, 6, 3],\n [-7, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[7, -5, 5],\n [10, -7, 8],\n [-6, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[3, -2, -7],\n [-2, -3, -4],\n [-7, -4, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-72
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, 6, 5],\n [0, 2, 1],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-2, -1, -6],\n [-8, 9, -1],\n [6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -9, -4],\n [-9, 10, -7],\n [-4, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -4, -5],\n [0, -4, 9],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
-2
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-3, -4, 4],\n [-4, 10, -6],\n [4, -6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
47
MATH
[ { "content": "Calculate the inverse matrix of 1/60 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, 6, 8],\n [-9, -1, 6],\n [-6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
5
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-2, -8, 4],\n [0, 8, -8],\n [0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-9, -3, -1],\n [0, -1, -6],\n [0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-72
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[8, 6, 1],\n [6, -6, 7],\n [1, 7, 3]]\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 1/60 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[6, -9, 0],\n [0, -6, 0],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-15
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -10, 0],\n [-7, -7, -5],\n [7, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-10
MATH