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[ { "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, -1],\n [1, -1, 4],\n [-5, 9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
379
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, -2, -1],\n [0, -6, 0],\n [0, 0, 4]]\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[[8, 0, 4],\n [0, -8, -2],\n [4, -2, -4]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-2, 1, 8],\n [1, 0, -3],\n [8, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
260
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, -9, 8],\n [-6, 10, 8],\n [8, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-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[[4, 2, -4],\n [2, 7, 0],\n [-4, 0, -3]]\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 at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -2, -1],\n [-2, -4, 3],\n [-1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
5
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[10, 2, 5],\n [-1, -9, -3],\n [9, -6, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
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, 3, -6],\n [3, -6, 6],\n [-6, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
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[[4, 1, -5],\n [1, -7, 6],\n [-5, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Find the value at position (1, 3) of the inverse of matrix 1/60 * A where A =\n[[1, 8, -9],\n [-3, 1, -2],\n [2, 9, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
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, -1, -2],\n [0, -7, -10],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
4
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[[-9, 10, -1],\n [-5, -1, -3],\n [-7, 4, -10]]\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[[9, -4, 10],\n [-4, -1, -9],\n [10, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-50
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[[0, 0, 2],\n [0, 10, 0],\n [2, 0, 4]]\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 value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[4, 2, -2],\n [2, -3, 2],\n [-2, 2, 3]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 6, -3],\n [0, 2, 10],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{You...
660
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, -2, -8],\n [0, -3, -2],\n [0, 0, -8]]\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[[-10, -6, -6],\n [-3, -7, -9],\n [4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "Find the value at position (3, 2) of the inverse of matrix 1/60 * A where A =\n[[-1, 5, 3],\n [0, 2, 0],\n [0, 0, -3]]\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 1/60 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[5, -9, -5],\n [1, -4, -10],\n [-4, -3, 1]]\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[[9, 5, 10],\n [9, 4, -1],\n [6, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
3
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/60 * A where A =\n[[-4, 4, 5],\n [-7, 0, -3],\n [-4, 3, -7]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, -2, 7],\n [-2, 6, 0],\n [7, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[-9, -2, 6],\n [-2, -3, 6],\n [6, 6, 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[[-3, 1, -5],\n [0, 3, -5],\n [0, 0, 5]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -9, 6],\n [0, 8, -8],\n [0, 0, 10]]\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[[-4, -1, 2],\n [-1, -3, 4],\n [2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
31
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[[6, 0, 4],\n [0, 3, 4],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
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[[-7, -7, -1],\n [-4, 4, 8],\n [-7, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
162
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-6, 8, -7],\n [0, 3, 9],\n [0, 0, 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 trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[5, 1, 2],\n [1, 6, -2],\n [2, -2, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
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[[7, 0, 0],\n [0, -1, 0],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/60 * A where A =\n[[-4, 8, 6],\n [8, 7, -6],\n [6, -6, 7]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -8, -8],\n [0, -4, 10],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
41
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[[10, 5, -10],\n [-8, -4, -6],\n [9, 0, -10]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 8, -2],\n [8, 5, -2],\n [-2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7
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, 1, -7],\n [8, -10, 8],\n [-5, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
249
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-5, -6, -3],\n [-6, 5, 0],\n [-3, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-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[[10, -3, -1],\n [-3, 2, -6],\n [-1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-14
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, 0, -9],\n [7, -2, -2],\n [-4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
4
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, -10, -4],\n [0, 9, 4],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-7
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[[-7, 1, -2],\n [0, -3, 7],\n [0, 0, -5]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[2, -6, 10],\n [0, -6, -1],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
270
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[[5, 3, 2],\n [-1, 4, 0],\n [0, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
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[[8, 6, 8],\n [6, -2, 7],\n [8, 7, 5]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[3, 0, 3],\n [2, 5, -8],\n [4, -6, 1]]\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[[5, -3, 1],\n [0, -5, 6],\n [0, 0, 3]]\nRound your answer to the nearest integer.\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 all entries rounded to the nearest integer?\n[[2, -6, 3],\n [0, 1, -5],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-315
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, -2, 10],\n [0, -3, -2],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[7, 5, -3],\n [10, 2, 8],\n [-9, -3, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
66
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[5, 3, -1],\n [0, 6, -5],\n [0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
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[[-4, -5, -1],\n [0, -7, -5],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
105
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-2, -10, 6],\n [0, 7, 4],\n [-2, -7, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
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, 10, -6],\n [0, -9, 1],\n [0, 0, 10]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, -3, 3],\n [-3, 2, -2],\n [3, -2, -8]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 5, -2],\n [0, -5, 10],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-20
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, 4, 0],\n [0, 3, 9],\n [0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-360
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[2, -4, 0],\n [-4, 9, 2],\n [0, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[4, -8, 7],\n [6, 1, -9],\n [8, 9, 4]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 7, 0],\n [0, -8, 2],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
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, 7],\n [0, 7, -9],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
-11
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[[-3, -9, 10],\n [0, -6, -6],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
42
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[[-9, 9, -8],\n [-4, -1, -6],\n [-1, -9, 7]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -2, 1],\n [-2, 7, -5],\n [1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
-109
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[[3, 5, -9],\n [10, 0, -10],\n [-2, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
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[[8, -3, 0],\n [0, -5, -10],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
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[[-9, 2, 7],\n [2, -7, 8],\n [7, 8, -3]]\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[[-4, -2, 6],\n [-2, -4, -1],\n [6, -1, 5]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, 1, 4],\n [1, 9, 9],\n [4, 9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
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[[-8, 4, 5],\n [-3, 8, -1],\n [-6, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
2
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[[-2, 7, 2],\n [0, -7, 6],\n [0, 0, 7]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[7, -3, 9],\n [0, 9, -2],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
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, 4, -3],\n [4, 8, -4],\n [-3, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-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[[-5, 3, 8],\n [3, -6, 0],\n [8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your...
10
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, -5, -1],\n [0, -7, 9],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-74
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[[7, 0, -2],\n [0, 0, 7],\n [-2, 7, 2]]\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 value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 0, 1],\n [0, 2, -2],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
0
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[[-6, -2, -3],\n [1, -2, 9],\n [-5, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Y...
28
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, 2, 0],\n [2, 5, -2],\n [0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
56
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, 6],\n [8, -7, 4],\n [6, 4, -2]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[9, -10, -7],\n [0, 6, 6],\n [0, 0, 8]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[7, -6, -2],\n [0, 7, -9],\n [0, 0, 3]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -2, -1],\n [-2, -1, 10],\n [-1, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
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, -9, 10],\n [0, -2, 10],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
694
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-6, -7, 9],\n [0, -9, -5],\n [0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
61
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[[-5, 2, -9],\n [10, 7, -6],\n [-7, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
44
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[[3, 7, 10],\n [0, 7, 2],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[0, 1, 6],\n [1, 8, -6],\n [6, -6, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
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, -4, 8],\n [-4, -10, 2],\n [8, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
-8
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[[1, -4, 2],\n [-4, 8, -2],\n [2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
257
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-5, 4, 5],\n [8, 1, -5],\n [4, 10, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
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[[-6, -7, -6],\n [-7, 9, 2],\n [-6, 2, -2]]\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 at position (3, 2) rounded to the nearest integer?\n[[-3, 5, 8],\n [0, -10, -5],\n [0, 0, -5]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 10, 6],\n [0, -2, -7],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-237
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, 4, 4],\n [2, -10, -4],\n [-2, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
20
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[[-1, 10, -6],\n [-3, -3, 6],\n [-1, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-35
MATH
[ { "content": "For the inverse of 1/60 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[8, -4, -4],\n [-4, 6, 2],\n [-4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
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, -4, 2],\n [-3, 7, 2],\n [-10, 5, 9]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 9, -3],\n [0, 1, 9],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
340
MATH