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[ { "content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[-9, 1, 8],\n [0, -5, 6],\n [0, 0, -4]]\nRound your answer to the nearest integer.\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[[9, -4, -1],\n [7, -6, -8],\n [5, -6, -3]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 8, 1],\n [-7, 8, -7],\n [0, -3, 5]]\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[[-6, -8, 6],\n [-8, 0, -9],\n [6, -9, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-9
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/60 * A where A =\n[[8, 3, 6],\n [0, 6, 9],\n [0, 0, 9]]\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 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, -2, -2],\n [-1, -4, 8],\n [7, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/60 * A where A =\n[[6, 1, 7],\n [0, -3, -4],\n [0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
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[[-2, 8, 4],\n [-2, 6, 0],\n [7, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
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[[-2, -6, 10],\n [0, 4, 4],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12
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[[-5, -4, -5],\n [0, -3, 0],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-20
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-8, 2, -2],\n [2, 7, 6],\n [-2, 6, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-28
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[10, -1, -2],\n [10, 7, 8],\n [2, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
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[[0, 1, 7],\n [8, -7, -6],\n [-2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the value at position (3, 1) of the inverse of matrix 1/60 * A where A =\n[[1, -9, 7],\n [0, 8, 10],\n [0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[-8, 1, 5],\n [3, 10, -8],\n [1, 0, -6]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 4, 7],\n [0, 9, 0],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
11
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[6, -6, -2],\n [7, 8, -8],\n [-3, -6, -5]]\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 (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 6, 6],\n [6, 9, -2],\n [6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
7
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[8, 0, -4],\n [-8, -4, -6],\n [6, -6, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
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[[-10, 6, -6],\n [-1, 6, -7],\n [-9, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
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[[-3, -3, 4],\n [-3, 4, 6],\n [4, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
-11
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-7, -5, -3],\n [0, -7, -6],\n [0, 0, 6]]\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 1/60 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, -6],\n [-9, 2, 2],\n [-6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-19
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[[-10, 2, -2],\n [2, -7, -2],\n [-2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
570
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-4, -6, 3],\n [0, 4, 7],\n [0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-38
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[[-1, 5, 10],\n [0, -4, -1],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
-75
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[[0, -4, -1],\n [-4, 5, -6],\n [-1, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Y...
-13
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-10, 2, -2],\n [2, 6, 2],\n [-2, 2, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[0, -2, 4],\n [-2, 8, 4],\n [4, 4, -1]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, -2, -10],\n [0, -5, -6],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-12
MATH
[ { "content": "Find the value at position (1, 1) of the inverse of matrix 1/60 * A where A =\n[[1, -1, -7],\n [0, 4, 4],\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 value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[6, 6, 8],\n [6, -4, -6],\n [8, -6, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-4, 0, 4],\n [0, 5, -10],\n [0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-33
MATH
[ { "content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 2, 2],\n [2, 7, 2],\n [2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-15
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[[-2, -8, 0],\n [-8, 10, 0],\n [0, 0, 5]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -2, -1],\n [-9, -3, -3],\n [-6, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
-200
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[[4, 6, 4],\n [-9, 5, -5],\n [-10, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
151
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[[4, -4, 8],\n [-4, -10, -4],\n [8, -4, -9]]\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 1/60 * A where A =\n[[-8, -7, 0],\n [-5, 1, -10],\n [0, 7, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
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, 2, 4],\n [2, -1, 5],\n [4, 5, 6]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, 4, -2],\n [4, 1, 4],\n [-2, 4, 3]]\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, 1) rounded to the nearest integer?\n[[5, -10, 0],\n [5, 10, 9],\n [2, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
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, -6],\n [-9, 8, -1],\n [-6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
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, -1, -4],\n [-1, 2, -1],\n [-4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
147
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[[1, -2, 10],\n [0, 10, 8],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
346
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[[10, 7, -3],\n [0, 10, -2],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-8, -5, -1],\n [10, 10, -1],\n [7, 10, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-28
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[[-2, -10, 0],\n [0, 3, 8],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-18
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[[-8, -6, -6],\n [-6, -5, -8],\n [-6, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-45
MATH
[ { "content": "Find the value at position (1, 1) of the inverse of matrix 1/60 * A where A =\n[[-3, -10, -8],\n [-6, 6, 5],\n [6, -5, -7]]\nRound your answer to the nearest integer.\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -5, 0],\n [-5, -8, 1],\n [0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
600
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[[8, 0, -2],\n [0, -4, 4],\n [-2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-255
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, -2, 9],\n [-2, -8, -3],\n [9, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-11
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[[-9, -6, -1],\n [0, -9, -5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
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[[1, -10, -8],\n [7, 6, -5],\n [-4, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[1, -10, 1],\n [2, -10, -3],\n [-6, -2, -7]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, 6, -7],\n [3, 9, 7],\n [-3, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10
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, -6, 4],\n [-1, -3, -1],\n [3, -10, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-34
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[[6, -8, 4],\n [-7, 4, -9],\n [5, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
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[[-8, -1, 4],\n [-1, 8, -6],\n [4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
-9
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, 1, -4],\n [7, 9, -5],\n [-9, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{You...
-8
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, 1, -9],\n [-6, -2, -2],\n [-5, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-1
MATH
[ { "content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[-4, 7, 6],\n [-8, -1, 3],\n [-5, 7, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-5, 10, -2],\n [0, -6, -10],\n [0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
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, 6, -2],\n [0, 2, 8],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-1, 3, -1],\n [0, -10, -5],\n [0, 0, -3]]\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 (1, 3) rounded to the nearest integer?\n[[-4, 0, 2],\n [0, 6, -2],\n [2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[5, 1, 0],\n [1, -9, 6],\n [0, 6, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-8, -8, -10],\n [0, 7, 5],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
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, -5, -3],\n [-6, 0, -6],\n [-10, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-35
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, 6, 5],\n [6, 3, 4],\n [5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[8, 8, 2],\n [0, -5, -5],\n [0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
73
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, -9, -3],\n [9, -3, 2],\n [8, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
672
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[[-6, 6, -4],\n [-4, 7, -4],\n [-1, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
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, -2, -8],\n [0, 10, -9],\n [0, 0, -8]]\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 at position (3, 2) rounded to the nearest integer?\n[[1, 4, 8],\n [3, -4, 5],\n [-6, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "Find the value at position (2, 3) of the inverse of matrix 1/60 * A where A =\n[[0, -2, 5],\n [-2, 1, -2],\n [5, -2, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
67
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[-10, -3, 8],\n [2, -5, -1],\n [-2, 4, -8]]\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[[-2, 7, -10],\n [10, -10, -1],\n [3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"...
30
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, -9, 2],\n [-3, -8, 0],\n [10, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-35
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, -9, 8],\n [0, 5, -4],\n [0, 0, 2]]\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 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, 8, 3],\n [0, 10, -1],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-20
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, 0, 2],\n [0, -8, -6],\n [2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
97
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, 2, -4],\n [2, -5, 6],\n [-4, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-44
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[1, 8, -9],\n [0, -9, -7],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12
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, -6, 9],\n [-2, -6, -10],\n [-8, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
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[[-6, 3, -9],\n [0, -3, -4],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-130
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-7, -1, -7],\n [-1, 5, 2],\n [-7, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
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, 0, -4],\n [-4, 5, -10],\n [-9, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-141
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, 2, 6],\n [0, 3, -10],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{You...
-33
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, 6, 2],\n [6, -8, 4],\n [2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[5, 6, -1],\n [0, 3, 10],\n [0, 0, -9]]\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 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-10, -4, 2],\n [-4, 4, -9],\n [2, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
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[[2, -6, 8],\n [-6, 7, -6],\n [8, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-136
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[[-4, 2, 4],\n [2, 9, 4],\n [4, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-5
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, 3, 6],\n [3, -3, 4],\n [6, 4, 8]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[0, -8, -7],\n [9, -4, -6],\n [8, 0, 4]]\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 value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -5, 1],\n [0, 4, -4],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
9
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, -7, -7],\n [0, -10, 2],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
62
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[7, -7, 7],\n [-7, 5, -6],\n [7, -6, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26
MATH