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[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[1, -6, 5, 12, -7],\n [5, -1, -4, -15, 15],\n [-3, -3, -13, 8, -2],\n [-11, 5, 6, 2, -5],\n [15, -8, 9, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
2
MATH
[ { "content": "Find the inverse of 1/150 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, 4, 4, -4, 9],\n [0, 3, -1, -13, -12],\n [0, 0, -4, 10, 10],\n [0, 0, 0, -2, 11],\n [0, 0, 0, 0, -10]]\n\nPresent the ans...
-499
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (5, 5) rounded to the nearest integer?\n[[-4, 5, -6, -11, 9],\n [0, -14, 3, -8, -9],\n [0, 0, 13, 14, -12],\n [0, 0, 0, -5, -3],\n [0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
-12
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[0, 7, -12, 8, 2],\n [7, -2, -1, 12, 13],\n [-12, -1, 7, 4, 0],\n [8, 12, 4, 11, 2],\n [2, 13, 0, 2, 15]]\n\nPresent the answer in LaTex fo...
101
MATH
[ { "content": "Find the value at position (2, 4) of the inverse of matrix 1/150 * A where A =\n[[14, -10, -7, 1, 3],\n [1, -1, 15, -14, -12],\n [9, -2, -6, 13, 7],\n [3, 5, -11, -14, -9],\n [4, 8, 7, 11, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
21
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, 2, -10, -6, 0],\n [2, 5, 1, 2, -4],\n [-10, 1, 3, 0, 6],\n [-6, 2, 0, 3, 2],\n [0, -4, 6, 2, 5]]\n\nPresent the answer in LaTex format: \\...
-2239
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 2, 8, -10, 8],\n [2, 4, 1, 8, 0],\n [8, 1, 4, 4, 1],\n [-10, 8, 4, 1, -3],\n [8, 0, 1, -3, -4]]\n\nPres...
135
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, 11, 3, 0, 0],\n [15, 7, 5, -12, 7],\n [-10, 2, -15, -14, -2],\n [-9, 12, 5, 11, -8],\n [-2, 13, 9, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
10
MATH
[ { "content": "Find the value at position (2, 1) of the inverse of matrix 1/150 * A where A =\n[[8, -2, -2, 2, 3],\n [-2, -9, 2, 6, 9],\n [-2, 2, -9, -4, 11],\n [2, 6, -4, -7, 3],\n [3, 9, 11, 3, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
1
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, -4, -3, -2, 7],\n [-14, -13, 4, 8, 4],\n [14, -9, 12, -11, 7],\n [10, 3, 8, -4, 8],\n [15, -3, -1, -14, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answe...
44
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, -3, 10, -7, 7],\n [0, 6, -15, 11, 6],\n [0, 0, -8, -3, -6],\n [0, 0, 0, 5, -11],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
33
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-7, -11, -8, 3, -2],\n [0, 1, 4, -3, 6],\n [0, 0, 15, 15, 9],\n [0, 0, 0, 9, 11],\n [0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe...
1192
MATH
[ { "content": "Find the value at position (5, 3) of the inverse of matrix 1/150 * A where A =\n[[7, 15, -13, -10, 2],\n [0, 4, 9, 8, 9],\n [0, 0, -6, -2, -7],\n [0, 0, 0, 3, -15],\n [0, 0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
0
MATH
[ { "content": "Find the inverse of 1/150 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, 12, 3, 1, -11],\n [0, 12, 7, 8, -13],\n [0, 0, 2, -3, -8],\n [0, 0, 0, 12, -11],\n [0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex fo...
809
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, -5, 7, 2, 5],\n [0, -13, -3, 12, 9],\n [0, 0, -14, 6, 9],\n [0, 0, 0, 15, 6],\n [0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
-21
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, -7, -11, 7, 5],\n [0, -12, -9, -2, 13],\n [0, 0, 2, -6, 14],\n [0, 0, 0, 15, 7],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your a...
184
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, 2, 1, 5, -9],\n [0, 4, 13, 8, 11],\n [0, 0, 5, 10, 8],\n [0, 0, 0, -5, 4],\n [0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
758
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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[[15, -12, 12, 0, -2],\n [-12, 5, 2, -12, -8],\n [12, 2, -7, -4, 6],\n [0, -12, -4, -11, -13],\n [-2, -8...
108
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, -1, 14, 13, -4],\n [0, -6, 8, 5, 2],\n [0, 0, -5, -4, 11],\n [0, 0, 0, -12, 5],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-88
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-6, -13, 5, 11, -6],\n [0, -4, -10, 4, -7],\n [0, 0, -7, -9, -10],\n [0, 0, 0, 1, 10],\n [0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
104
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[14, 2, -1, 3, 6],\n [2, -13, 2, 9, 3],\n [-1, 2, 1, 8, -9],\n [3, 9, 8, -4, -2],\n [6, 3, -9, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
69
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[7, 1, -4, -6, 4],\n [0, -1, 0, -15, 2],\n [0, 0, 8, -1, -5],\n [0, 0, 0, -2, -2],\n [0, 0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
3392
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[8, -5, 8, 3, -10],\n [10, -15, -6, 13, -13],\n [14, 1, -12, 14, -11],\n [-7, 4, 9, -10, 9],\n [15, -12, 12, 14, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-148
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 6, 5, 12, 3],\n [6, -9, 2, 8, 6],\n [5, 2, -12, -1, -8],\n [12, 8, -1, 9, -4],\n [3, 6, -8, -4, -1...
586
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-11, 0, 2, 10, 1],\n [0, -2, -6, -4, 10],\n [0, 0, -10, 6, 15],\n [0, 0, 0, -8, -10],\n [0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format...
-109
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[0, -1, -12, -4, 15],\n [13, 9, -13, 12, 15],\n [8, -12, 7, 2, -9],\n [-4, -13, 5, 13, -11],\n [13, 3, -1, 12, -9]]\n\nPresent the answer in LaTex forma...
-21
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[11, -10, 3, 11, -3],\n [-12, -12, -13, -4, -13],\n [10, 5, -6, 10, 0],\n [9, -7, -13, -5, 5],\n [-6, -14, 0, 2, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-2
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[14, -1, -2, 4, -3],\n [-1, 6, -12, 4, 6],\n [-2, -12, 3, 1, 4],\n [4, 4, 1, 15, -2],\n [-3, 6, 4, -2, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your an...
126
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, -9, -11, 11, 3],\n [-1, -3, -11, -11, 12],\n [14, -12, 0, 7, 12],\n [11, 4, 15, 1, -6],\n [6, 3, -9, 11, -14]]\n\nPresent the answer in La...
-285
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -2, 2, 10, 11],\n [-2, 6, -5, -10, 5],\n [2, -5, 11, -4, 2],\n [10, -10, -4, -4, -1],\n [11, 5, 2, -1, 4]]\n\nPresen...
19
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[0, 5, -4, 12, 5],\n [7, -6, -8, 6, -14],\n [9, -14, -9, 13, 5],\n [13, 0, 6, 2, 0],\n [-6, 12, 3, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your...
14
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 12, -8, -1, 14],\n [4, -7, 9, 1, -4],\n [-2, -14, -7, -1, -6],\n [-9, -6, -6, -8, 2],\n [-6, -11, -10, 15, -6]]\n\nPresent the answer in LaTex format: \\...
31
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 8, 2, -2, 2],\n [-15, -3, -5, -12, -10],\n [0, -7, 9, 3, 0],\n [-7, 10, 4, 4, 2],\n [5, -2, -13, 5,...
184
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[-1, 6, -2, 0, -7],\n [-5, -14, -2, 13, -13],\n [10, -12, -15, 0, -9],\n [8, -9, 7, -3, 13],\n [-11, -8, 6, 8, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-1407
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, -14, -3, 14, 1],\n [-8, 4, -3, -6, -1],\n [-13, -14, 13, 5, -3],\n [5, -7, 7, -1, 8],\n [-10, -9, 13, -1...
-126
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, -8, -10, -11, 4],\n [0, -3, -15, -9, 8],\n [0, 0, -12, 4, 1],\n [0, 0, 0, 2, 2],\n [0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{...
-350
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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[[15, -3, -8, 7, -15],\n [-8, 6, -11, 6, 2],\n [4, 3, -13, -6, -9],\n [5, 12, -5, -15, 9],\n [2, -9, -7, 9, 1...
14
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-15, -12, 15, -11, -13],\n [-8, -9, -5, -10, -8],\n [-10, -1, -12, -7, -2],\n [4, -6, 2, 10, -15],\n [2, 3, -9, 12, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in L...
-23
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-11, 8, -10, -12, 7],\n [-2, 13, 15, 12, 1],\n [-5, -9, -11, 14, 9],\n [0, 15, -1, -4, -8],\n [-14, 3, -11, 4, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex f...
-27
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (3, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, -7, -1, 0, -1],\n [1, 5, -15, -15, 1],\n [-5, -4, 12, -10, -10],\n [-7, -9, -1, 1, 3],\n [-14, -9, 13, -15, -1...
7
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (3, 5) rounded to the nearest integer?\n[[4, -3, -3, 12, -4],\n [4, -11, 1, 4, -10],\n [0, -14, -2, 6, 12],\n [-7, -6, -9, -11, 12],\n [9, 2, -7, -7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-2
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/150 * A where A =\n[[-15, -2, -8, 9, 3],\n [-2, 3, 7, -13, -4],\n [-8, 7, 11, 1, 10],\n [9, -13, 1, -8, -1],\n [3, -4, 10, -1, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
-10
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, -14, 10, -13, -1],\n [0, -2, 15, 6, 6],\n [0, 0, 4, -10, 2],\n [0, 0, 0, 14, 1],\n [0, 0, 0, 0, 4]]...
9665
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 5, 14, -7, -1],\n [0, -4, 5, 11, 14],\n [0, 0, 7, -9, 7],\n [0, 0, 0, -5, 15],\n [0, 0...
591
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 5, -11, 13, 1],\n [0, -14, -3, -14, -4],\n [0, 0, 7, 7, 5],\n [0, 0, 0, -1, -8],\n [0, 0, 0, 0, -6]]\n\nPresent the ...
-11
MATH
[ { "content": "Find the inverse of 1/150 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, 7, 2, 2, -1],\n [0, 2, -15, 0, 5],\n [0, 0, -3, 10, 3],\n [0, 0, 0, 7, -3],\n [0, 0, 0, 0, -5]]\n\nPresent the answer in L...
-1968
MATH
[ { "content": "Find the inverse of 1/150 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, -4, -8],\n [5, -15, 10, 12, 3],\n [-6, 10, 15, -4, 2],\n [-4, 12, -4, -8, 12],\n [-8, 3, 2, 12, -10]]\n\nPresent the answer in L...
194
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, -4, -8, -8, 13],\n [-4, 6, -4, -11, -2],\n [-8, -4, -1, 12, -3],\n [-8, -11, 12, 15, -4],\n [13, -2, -3, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-317
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 12, -11, 1, 7],\n [0, -10, -3, 5, 13],\n [0, 0, -5, -4, 6],\n [0, 0, 0, -4, 8],\n [0, 0, 0, 0, -14]]\n\...
-131
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, 4, -4, 5, 13],\n [5, 11, -5, 14, -4],\n [-11, -11, 7, 6, 3],\n [11, -12, -8, -12, 15],\n [6, -4, -6, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
9
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-15, 8, -2, -3, -7],\n [-2, 9, 7, -11, -4],\n [-1, -13, -11, -15, 10],\n [-10, -11, 12, 8, 11],\n [11, -7, 8, 15, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed...
-19
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-5, 5, -2, -6, 4],\n [5, 0, 9, 4, -7],\n [-2, 9, -15, -11, -3],\n [-6, 4, -11, -5, -1],\n [4, -7, -3, -1, -6]]\n\nPresent the answer in LaTex format: \...
-15
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[2, -3, -3, 8, 7],\n [9, -5, -4, -5, -11],\n [14, -3, 0, 1, 13],\n [7, -5, 2, -14, 13],\n [2, 2, 12, 15, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
-24
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -5, -8, -4, 13],\n [0, -15, -1, 13, -10],\n [0, 0, 6, -12, 9],\n [0, 0, 0, -3, -10],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTe...
611
MATH
[ { "content": "Find the value at position (4, 2) of the inverse of matrix 1/150 * A where A =\n[[-4, -6, -8, 4, -2],\n [-6, 15, -2, -1, 2],\n [-8, -2, 4, 5, -14],\n [4, -1, 5, -7, -13],\n [-2, 2, -14, -13, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
11
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[5, 0, -8, -8, -4],\n [0, -5, 10, 4, -4],\n [-8, 10, 5, -6, -2],\n [-8, 4, -6, -15, -4],\n [-4, -4, -2, -4, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your a...
43
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-9, -12, -1, 3, 12],\n [-12, 4, -8, 0, 8],\n [-1, -8, 3, 7, 4],\n [3, 0, 7, 10, -10],\n [12, 8, 4, -10, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format...
111
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-6, 10, 1, -7, -11],\n [0, 13, -11, 14, 10],\n [0, 0, -4, 9, -12],\n [0, 0, 0, 3, 1],\n [0, 0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your ans...
775
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 10, -2, 2, 13],\n [10, 1, -14, 3, -4],\n [-2, -14, 2, -8, 10],\n [2, 3, -8, 4, -6],\n [13, -4, 10, -6, 10]]\n\nPresent...
415
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-14, 8, 0, -4, -3],\n [8, 4, 4, 6, 2],\n [0, 4, 7, -2, 9],\n [-4, 6, -2, -14, 4],\n [-3, 2, 9, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
3
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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[[13, 13, -7, -8, 5],\n [-11, -3, -6, -11, -13],\n [-11, -14, -15, 5, 2],\n [13, 10, 15, -1, 12],\n [0, 15, 1...
-3
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, 4, 12, -3, -10],\n [4, 1, 6, 6, -2],\n [12, 6, 11, -6, 5],\n [-3, 6, -6, 13, 5],\n [-10, -2, 5, 5, 1]]\n\nPresent the answer in LaTex ...
150
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[3, 2, -2, -5, 4],\n [2, 0, -13, 0, -10],\n [-2, -13, 8, -7, -8],\n [-5, 0, -7, 14, 1],\n [4, -10, -8, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-36
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[-11, 15, 15, 7, 14],\n [12, -3, 7, 7, -8],\n [12, -13, 3, 10, -7],\n [1, 0, 13, -3, 3],\n [1, -7, 0, 7, 6]]\n\nPresent the answer in LaTex format: \\bo...
4
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (2, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 4, -5, -5, 1],\n [0, 4, -14, -9, -13],\n [-14, 14, 5, 5, 3],\n [-11, -13, -12, -13, -8],\n [2, 4, 9, 0, 11]]\n\n...
4
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-4, -7, -6, 12, -1],\n [-7, 9, 6, -4, -6],\n [-6, 6, -7, 7, 8],\n [12, -4, 7, -9, 0],\n [-1, -6, 8, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe...
114
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-15, -1, 1, 4, 0],\n [-1, -8, 4, 6, -6],\n [1, 4, -4, -2, -8],\n [4, 6, -2, 11, 1],\n [0, -6, -8, 1, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your an...
114
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 1, -13, 5, -6],\n [1, 0, 2, 8, 4],\n [-13, 2, -10, -2, -4],\n [5, 8, -2, -7, -6],\n [-6, 4, -4, -6, 0]]\n\nPresent t...
101
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, -4, 2, 8, 4],\n [-3, 11, 12, 1, 6],\n [15, 8, -10, 5, -12],\n [5, -10, 12, -7, -9],\n...
18
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[11, 12, -2, 13, 2],\n [12, -12, -8, 0, -8],\n [-2, -8, -2, -7, 0],\n [13, 0, -7, -9, 7],\n [2, -8, 0, 7, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Yo...
1649
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 9, 0, 3, 12],\n [0, 13, -13, -8, 6],\n [0, 0, -2, 11, 10],\n [0, 0, 0, 10, -13],\n [0, 0, 0, 0, 5]]\n\nPresent the an...
1303
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-3, -8, -13, 15, -3],\n [12, 10, -11, 9, 6],\n [6, 5, 13, 11, 12],\n [12, 9, -1, -3, 11],\n [-10, -1, 7, -7, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed...
182
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (5, 4) rounded to the nearest integer?\n[[9, -15, 7, 15, 15],\n [-2, -2, 10, 12, -9],\n [10, 4, 11, 10, 14],\n [-12, 5, -9, -6, -7],\n [-6, 4, 14, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
9
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 2, 8, 8, -4],\n [0, -9, -13, 8, 11],\n [0, 0, -15, 3, -1],\n [0, 0, 0, 12, 5],\n [0, 0, 0, 0, -9]]\n\nPresent th...
-17
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, -7, 0, 10, -2],\n [-7, 13, -9, -13, -11],\n [0, -9, -3, 13, 4],\n [10, -13, 13, -14, 0],\n [-2, -11, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-66
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[6, -15, -10, 6, 6],\n [0, -6, 9, -3, 8],\n [0, 0, -3, 6, 2],\n [0, 0, 0, -3, -12],\n [0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answ...
1731
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 14, 13, 7, -2],\n [5, 11, 8, 0, 5],\n [8, -8, -12, -1, -14],\n [0, -10, 11, -12, -12],\n [0, -5, -...
355
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[8, -12, 4, -4, 0],\n [-12, -10, -2, 6, 2],\n [4, -2, -5, 8, 5],\n [-4, 6, 8, 11, -2],\n [0, 2, 5, -2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer...
98
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-10, 8, 2, 6, -7],\n [8, 9, 0, -2, 10],\n [2, 0, 4, -6, -3],\n [6, -2, -6, -6, 10],\n [-7, 10, -3, 10, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answ...
-48
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, 13, -1, 5, 15],\n [14, -11, 3, 3, -5],\n [8, 5, -11, 6, -14],\n [13, 0, -10, -13, -13],\n [5, -15, 12, -11, 5]]\n\nPresent the answer in LaTex format: \\...
350
MATH
[ { "content": "Find the inverse of 1/150 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, 10, 4, -10, 11],\n [15, -11, 13, 5, 4],\n [8, 0, 9, 8, 1],\n [-6, -5, -7, -14, 9],\n [10, 9, 8, -6, -11]]\n\nPresent the answer in LaTe...
8376
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[1, -9, -12, 3, 6],\n [0, 11, 4, 11, -14],\n [0, 0, -9, -7, -12],\n [0, 0, 0, -4, 2],\n [0, 0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
1033
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, 15, -5, 15, 9],\n [0, 5, -6, 8, -12],\n [0, 0, -10, 12, 7],\n [0, 0, 0, -15, -8],\n [0, 0, 0, 0, -7]]\n\nPresent the ...
-237
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, -13, -14, 1, -12],\n [0, -10, -11, -1, -11],\n [0, 0, 2, 15, -3],\n [0, 0, 0, 4, -12],\n [0, 0, 0, 0, 1...
72
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, 0, 0, -12, 2],\n [0, 4, -6, -4, -6],\n [0, -6, -4, 0, 4],\n [-12, -4, 0, 7, 0],\n [2, -6, 4, 0, -9]]\n\nPresent the answer in LaTex format:...
-24
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -4, -8, 5, -5],\n [-4, -14, 2, -8, 2],\n [-8, 2, -5, -9, 0],\n [5, -8, -9, 12, 4],\n [-5, 2, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
-17
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 6, 3, -7, 15],\n [0, -5, 14, 14, 3],\n [0, 0, 12, -13, 4],\n [0, 0, 0, -12, -10],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format...
-58
MATH
[ { "content": "Find the inverse of 1/150 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, 1, -4, -4],\n [10, 15, -2, 6, -1],\n [1, -2, 3, -2, -14],\n [-4, 6, -2, -4, 2],\n [-4, -1, -14, 2, -8]]\n\nPresent th...
-72
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 11, -9, -9, -1],\n [-4, -13, -8, -6, 7],\n [2, 3, -3, -8, 9],\n [12, 14, -10, -14, 9],\n [-15, -9, -1, -7, -10]]\n\nPresent the answer in LaTex format: ...
-14
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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, -14, 8, 13, -7],\n [13, 3, 0, 4, 3],\n [-2, -7, 4, 12, 3],\n [10, -9, 14, 4, -10],\n [-8, 6, -11, -...
452
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, 8, -4, -5, -3],\n [-14, 13, -10, -5, -7],\n [4, -11, -11, 4, 1],\n [-14, 6, -5, -11, -15],\n [-13, 6, -14, -7, 9]]\n\nPresent the answer in LaTex format: \\boxe...
213
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, 14, 9, 1, -14],\n [9, -15, 5, -4, -11],\n [-1, -13, -1, 6, 10],\n [6, -8, 8, -13, -6],\n [10, -1, 1, -5, 12]]\n\nPresent the answer in LaTe...
15
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[13, -11, 12, 1, 8],\n [0, 13, -4, 5, 1],\n [0, 0, -14, 1, -2],\n [0, 0, 0, -3, -12],\n [0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{...
0
MATH
[ { "content": "Find the inverse of 1/150 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, 0, -8, 4],\n [2, -12, 6, 10, 4],\n [0, 6, 12, 7, 9],\n [-8, 10, 7, 8, -1],\n [4, 4, 9, -1, -13]]\n\nPresent the answer in LaTex form...
921
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, 3, 13, 1, 7],\n [-8, 12, -10, 0, -9],\n [7, 11, 12, 14, 10],\n [-13, 7, 11, -13, 3],\n [7, 1, -13, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answ...
-18
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (5, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 1, 15, -7, -13],\n [-6, -2, 9, 2, -7],\n [12, 2, 11, -14, 12],\n [12, -8, -10, -1, -12],\n [5, 11, 8, 12, -4]]\...
3
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[10, 11, -4, -2, 7],\n [11, -7, 0, 7, -10],\n [-4, 0, 2, -8, -6],\n [-2, 7, -8, 8, -7],\n [7, -10, -6, -7, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
14
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, -1, 11, 4, -11],\n [13, 7, 4, -11, -3],\n [-2, -11, -4, 10, -11],\n [15, -15, 11, 9, 12],\n [-11, -9, -10, 4, 4]]\n\nPresent the answe...
430
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[13, 11, -5, -8, 15],\n [-11, 15, 7, 14, -7],\n [9, -8, -5, -7, -1],\n [-1, 4, 5, 5, -14],\n [-7, -11, -6, -5, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxe...
315
MATH
[ { "content": "Find the inverse of 1/150 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, -7, -14, -2, 10],\n [-11, 6, -5, -11, -12],\n [1, -15, 15, -7, -14],\n [5, -10, -4, 2, -8],\n [1, -13, -7, -2, -12]]\n\nP...
2956
MATH