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[ { "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, 0],\n [8, -3, 4],\n [0, 4, -2]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 0, 1],\n [0, 8, -4],\n [0, 0, -2]]\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, -4, -8],\n [0, 5, -4],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
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, 8],\n [-8, 2, -6],\n [10, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
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, -2, 2],\n [-2, -7, -4],\n [2, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
53
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, -8, 0],\n [0, 5, -4],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
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, -5, -9],\n [0, 6, 8],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your...
-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[[-4, -7, -9],\n [0, -8, 7],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32
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, -3, 7],\n [-7, 9, -2],\n [10, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{You...
9
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, -4, -5],\n [-4, -2, 3],\n [-5, 3, -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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -3, -7],\n [0, 4, 9],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
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[[2, 0, 7],\n [9, -9, 10],\n [-7, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
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, -7, 1],\n [10, 2, 7],\n [-4, -5, 5]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 9, 3],\n [-2, 3, 10],\n [-10, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
5
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, -9, -2],\n [5, 9, -1],\n [-9, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
-57
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, 9, -7],\n [0, -5, -5],\n [0, 0, 7]]\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 absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 2, 2],\n [2, -5, 8],\n [2, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
63
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[[-9, 1, 4],\n [1, 6, 4],\n [4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
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[[-2, 2, -10],\n [-4, -4, 8],\n [-9, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
-22
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, 0, 4],\n [0, -5, 4],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-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[[-4, 4, -3],\n [4, 3, 1],\n [-3, 1, 5]]\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[[1, -6, 9],\n [-9, -10, 5],\n [-7, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[4, -4, 3],\n [-4, 4, 3],\n [3, 3, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-20
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[6, 5, -7],\n [5, 6, 2],\n [-7, 2, 7]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, 10, -2],\n [-8, -3, 0],\n [3, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[1, 0, 3],\n [0, 6, -6],\n [0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
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[[-3, 3, -5],\n [3, 0, -8],\n [-5, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
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, 6, -9],\n [0, 9, 4],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
162
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[[10, -4, 9],\n [-1, -6, -3],\n [4, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
46
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, -4, 1],\n [-9, -1, -8],\n [6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
76
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[[-5, -4, -1],\n [0, 2, 3],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-60
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[0, 1, 4],\n [-6, -10, 2],\n [4, -4, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
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[[-1, -7, -2],\n [-7, -10, -1],\n [-2, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[7, 4, -6],\n [4, -1, 2],\n [-6, 2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[8, -1, -2],\n [-1, 1, 3],\n [-2, 3, 7]]\nRound your answer to the nearest integer.\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[[1, 2, -9],\n [-10, 5, -7],\n [4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
74
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, 10, 2],\n [3, -2, -8],\n [9, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
10
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[[6, -6, 0],\n [-6, 4, -1],\n [0, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-61
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, -3],\n [-3, -1, 4],\n [-1, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-149
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, 0, -6],\n [0, 2, 1],\n [-6, 1, 2]]\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 value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-9, -4, -7],\n [0, -8, 6],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-6, -4, -10],\n [0, 5, -1],\n [0, 0, -7]]\nRound your answer to the nearest integer.\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 at position (3, 1) rounded to the nearest integer?\n[[-4, 2, 2],\n [2, -3, 4],\n [2, 4, -9]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -6, 3],\n [0, -5, 0],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-6, -8, 5],\n [0, 7, -10],\n [0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
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, 0],\n [0, 4, 3],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
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[[-4, 6, 1],\n [6, -9, 0],\n [1, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
40
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[7, 2, -2],\n [2, -6, 3],\n [5, -2, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[9, -4, 2],\n [-4, -5, 6],\n [2, 6, 0]]\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 at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[3, -2, 4],\n [-2, 7, -5],\n [4, -5, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-9, -2, -2],\n [-2, -3, 1],\n [-2, 1, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-41
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, 0, 2],\n [0, -10, 2],\n [2, 2, 2]]\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[[10, 8, -1],\n [0, -7, -10],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-9, -1, 9],\n [3, -1, 10],\n [4, -10, -5]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[7, 4, -7],\n [0, -1, -7],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-420
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[[-6, -9, -2],\n [5, -9, -5],\n [-7, 7, 6]]\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 value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 2, 4],\n [2, -8, 0],\n [4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
12
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[[-1, -10, 9],\n [0, -3, 7],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
6
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[6, -7, -3],\n [-7, -7, 1],\n [-3, 1, -4]]\nRound your answer to the nearest integer.\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[[-9, -1, 7],\n [0, -6, -1],\n [0, 0, 4]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, 2, -7],\n [2, 10, 5],\n [-7, 5, 1]]\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[[-8, -6, 7],\n [9, -6, -10],\n [-5, -6, 1]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[0, 0, -3],\n [-3, 7, -7],\n [5, -2, 9]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 3, 2],\n [0, -5, 3],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
-8
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[9, 6, -5],\n [0, 5, -5],\n [0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[4, -10, 8],\n [0, -1, -7],\n [0, 0, 2]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 10, 0],\n [4, -9, -4],\n [1, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{You...
22
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[-1, 1, 2],\n [1, 4, 0],\n [2, 0, 3]]\nRound your answer to the nearest integer.\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[[-9, 0, 3],\n [0, -4, 3],\n [3, 3, 8]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[4, -10, -2],\n [8, -7, 10],\n [-10, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
6
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[[6, -3, -6],\n [1, 5, 0],\n [9, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, 7, 2],\n [0, 5, -6],\n [0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
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[[-8, -10, 3],\n [0, -10, 1],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-87
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, 0],\n [2, -8, 9],\n [0, 9, -2]]\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[[1, 9, 9],\n [0, -10, -6],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
84
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[5, -2, 0],\n [-2, -7, -4],\n [0, -4, -6]]\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 value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -4, 1],\n [-4, -10, 0],\n [1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-55
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[[5, 7, 2],\n [-5, 9, -1],\n [3, 0, -6]]\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, 7, -9],\n [0, 7, -9],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
43
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[[-7, 10, 1],\n [-7, 4, -5],\n [3, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
-53
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[[10, -6, 5],\n [-6, 1, 3],\n [5, 3, -5]]\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 (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -4, -2],\n [-4, -5, 6],\n [-2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
-4
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[[-3, -7, 5],\n [0, -5, -10],\n [0, 0, 4]]\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 value at position (1, 2) rounded to the nearest integer?\n[[7, 3, -8],\n [0, 6, 8],\n [0, 0, -2]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 2, 1],\n [2, -10, -4],\n [1, -4, -9]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 7, 4],\n [-10, -9, -9],\n [3, -1, -6]]\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[[3, 0, -5],\n [-9, 10, 5],\n [9, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
61
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[[6, 2, 2],\n [0, 9, -1],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-10, -7, 1],\n [0, -4, 0],\n [0, 0, -6]]\nRound your answer to the nearest integer.\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 all entries rounded to the nearest integer?\n[[8, -10, 10],\n [-5, 1, 8],\n [-2, -8, 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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, -6, -8],\n [5, -5, -10],\n [4, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[-4, -5, -8],\n [-5, 10, 4],\n [-8, 4, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[10, -10, 2],\n [-3, -1, -9],\n [2, -9, -9]]\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 value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[3, -7, -1],\n [-7, 1, -2],\n [-2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
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, 6, 1],\n [0, 1, -4],\n [0, 0, 10]]\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 at position (2, 2) rounded to the nearest integer?\n[[10, -1, 2],\n [0, -1, -3],\n [0, 0, 9]]\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[[-7, 0, 2],\n [0, 9, -1],\n [0, 0, -10]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[6, -6, 4],\n [-6, 7, -6],\n [4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
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[[6, 6, 3],\n [-1, 6, 1],\n [10, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
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, -4, 0],\n [6, 9, 8],\n [6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
64
MATH