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[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-9, -4, -3, 8, 8],\n [-8, -12, -10, -14, -14],\n [8, -13, -6, -9, -6],\n [8, -9, -10, 9, -12],\n [9, -5, -7, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Y...
40
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-11, 0, -10, -6, -3],\n [0, 4, -4, -10, 5],\n [-10, -4, -13, -6, -4],\n [-6, -10, -6, -4, 2],\n [-3, 5, -4, 2, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\box...
966
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[[-4, 4, -5, -13, 0],\n [-13, 1, -6, 8, 0],\n [-10, 3, 5, -11, 1],\n [-11, 3, -15, -2, -13],\n [-1, -10, 13, 11, 12]]\n\nPresent the answer in La...
28
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, 13, -12, 10, -10],\n [14, -10, 1, 8, -13],\n [4, -2, -13, 11, -15],\n [-3, 10, -2, -11, -12],\n [-10, 14, -1, 11, 5]]\n\nPresent the an...
188
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[-1, -15, -2, 9, 15],\n [15, 5, 13, 0, 4],\n [-15, -9, 1, 3, -2],\n [-2, 1, -11, -1, -10],\n [-7, 14, 12, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
18
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[[12, 11, 2, 15, 13],\n [0, 11, 7, -1, -6],\n [0, 0, 6, -4, -4],\n [0, 0, 0, 2, -1],\n [0, 0, 0, 0, -14]]\n\nPresent the an...
47
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[[3, 1, -9, 12, 11],\n [0, -4, -5, 4, -6],\n [0, 0, -8, 8, 13],\n [0, 0, 0, -1, -15],\n [0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"...
1661
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[[-8, -11, -12, -10, -10],\n [0, 10, -8, -10, -6],\n [0, 0, -2, 10, -2],\n [0, 0, 0, -12, -4],\n [0, 0, ...
935
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[[3, 14, 7, -15, 1],\n [0, 14, 12, -5, 0],\n [0, 0, 1, 14, 9],\n [0, 0, 0, 6, 11],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answ...
4
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[[-13, -5, 15, -3, -15],\n [0, -10, 9, -9, 15],\n [0, 0, -15, 0, -3],\n [0, 0, 0, 8, 10],\n [0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex ...
444
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[[11, -15, -10, 12, 3],\n [12, -5, 11, 3, 12],\n [8, -5, 8, -4, -6],\n [14, 11, 7, 13, 10],\n [4, -1, -1...
109
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[[-14, -8, 11, 9, 14],\n [12, -4, 2, 5, -11],\n [2, 9, 0, -2, 0],\n [8, 11, -7, 14, 0],\n [...
-21
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[[-13, 4, -7, 6, 6],\n [4, -12, 1, 9, 5],\n [-7, 1, -9, 0, -2],\n [6, 9, 0, -10, -8],\n [6, 5, -2, -8, -3]]\n\nPresent the answ...
45
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[[6, 0, 0, -8, -12],\n [0, -15, 0, -8, 2],\n [0, 0, 1, 4, 2],\n [-8, -8, 4, 4, 5],\n [-12, 2, 2, 5, -6]]\n\nPresent the answer in LaTex format: \...
-99
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[4, 8, 1, -10, -4],\n [12, 6, 4, 3, -5],\n [-7, -11, 14, -2, 11],\n [9, -9, -15, -7, -15],\n [6, 11, 6, 15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
5
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[[14, -7, -15, -5, -2],\n [-2, 6, 5, 1, -8],\n [7, -8, 10, 13, -15],\n [7, 12, 12, 2, -4],\...
-28
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[[13, -1, -12, -12, 0],\n [-1, -3, 11, 12, 10],\n [1, 2, 1, 12, 14],\n [-15, 2, -5, 2, -6],\n [-5, -15, ...
369
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[12, 2, 2, -6, 14],\n [13, -8, -10, 11, -15],\n [-14, -11, 3, -11, 5],\n [6, 6, 0, 0, -3],\n [-5, -10, -13, -8, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-39
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[1, -1, 13, 9, -9],\n [0, 7, -5, 10, -5],\n [0, 0, 7, 7, 12],\n [0, 0, 0, -2, 9],\n [0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{You...
190
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-7, 10, -6, -14, -15],\n [-12, 13, 13, 10, 5],\n [5, 5, 6, 14, -13],\n [7, -4, -11, -13, -14],\n [2, -7, -6, 14, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\bo...
2916
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[[-11, 3, -6, -3, 2],\n [3, 14, -9, -2, 2],\n [-6, -9, 9, 0, -8],\n [-3, -2, 0, -1, -8],\n [2, 2, -8, -8, 6]]\n\nPresent the answer in LaTex...
268
MATH
[ { "content": "Find the value at position (4, 4) of the inverse of matrix 1/150 * A where A =\n[[-15, -3, -8, -4, -10],\n [-3, -12, -3, -5, 6],\n [-8, -3, 4, -14, -1],\n [-4, -5, -14, 14, 2],\n [-10, 6, -1, 2, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your ans...
-549
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[2, 10, 12, -10, 12],\n [0, 13, -14, 1, -1],\n [0, 0, 1, 4, 11],\n [0, 0, 0, -4, 9],\n [0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\b...
-2334
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[[-10, 3, -12, 13, 4],\n [0, -12, 15, -8, 15],\n [0, 0, -11, -12, 0],\n [0, 0, 0, -10, 8],\n [0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
0
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[[9, 6, 5, -11, 4],\n [0, -5, -11, 13, 9],\n [0, 0, -9, 12, 6],\n [0, 0, 0, 6, -1],\n [0, 0...
-38
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[[7, -3, 12, -15, 8],\n [0, 15, -10, 7, 9],\n [0, 0, -10, 5, -13],\n [0, 0, 0, 7, 7],\n [0, 0, 0, 0, -12]]\n\nPresent the answe...
26
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[[-8, -11, 14, -12, 14],\n [0, -8, 7, -11, 12],\n [-3, -1, 13, -10, -14],\n [-3, -11, 5, -7, -11],\n [14, -6, -13, 15, 14]]\n\nPresent the answer in LaTex form...
24
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[[-8, 2, 3, 0, -9],\n [0, -11, 4, 15, 3],\n [0, 0, -9, -4, -1],\n [0, 0, 0, -8, -12],\n [0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your a...
322
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[[-2, 14, -6, -4, -12],\n [-7, -9, -15, 1, 12],\n [7, -13, 7, -9, 9],\n [-15, -3, 10, 11, 13],\n [6, 13, 13, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-12
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[4, 2, 4, -2, 5],\n [2, 1, 2, -5, -13],\n [4, 2, -4, -9, 4],\n [-2, -5, -9, -4, -8],\n [5, -13, 4, -8, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your ...
974
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, 3, -10, 13, 12],\n [0, -1, -3, -13, -2],\n [0, 0, -9, 5, -11],\n [0, 0, 0, 9, -13],\n [0, 0, 0, 0, -1]]\...
-275
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[[11, -5, 8, 9, 13],\n [0, -5, -5, 9, 5],\n [0, 0, -1, 11, -8],\n [0, 0, 0, 13, -14],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your an...
10
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[-7, 8, 15, -11, -13],\n [0, -6, -4, 12, -1],\n [0, 0, -1, -4, 12],\n [0, 0, 0, -5, -7],\n [0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
-228
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, -4, -6, -9, -6],\n [-13, -15, 2, -15, -6],\n [5, 12, 15, 1, -6],\n [-4, 15, -7, 3, 13],\n [-11, -1...
121
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, -6, -8, 11, -4],\n [0, 14, 13, 7, 15],\n [0, 0, -6, 10, 15],\n [0, 0, 0, 7, 11],\n [0,...
-964
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[[-11, 1, -7, 10, 3],\n [-8, 0, -7, -9, 7],\n [-8, -1, -1, 8, 1],\n [-6, 6, 7, 15, 1],\n [3, -11, 5, 7, -5]]\n\nPresent the answer in LaTex format: \\box...
-113
MATH
[ { "content": "Find the value at position (1, 2) of the inverse of matrix 1/150 * A where A =\n[[-11, -5, -8, -3, 9],\n [-1, -13, -3, -6, 6],\n [-6, 5, 3, -9, 10],\n [1, -10, -10, 11, 1],\n [10, -5, -11, 9, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
4
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[6, -15, -5, -10, 3],\n [0, -2, 9, 12, 10],\n [0, 0, 10, 12, 10],\n [0, 0, 0, -1, 3],\n [0, 0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
-160
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[[-5, 12, 8, 13, -3],\n [0, -1, 0, 9, 10],\n [0, 0, 14, -10, 8],\n [0, 0, 0, 14, 6],\n [0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your an...
76
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[4, -8, -3, 0, -6],\n [-8, 4, 10, 6, -3],\n [-3, 10, 14, -2, 12],\n [0, 6, -2, -15, -6],\n [-6, -3, 12, -6, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex forma...
27
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[[-14, -9, 2, -5, 8],\n [0, -2, 2, -15, 6],\n [-5, -8, -7, -14, -14],\n [-5, -6, -15, 1, 7],\n [13, -13, 9, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your ans...
0
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[10, -12, 0, 4, 2],\n [15, -5, -9, -2, 13],\n [13, -6, 7, -9, -5],\n [11, 10, 9, -13, -9],\n [12, 9, 10, -5, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
18
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[10, -4, -1, 3, 15],\n [0, -4, 3, 7, 0],\n [0, 0, 4, -5, -6],\n [0, 0, 0, -1, -7],\n [0, 0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
7044
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, 12, 9, -9, 3],\n [1, 15, 8, -3, 4],\n [-10, 3, -2, 10, 2],\n [1, -14, -1, 7, 1],\n [-14, -6, 6, 3, -3]]\n\nPresent the answer in LaTex...
544
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-11, -3, 10, 13, -8],\n [-3, 11, -7, 9, -6],\n [7, -10, 3, 14, 5],\n [9, 15, -9, 9, -4],\n [-7, -3, 7, -2, -14]]\n\nPresent the answer in LaTex format:...
-12
MATH
[ { "content": "Find the value at position (5, 5) of the inverse of matrix 1/150 * A where A =\n[[-6, 12, -13, -2, -10],\n [7, -7, 14, -7, 7],\n [1, -3, -1, -11, -1],\n [15, 13, 2, 13, -4],\n [2, -9, 11, 9, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer...
-7
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-13, 12, 4, -15, -13],\n [6, -3, 9, -9, 7],\n [2, -1, 14, 10, 12],\n [4, -14, -9, 12, 15],\n [-6, -10, 8, 11, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex f...
-13
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[[7, -3, -6, -4, -11],\n [0, 9, -13, 8, 15],\n [0, 0, 2, 8, -2],\n [0, 0, 0, 4, 10],\n [0, ...
831
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[[12, -11, -10, 10, -6],\n [12, -2, 13, 5, 12],\n [0, -12, -2, -2, 2],\n [1, -6, 12, -15, -2],\n [-9, 12, 2, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
-5
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[[-4, 11, -15, 5, -11],\n [1, -13, -3, -15, 11],\n [11, -14, -2, 8, -6],\n [1, -3, -7, -8, 12],\n [6, -4, 6, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-4
MATH
[ { "content": "Calculate the inverse matrix of 1/150 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[[-4, -4, 13, -2, -12],\n [0, -2, 15, 3, -5],\n [0, 0, -15, -14, 13],\n [0, 0, 0, -5, -6],\n [0, 0, 0, 0, 3]]\n\nPres...
-10
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[[-11, 5, 1, -2, 14],\n [0, -10, 15, 5, -13],\n [0, 0, 4, -14, 1],\n [0, 0, 0, 5, 14],\n [0, 0, 0, 0, -11]]\n\nPresent the answ...
242
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, -7, 4, -5, 4],\n [-7, 4, 0, 2, -2],\n [4, 0, -2, 6, 4],\n [-5, 2, 6, -3, -2],\n [4, -2, 4, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-92
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-7, 4, 5, 10, 10],\n [-10, -12, -13, -3, 5],\n [14, -4, 2, -7, -5],\n [-4, 14, -3, 13, 4],\n [9, 10, 2, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-8
MATH
[ { "content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-1, -13, 3, 9, 7],\n [0, 12, 13, 1, -14],\n [0, 0, 7, 3, 2],\n [0, 0, 0, -4, -12],\n [0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-229
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-7, 4, -4, -3, 6],\n [0, -9, -15, -1, -15],\n [0, 0, -1, 15, 14],\n [0, 0, 0, 13, -6],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxe...
0
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-13, -5, -14, -9, -6],\n [-2, 13, 0, -14, -7],\n [12, 14, -8, 11, 15],\n [-1, 7, 10, -12, 12],\n [-2, 0, -13, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"...
23
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[[11, -12, 10, -1, 4],\n [-12, -5, 0, -11, 2],\n [10, 0, 3, -12, -12],\n [-1, -11, -12, -12, 1],\n [4, 2, -12, 1, 5]]\n\nPr...
33
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, 3, 9, -9, 2],\n [0, -12, -3, -13, -5],\n [0, 0, 6, 12, 12],\n [0, 0, 0, -6, 3],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex form...
351
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[[1, -1, 10, -2, -15],\n [0, -11, 7, -15, -5],\n [0, 0, 14, -13, 10],\n [0, 0, 0, 6, -7],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
183
MATH
[ { "content": "Find the sum of all entries of the inverse of matrix 1/150 * A where A =\n[[12, -7, 6, 1, 3],\n [0, 14, -3, 10, 7],\n [0, 0, -9, 7, -10],\n [0, 0, 0, 14, -3],\n [0, 0, 0, 0, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
11
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[[2, 4, 0, 1, 6],\n [4, 13, -7, -1, -9],\n [0, -7, 1, -14, 2],\n [1, -1, -14, -1, -5],\n [6, -9, 2, -5, -7]]\n\nPresent the answer in LaTex forma...
31
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[[12, -2, 9, 15, -3],\n [-1, 2, 0, -1, -1],\n [-14, 5, -14, -8, 6],\n [-8, -15, 14, 4, -1],\n [-6, 5, 6, -10, 12]]\n\nPresent the answer in LaTex format: \\box...
49
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[-3, 8, -7, 3, 0],\n [12, 4, -2, -9, 12],\n [-4, -6, -7, 9, -9],\n [3, 15, -9, 12, -8],\n [-2, -1, -15, -15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
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[[13, -8, -14, 2, -8],\n [-7, 10, 11, -12, -1],\n [11, -14, 1, 13, 15],\n [-9, -14, 5, 14, -13],\n [3, 6, -10, 7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
68
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[[-2, 12, 6, -6, -3],\n [0, -14, 7, -12, -12],\n [0, 0, -8, -12, 7],\n [0, 0, 0, -11, 15],\n [0, 0, 0, 0, 13]]\n\nPresent t...
-330
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-5, 12, -2, 14, -9],\n [0, -1, -4, 1, -1],\n [-15, 11, 13, 8, -14],\n [-12, 15, -4, -12, 11],\n [3, -5, 9, 12, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex ...
-50
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[[14, 11, 14, -6, -6],\n [0, -12, 5, 2, 14],\n [0, 0, -15, 2, -4],\n [0, 0, 0, -9, -2],\n [0, 0, 0, 0, -14]]\...
-39
MATH
[ { "content": "For the inverse of 1/150 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[-1, 8, -2, 2, 14],\n [0, -6, -1, -8, -9],\n [0, 0, -15, 5, 12],\n [0, 0, 0, -3, 6],\n [0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
-25
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[[-6, 6, -13, -11, -12],\n [0, 3, 14, -1, -15],\n [0, 0, 9, 10, 5],\n [0, 0, 0, 13, 7],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format...
66
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, -15, 10, -1, 11],\n [11, 10, 3, 12, 6],\n [-7, -7, -4, 10, -8],\n [-1, 9, 2, 8, -9],\n [-11, 14, 4, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed...
23
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[[-2, 14, 7, -7, 7],\n [0, 13, 9, -2, -15],\n [0, 0, -11, -12, -9],\n [0, 0, 0, 12, 14],\n ...
690
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[[6, -3, 5, -14, 11],\n [0, 15, -5, -7, 2],\n [0, 0, -3, -11, -11],\n [0, 0, 0, 10, -14],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{You...
-63
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[[-3, -2, 11, 8, -11],\n [0, -9, -3, 2, -3],\n [0, 0, 14, 5, -15],\n [0, 0, 0, 14, 3],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
32
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-4, 2, 8, 3, 11],\n [0, -6, 9, 1, -1],\n [0, 0, -3, -11, -1],\n [0, 0, 0, 11, -13],\n [0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\b...
-138
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[[6, -7, -8, -2, 4],\n [-1, -2, 1, 11, -3],\n [15, -3, 6, 2, -1],\n [-2, -4, -5, 2, 14],\n [-2, 7, 5, -2, -3]]\n\nPresent the answer in LaTex for...
58
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, 8, -9, -4, -2],\n [0, -5, 2, 6, 3],\n [0, 0, -3, 1, -14],\n [0, 0, 0, -12, 5],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
-41
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[3, 1, -6, -11, -2],\n [0, 9, -15, 9, -6],\n [0, 0, -6, 12, 12],\n [0, 0, 0, 4, 5],\n [0, 0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe...
907
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[1, 8, 1, -3, -14],\n [9, -1, 14, -1, -10],\n [-6, 4, 14, -10, -11],\n [12, 9, -7, -9, -5],\n [10, -1, 14, -3, 6]]\n\nPresent the answer in LaTex format...
-8
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[3, 5, -15, -15, -15],\n [-14, 8, -15, 2, 15],\n [-8, -14, -11, 5, -4],\n [-10, -12, -15, -2, 10],\n [-11, 0, 9, -2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in L...
-10
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, -5, -1, 1, -2],\n [0, -13, -3, -1, 12],\n [0, 0, -5, -3, 14],\n [0, 0, 0, -5, 14],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-18
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -2, 12, -8, -2],\n [-2, 12, -9, 0, 4],\n [12, -9, 4, -12, -5],\n [-8, 0, -12, 10, 0],\n [-2, 4, -5, 0, -9]]\n\...
-10
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, -7, 4, -7, -13],\n [-4, -14, -5, -8, 6],\n [13, -3, 14, 14, -3],\n [-6, -7, -5, -12, 2],\n [4, -12, 0, 5, -12]]\n\nPresent the answer in LaTex forma...
249
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, -11, 9, 14, -6],\n [0, -2, -5, -9, -7],\n [0, 0, 3, 6, -9],\n [0, 0, 0, 6, -1],\n [0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
671
MATH
[ { "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[[13, -4, -12, 8, -12],\n [-11, -3, -14, 13, -3],\n [-4, -3, 6, 0, -5],\n [-10, -15, -3, -11, 9],\n [-14, 11, 3, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answe...
-15
MATH
[ { "content": "Find the inverse of 1/150 times the matrix and calculate the value at position (4, 5) of the inverse. Round your answer to the nearest integer:\n[[8, -8, -8, 2, -4],\n [-8, 9, 2, -3, 2],\n [-8, 2, 5, 5, 9],\n [2, -3, 5, -1, 6],\n [-4, 2, 9, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
15
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[[15, -13, -7, -5, -14],\n [0, 15, -1, -2, 3],\n [0, 0, -9, 3, -15],\n [0, 0, 0, 1, 11],\n [0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
168
MATH
[ { "content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[13, 10, -1, 9, -12],\n [0, 7, -9, 4, 4],\n [0, 0, -2, -15, -7],\n [0, 0, 0, -9, 14],\n [0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your an...
1440
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[[-13, -2, -6, 2, -2],\n [-2, -4, 2, 5, -3],\n [-6, 2, -8, -8, -4],\n [2, 5, -8, 7, -4],\n [-2, -3, -4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
-87
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[[-11, -8, 2, -7, 10],\n [0, -7, -4, 0, 10],\n [0, 0, 1, -9, 13],\n [0, 0, 0, -6, -7],\n [0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex f...
1413
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, -7, -15, -3, 4],\n [-1, -15, 11, -12, 0],\n [-5, -1, 10, 15, -8],\n [3, 4, -4, -9, 7],\n [7, -1, -12, -13, 2]]\n\nPresent the answer i...
408
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[[-3, 3, -14, 6, -2],\n [3, 8, -2, 8, -4],\n [-14, -2, 7, 0, 3],\n [6, 8, 0, -9, 2],\n [-2, -4, 3, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed...
13
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[[-11, -1, -10, 15, -4],\n [7, 8, -10, -8, 4],\n [1, -6, -11, 14, -1],\n [9, 13, 7, 9, 14],\n [2, 6, 14, 13, ...
-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[[-13, -12, -4, 14, 5],\n [0, -10, -5, 4, 13],\n [0, 0, 4, 10, -9],\n [0, 0, 0, 4, 11],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
-32
MATH
[ { "content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[3, 13, 7, 8, -6],\n [13, -4, 4, -10, 10],\n [7, 4, -6, 10, 12],\n [8, -10, 10, 13, -1],\n [-6, 10, 12, -1, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex form...
7
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[[-11, -1, -15, -2, 5],\n [0, 9, 10, -9, 4],\n [2, -4, 2, -7, 15],\n [1, -13, 4, 3, 3],\n [0, -7, 5, 11, -2]]\n\nPresent th...
-1
MATH
[ { "content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 0, 4, 8, 7],\n [0, 12, -6, 4, -8],\n [4, -6, -15, 2, 0],\n [8, 4, 2, 2, -12],\n [7, -8, 0, -12, -9]]\n\nPresent...
-14
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[[-2, 5, -11, -15, 10],\n [0, 4, -8, -5, -6],\n [0, 0, -9, -8, -7],\n [0, 0, 0, 3, 12],\n [0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
33
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[[7, -3, 2, 7, -2],\n [-3, 6, 5, 7, -4],\n [2, 5, 10, 0, 14],\n [7, 7, 0, 15, -7],\n [-2, -4, 14, -7, 7]]\n\n...
-91
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[[-13, 2, -9, -11, -2],\n [-4, -15, -8, -9, -6],\n [0, -1, 7, -2, -5],\n [11, -15, 15, -9, ...
-22
MATH