messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
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[
{
"content": "Calculate the inverse matrix of 1/180 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, 2, 0, 8, -8, 11],\n [2, -11, 8, 3, -2, -12],\n [0, 8, -7, -8, 4, -2],\n [8, 3, -8, -11, 0, -6],\n [-8, ... | 440 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-12, 0, 2, -2, 6, 8],\n [0, -3, 0, 5, -8, 2],\n [2, 0, 1, 10, -10, -4],\n [-2, 5, 10, -3, 6, 9],\n [6, -8, -10, 6, 13, -2],\n [8, 2, -4, 9, -2, -14]]\n\nPresent the... | 8542 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 6, -2, -4, 6, 14],\n [6, -10, 4, -6, 15, -2],\n [-2, 4, -2, 0, 0, 2],\n [-4, -6, 0, 4... | -212 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 3, -1, -4, -3, -4],\n [-11, -3, 0, 3, 11, 9],\n [-14, 13, 8, 3, -12, -5],\n [3, -1, 10, 0, -11, 8],\n [... | 69 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -1, 10, -2, -8, 5],\n [-1, 2, 5, 0, -6, 3],\n [10, 5, -5, 8, -8, -6],\n [-2, 0, 8, 12, -7, -6],\n [-8, -6, -8, -7, 15, 4],\n [5, 3, -6, -6, 4, 3]]\n\nPres... | 464 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 3, 10, 2, -9, -10],\n [0, 2, 8, -5, 1, 12],\n [0, 0, 14, -4, -13, -11],\n [0, 0, 0, -6, 0, -12],\n [0, 0, 0, 0, -14, -5],\n [0, 0, 0, 0, 0, -11]]\n\nPrese... | 85 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[9, 1, 2, -1, -7, -15],\n [3, 9, 10, 11, 12, 14],\n [-1, 6, 9, -9, 15, -4],\n [-7, 1, -15, -6, 13, -2],\n [14, -15, 7, 3, -2, 10],\n [11, 5, -3, 15, 7, -5]]\nRound your answer to the nearest integer.\n\nPresen... | 42 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-8, 3, 13, 15, -6, 8],\n [0, 2, 0, 8, -10, -14],\n [0, 0, -11, 3, -12, 3],\n [0, 0, 0, 5, 11, -11],\n [0, 0, 0, 0, -11, 12],\n [0, 0, 0, 0, 0, 6]]\nRound your answer to the nearest integer.\... | 398 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, 11, -2, -13, 2, -10],\n [0, -10, -4, -15, -1, 8],\n [0, 0, 11, 2, 1, 11],\n [0, 0, 0, 13, 15, 2],\n [0, 0, 0, 0, 4, 15],\n [0, 0, 0, 0, 0, 15]]\n\nP... | -256 | MATH |
[
{
"content": "Find the value at position (5, 1) of the inverse of matrix 1/180 * A where A =\n[[-8, -2, 10, 8, 6, -8],\n [-2, -6, -8, -4, 4, 2],\n [10, -8, -5, 2, -8, 13],\n [8, -4, 2, 6, -5, 2],\n [6, 4, -8, -5, -1, 4],\n [-8, 2, 13, 2, 4, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in... | 16 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 3, 11, -15, -15, -1],\n [10, 8, 10, -11, -4, 8],\n [5, 9, 6, -15, 9, 2],\n [-6, -15, 1, -4, 1, -2],\n [7, -13, -7, -11, -6, 5],\n [-8... | 221 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[-11, 7, -14, 8, -6, 13],\n [11, -15, 13, 7, 13, 8],\n [13, 15, 2, 1, -12, -14],\n [-13, -... | 9 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[-12, -4, 7, -10, -8, 3],\n [-10, -7, 3, -12, -11, 4],\n [-7, 11, 11, 13, 13, 11],\n [-8, -5, 8, -14, 1... | 728 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 5) of the inverse. Round your answer to the nearest integer:\n[[0, -2, 2, -2, 0, 10],\n [-2, 1, 0, -8, 4, 11],\n [2, 0, -5, 2, -9, -4],\n [-2, -8, 2, 14, -5, 12],\n [0, 4, -9, -5, 3, -3],\n [10, 11, -4, 12, -3, 4]]\... | -1 | MATH |
[
{
"content": "Find the value at position (6, 2) of the inverse of matrix 1/180 * A where A =\n[[1, 4, 5, 6, -4, -4],\n [4, 1, 4, 12, 0, 4],\n [5, 4, -3, 2, 8, -8],\n [6, 12, 2, -9, 8, 0],\n [-4, 0, 8, 8, 3, -1],\n [-4, 4, -8, 0, -1, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex... | 15 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[11, 6, 8, 6, -6, 0],\n [6, -11, 2, 3, 4, 10],\n [8, 2, 5, -10, 0, -3],\n [6, 3, -10, -12, -4, 4],\n [-6, 4, 0, -4, -15, -10],\n [0, 10, -3, 4, -10, -8]... | -37 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, -3, 15, 3, 7, -11],\n [-13, -5, -4, 3, 4, -14],\n [6, -5, 14, 1, 14, -5],\n [-6, -7, 0, 12, 2, -6],\n [11, 1, 8, 1, -13, 2],\n [-12, -... | 255 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 9, 8, 7, -7, 11],\n [-6, -9, 1, 5, 5, 12],\n [12, -6, -11, -1, -14, 0],\n [15, 7, -12, -4, 8, -3],\n [-14, -13, -6, -9, -7, -4],\n [13, 7, 4, 13, ... | -206 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-12, 15, 10, 9, 5, 5],\n [10, -6, 8, 5, -2, -10],\n [-13, 14, -6, -9, 12, -11],\n [-2, -5, -9, -13, -4, 2],\n [7, 8, 10, -5, 9, -4],\n [3, 7, 13, 1, 1, -5]]\nRound your answer to the nearest integer.\n\n... | 668 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 4, 12, -4, 0, 0],\n [4, -12, 4, 3, -2, 8],\n [12, 4, -12, 1, 2, 2],\n [-4, 3, 1, -3, -8, 0],\n [0, -2, 2, -8, -8, -5],\n [0, 8, 2, 0, ... | 328 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 6, 13, -15, 15, 15],\n [6, 14, 5, -4, -15, 11],\n [-8, 11, -7, 2, -2, 14],\n [3, -6, -... | -117 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 2, -14, 2, 12, 7],\n [0, -13, 14, 6, 14, -9],\n [0, 0, 10, -12, -5, 4],\n [0, 0, 0, -2, -4, -6],\n [0, 0, 0, 0, ... | -108 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 15, 1, -3, 1, 5],\n [0, 10, -9, 3, -14, 13],\n [0, 0, 13, 13, -11, 12],\n [0, 0, 0, 14, 1, 2],\n [0, 0, 0, 0, 15, -8],\n ... | 215 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[11, 10, 10, -10, -11, -6],\n [10, -9, -6, 4, 2, -2],\n [10, -6, -11, 4, -2, -2],\n [-10, 4, 4, -6, -10, -2],\n [-11, 2, -2, -10, 1, 4],\n [-6, -2, -2, -2, 4, -5]]\nRound your answer to the nearest integer.\n\nPresent the a... | -92 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 15, -2, -3, 9, 12],\n [0, -8, -12, 11, -6, 11],\n [0, 0, -13, 13, 8, -2],\n [0, 0, 0, -2, 14, 12],\n [0, 0, 0, 0, -9, -3],\n [0, 0, 0... | 1041 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[2, 10, -5, -8, 2, -4],\n [10, -11, -6, 6, 4, 2],\n [-5, -6, 12, 1, -6, 4],\n [-8, 6, 1, 7, -4, 1],\n [2, 4, -6, -4, 15, 6],\n [-4, 2, 4, 1, 6, 10]]\n\n... | 1854 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -4, -6, 14, -14, -5],\n [0, 9, -9, 6, -3, -15],\n [0, 0, 6, -10, 14, 8],\n [0, 0, 0, 15, -11, 4],\n [0, 0, 0, 0, 15, ... | 143 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, -14, -8, 11, -8, 9],\n [3, 13, 12, -1, 5, 4],\n [4, -12, -13, 6, -6, 15],\n [-2, 15, 0, -13, 2, 5],\n [15, -12, -1, -10, -10, -4],\n [11, 2... | 50 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (6, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 8, -5, 8, -13, 12],\n [0, 3, 10, -6, -15, -9],\n [0, 0, 10, 6, 10, -14],\n [0, 0, 0, 15, 15, 12],\n [0, 0, 0, 0... | 0 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-2, -3, -6, -5, 9, -12],\n [-5, 10, 14, -13, -11, 3],\n [0, -7, -12, 9, 3, 10],\n [-1, 0, 7, -6, -11, 7],\n [-5, -9, 9, -5, 14, -4],\n [-10, -4, 2, -8, -1, 4]]\nRound your answer to the near... | -38 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[2, -1, 0, -5, -2, -9],\n [-1, 4, -6, 3, -11, -5],\n [0, -6, -7, 2, 6, 1],\n [-5, 3, 2, -1, -2, -2],\n [-2, -11, 6, -2, 4, -2],\n [-9, -5, 1, -2, -2, -1]]\n\nPresent the ... | 59 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 14, -1, 0, -2, -2],\n [14, -14, -4, 0, 6, 9],\n [-1, -4, 4, -12, -6, -4],\n [0, 0, -12, 6, -2, -8],\n [-2, 6, -6, -2, -7,... | 57 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -8, -4, -10, 0, 2],\n [-8, -5, -1, 0, 6, 6],\n [-4, -1, 8, -4, -14, 0],\n [-10, 0, -4, 12, 2, 3],\n [0, 6, -14, 2, -... | -44 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -10, -4, 12, 3, 3],\n [11, 6, -2, -3, -9, 10],\n [4, 3, 12, 14, -1, 1],\n [-1, -12, 8, 1, -9, 11],\n [-15, -4, -6, -8, -3, -7],\n [9, -10, 1, -1, 0, -6]]\n\nPre... | 203 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[2, 7, -11, -15, 5, 10],\n [-5, -10, -8, -2, -5, 9],\n [-10, -3, -3, 6, 4, -11],\n [10, 0, 8, -14, -10, 0],\n [4, 15, 8, 5, 9, 2],\n [1, -12, -1, 9, -2, -14]]\nRound your answer to the nearest integer.\n\nPres... | 46 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[9, -7, 13, 11, 11, 13],\n [0, 9, -11, -3, 15, 9],\n [0, 0, 5, 1, 6, -4],\n [0, 0, 0, -8, -5, 12],\n [0, 0, ... | 19 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -6, -13, 10, 13, 1],\n [3, -1, -5, -11, 7, -8],\n [1, -2, -13, -13, -5, -4],\n [-2, 5, 0, -11, 5, 8],\n [-15, -4, 12, -10, 10, -1],\n... | 232 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 2, -8, 0, 1, -2],\n [2, -3, 4, -10, 4, 1],\n [-8, 4, -5, 2, -1, -5],\n [0, -10, 2, -4... | 47 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[13, -12, -10, -15, 14, 13],\n [0, 4, 9, -6, 6, -15],\n [0, 0, -4, 11, 3, 5],\n [0, 0, 0, -4, -2, -7],\n [0, 0, 0, 0, 8, 3],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex forma... | -1395 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, 8, 11, 6, -14, 13],\n [10, 0, 11, -9, 1, -12],\n [6, -10, -13, 0, -7, -4],\n [-4, 14, 12, -15, 11, 1],\n [12, -8, 5, 4, 14, 14],\n [6, 15, 3, -7, 12, 11]]\nRound your answer to the nearest integer.\... | 195 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -11, -2, 13, -14, -5],\n [-4, 11, 6, -15, 9, -5],\n [11, 6, 0, -10, 2, -7],\n [-1, 9, -12, 13, -1, -14],\n [13, -5, -8, -2... | -17 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -14, 13, -5, 9, 9],\n [0, 5, -7, 0, 11, 6],\n [0, 0, 10, 1, -15, 10],\n [0, 0, 0, -4, -1, 15],\n [0, 0, 0, 0, 8, 5],\n [0... | 77 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-1, 10, -10, 5, 4, -1],\n [10, -13, -12, 4, 2, 1],\n [-10, -12, 12, 12, 8, 5],\n [5, 4, 12, 10, 7, -5],\n [4, 2, 8, 7, -7, 2],\n [-1, 1, 5, -5, 2, -1]]\nRound your answer to the nearest integer.\n\nPresent th... | 119 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 5) of the inverse. Round your answer to the nearest integer:\n[[3, -10, 10, -12, 3, 3],\n [-10, 14, -2, 8, -2, 3],\n [10, -2, 4, 8, 3, -12],\n [-12, 8, 8, -5, 0, 8],\n [3, -2, 3, 0, -5, 4],\n [3, 3, -12, 8, 4, -7]]\... | 19 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 5, 0, -12, 2, 2],\n [5, 6, 12, 2, -10, -7],\n [0, 12, -6, -4, -2, -2],\n [-12, 2, -4, -12, 6, -11],\n [2, -10, -2, 6, ... | -313 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/180 * A where A =\n[[-9, -4, 5, 0, 2, 2],\n [-4, 2, -3, 0, -2, 0],\n [5, -3, -6, -8, 6, -4],\n [0, 0, -8, -11, 8, 0],\n [2, -2, 6, 8, -6, 9],\n [2, 0, -4, 0, 9, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTe... | 2 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 2, 14, 0, 3, -11],\n [0, 4, -9, 3, 8, 1],\n [0, 0, -14, -7, 15, 14],\n [0, 0, 0, -7, -2, -10],\n [0, 0, 0, 0, 13, -9],\n [0, 0, 0, 0, ... | 1528 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 4, -6, -10, -8, -7],\n [10, -1, -6, -2, 4, 2],\n [13, -1, -12, -14, 1, -3],\n [0, -4, 1, 10, 8, 14],\n [2, 13, 8, 1, -5, -1],\n [7, 0,... | 570 | MATH |
[
{
"content": "Find the value at position (6, 3) of the inverse of matrix 1/180 * A where A =\n[[5, 4, -12, 9, -4, -6],\n [4, 0, 3, 12, -2, -6],\n [-12, 3, 12, 6, 2, -12],\n [9, 12, 6, -3, 2, 4],\n [-4, -2, 2, 2, -3, -8],\n [-6, -6, -12, 4, -8, -11]]\nRound your answer to the nearest integer.\n\nPresent the answ... | 15 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, 0, -2, 8, 1, -2],\n [0, -11, -4, -4, -5, 1],\n [-2, -4, 5, -3, 4, -7],\n [8, -4, -3, 0, 1, -4],\n [1, -5, 4, 1, -1, 6],\n [-2, 1, -7, -4, 6, 11]]\n\nPresent the... | 250 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 10, -6, -5, 12, -12],\n [0, 2, 12, -5, -14, -3],\n [0, 0, -13, 6, -13, 13],\n [0, 0, 0, 10, -4, 15... | 22184 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-3, 2, 8, 12, -14, 1],\n [-12, -2, -1, 12, 11, -6],\n [-2, -6, 8, -10, -2, -12],\n [12, 8, -2, 6, -11, -6],\n [13, 1, 7, 1, -4, -2],\n [-7, -12, 0, 12, 15, -3]]\nRound your answer to the nea... | 19 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[11, 11, -9, 12, 15, 1],\n [-11, -14, -4, -2, 12, 10],\n [15, -8, 6, 13, -11, 7],\n [9, -2, 10, -11, 11, -11],\n [7, 11, 13, -15, 1, 0],\n [-4, -11, 11, -5, -1, 8]]\n\nPresent th... | 33 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -2, 0, -7, -9, -15],\n [-2, 4, 6, -4, -2, 4],\n [0, 6, -1, 6, 6, -2],\n [-7, -4, 6, 3, 2, 3],\n [-9, -2, 6, 2, -4, 6]... | 23 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-12, -8, -1, 2, 4, 2],\n [-8, 4, 4, 6, 0, -6],\n [-1, 4, -9, 2, 6, 12],\n [2, 6, 2, -3, 12, 4],\n [4, 0, 6, 12, -14, 2],\n [2, -6, 12, 4, 2, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex fo... | 92 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -13, 9, -12, -7, -12],\n [-15, -9, 9, 13, 12, 1],\n [14, -13, 11, -3, 13, 6],\n [8, 3, -10, -15, -8, 10],\n [9, 3, 3, 1, ... | 41 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 1, 7, 8, -2, -6],\n [1, -14, -4, 6, 4, -1],\n [7, -4, 1, 5, -10, 0],\n [8, 6, 5, 4, 3, 4],\n [-2, 4, -10, 3, 14, 1],\n [-6, -1, 0, 4, 1, 8]]\n\nPresent t... | 42 | MATH |
[
{
"content": "Find the value at position (6, 3) of the inverse of matrix 1/180 * A where A =\n[[-5, -15, 9, 15, -14, -8],\n [0, -15, -12, 6, 0, -7],\n [0, 0, 4, -1, -9, -6],\n [0, 0, 0, -15, 5, 1],\n [0, 0, 0, 0, -7, -6],\n [0, 0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in ... | 0 | MATH |
[
{
"content": "Find the value at position (4, 3) of the inverse of matrix 1/180 * A where A =\n[[12, -15, 15, -9, 6, -10],\n [15, -12, -10, -12, 15, 14],\n [-9, 10, 10, -3, -11, -8],\n [1, 11, -3, 15, 13, 4],\n [-8, 10, 1, -5, -2, 10],\n [3, -13, 5, -11, 5, -13]]\nRound your answer to the nearest integer.\n\nPre... | -13 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -8, -15, 0, -11, 4],\n [0, 14, 4, -3, 3, -8],\n [0, 0, -1, -3, 11, 15],\n [0, 0, 0, 14, 10, 0],\n [0, 0, 0, 0, 13, 14],\n [0, 0, 0, 0... | 1239 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -3, 6, -7, 14, 1],\n [-2, 6, -10, 6, 15, -2],\n [6, 14, -1, -1, -11, 1],\n [12, -7, 14, 13, -7, 12],\n [14, 9, -8, 1, 12, ... | 31 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 1, -12, -7, 10, 2],\n [-12, 3, -7, 6, -8, 3],\n [-1, -1, -12, 14, -9, 10],\n [-13, 6, -1, -11, -8, ... | 315 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[7, -1, -12, 6, -2, 11],\n [15, 0, 1, -10, 0, 5],\n [-5, -3, -15, 8, 6, -5],\n [-13, 4, 9, -4, 10, 9],\n [7, 6, 1, 7, 8, 6],\n [13, -1, 14, -11, -7, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in La... | 25 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 2, -6, -2, -12],\n [0, -6, -15, 7, 13, 7],\n [0, 0, -8, -9, 8, -5],\n [0, 0, 0, 8, -13, -12],\n [0, 0, 0, 0, 10, 0]... | -1807 | MATH |
[
{
"content": "Find the inverse of 1/180 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[[3, 6, 12, -14, 15, -2],\n [0, -7, -6, 2, 1, 6],\n [0, 0, 14, -6, 1, -7],\n [0, 0, 0, 15, -4, -4],\n [0, 0, 0, 0, -5, -4],\n [... | 154 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[1, -6, 14, 11, -14, -8],\n [-12, -4, -12, -14, 0, -15],\n [-13, -5, 13, -10, 15, 5],\n [0... | 33 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-8, 0, -1, -2, 1, 1],\n [0, -3, -9, 5, 2, 8],\n [-1, -9, -5, 10, 6, 12],\n [-2, 5, 10, 2, -5, 3],\n [1, 2, 6, -5, 13, 10],\n [1, 8, 12, 3, 10, -6]]\nRound your answer to the nearest integer.\n\nPresent t... | 232 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, 6, 12, -9, 10, -5],\n [6, 13, 10, 3, 4, -6],\n [12, 10, 5, 8, -8, 2],\n [-9, 3, 8, 5, 8, 3],\n [10, 4, -8, 8, -12, -4],\n [-5, -6, 2, 3, -4, 1]]\n\nPresent the answer in LaTex for... | 67 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 2) of the inverse. Round your answer to the nearest integer:\n[[6, 6, 4, 14, -13, -2],\n [0, -9, 5, -10, 7, -5],\n [0, 0, -7, 12, -1, -11],\n [0, 0, 0, -3, 8, 2],\n [0, 0, 0, 0, -6, -8],\n [0, 0, 0, 0, 0, -2]]\n\nPr... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -2, 0, 13, -2, -2],\n [0, 13, -4, 11, -12, -9],\n [0, 0, 1, 2, -11, 9],\n [0, 0, 0, -10, -9, 10],\n [0, 0, 0, 0, 8, ... | 916 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[-11, 3, -5, -14, -5, -15],\n [-10, -11, 15, 4, 12, -11],\n [-5, -13, -12, -11, 9, 9],\n [... | 91 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[5, 12, -6, -3, 10, 11],\n [-12, 11, -2, 13, -9, -2],\n [12, 13, 2, 10, 14, -13],\n [5, -10, -14, -15, 13, -7],\n [-12, 6, -2, -13, -9, -2],\n [-15, -14, 4, 4, -10, 12]]\nRound your answer to... | 17 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[6, 5, 3, -9, -11, 4],\n [0, 2, -8, -2, 14, -13],\n [0, 0, 7, -10, -12, 7],\n [0, 0, 0, -3, -14, -5],\n [0, 0, 0, 0, 3, -8],\n... | -1889 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, 0, 12, 0, 13, -10],\n [0, -6, -4, 2, -9, -6],\n [12, -4, 11, -8, 2, 8],\n [0, 2, -8, 11, 5, 2],\n [13, -9, 2, 5, -3, 4],\n [-10, -6, 8, 2, ... | -209 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, 1, 11, -2, 9, -5],\n [0, 10, 14, -7, -8, 5],\n [0, 0, -7, 1, 13, 10],\n [0, 0, 0, 2, 15, -15],\n [0, 0, 0, 0, 13, 10],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format:... | -943 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -8, -11, 10, 7, 7],\n [-8, -12, 10, 1, -8, 0],\n [-11, 10, 7, -8, 11, -14],\n [10, 1, -8, 4, -6, 0],\n [7, -8, 11, -6, 10, -10],\n [7, 0, -14, 0, -10, 1... | -63 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -11, -4, -14, -15, 11],\n [0, -5, 12, -3, -3, 6],\n [0, 0, -12, -12, 11, 15],\n [0, 0, 0, -8, -5, 8],\n [0, 0, 0, 0, ... | 709 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 12, -4, 0, 11, 12],\n [5, 9, -13, -12, -3, -7],\n [-5, 6, 0, 15, 12, 6],\n [11, 9, -1, -7, 10, -12],\n [6, 10, 7, 13, -10, 4],\n [-14... | 158 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -14, 6, -12, -8, 1],\n [9, -8, -10, 3, 4, 0],\n [-14, 15, -6, 15, 5, -13],\n [-10, 10, -13, 0, -5, -10],\n [14, 4, -5, -3, 3, -2],\n [14, -4, 6, 5, 5, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer... | -23 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-5, -9, 0, 14, 14, -5],\n [0, 15, -3, 11, 9, -5],\n [0, 0, -15, 5, 3, 8],\n [0, 0, 0, -14, 2, -10],\n [0, 0, 0, 0, -10, 11],\n [0, 0, 0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex f... | 238 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-12, 9, 7, 8, 0, -2],\n [9, -5, 5, -9, -4, 6],\n [7, 5, 3, 6, -4, 10],\n [8, -9, 6, 2, 0, 0],\n [0, -4, -4, 0, -6, -10],\n [-2, 6, 10, 0, -10, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex f... | -498 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -5, 2, 4, 8, -6],\n [-5, -13, -8, 8, -4, -4],\n [2, -8, 6, -3, -10, 7],\n [4, 8, -3, 12, 0, 11],\n ... | 182 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-2, 11, 13, -10, -7, -4],\n [2, 1, -9, -12, 11, -5],\n [10, -4, -15, -15, 2, -12],\n [-3, 12, 5, 15, -10, 13],\n [13, 3, -2, 12, 11, 9],\n [14, 9, -15, -11, -4, -2]]\n\nPresent the an... | 24 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (5, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -4, -7, -2, -1, -3],\n [0, -3, -10, 8, -5, -4],\n [0, 0, -10, -7, -4, 15],\n [0, 0, 0, -8, -11, 6],\n [0, 0, 0... | 0 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[12, 8, -4, 10, -12, 2],\n [0, -4, 1, -4, 2, -13],\n [0, 0, 3, 3, -15, -4],\n [0, 0, 0, 12, 11, 8],\n [0, 0, 0, 0, 2, 9],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex f... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -10, 4, 14, -12, -8],\n [0, 6, -6, -15, -12, -1],\n [0, 0, -10, 2, -10, 1],\n [0, 0, 0... | -284 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-7, 0, -2, -10, -4, 5],\n [-7, -9, 10, -7, 13, 0],\n [-12, -1, 1, -4, 10, -6],\n [-8, 13, 10, 12, -2, -1],\n [-4, -7, -10, 0, 14, 11],\n [7, -3... | -18 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[10, -4, 0, 8, 8, 2],\n [-4, 7, 14, -1, -4, -12],\n [0, 14, 0, 4, -6, -6],\n [8, -1, 4, 4,... | 37 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, -11, 14, 15, 4, 15],\n [7, -15, -6, -14, 9, 1],\n [10, -6, 8, -10, 11, 6],\n [-12, -2, 2, -4, -4, -15],\n [-9, 12, 7, 4, -14, 15],\n [0, 7, ... | 20 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-8, 4, 1, -2, -2, 4],\n [4, -5, -5, -2, 9, -10],\n [1, -5, 9, 6, -5, -1],\n [-2, -2, 6, 11, 7, -4],\n [-2, 9, -5, 7, -6, 2],\n [4, -10, -1, -4, 2, 5]]\nRound your answer to the nearest integ... | -34 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -8, 2, 4, 9, -8],\n [-8, -12, -6, 1, -2, 0],\n [2, -6, -11, 0, 4, -7],\n [4, 1, 0, -2, -13, 4],\n [9, -2, 4, -13, -10, 4],\n [-8, 0, -7, 4, 4, 13]]\n\nPr... | 96 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -7, -8, -9, 4, 5],\n [0, 8, 13, 14, -11, -11],\n [0, 0, -13, -1, -5, 4],\n [0, 0, 0, -15, 14, -1],... | 486 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 1, -3, 5, -10, 4],\n [0, -7, -8, -4, -6, -15],\n [0, 0, 8, 5, -9, 15],\n [0, 0, 0, -13, -1, -11],\n [0, 0, 0, 0, -11, -2],\n [0, 0, 0, 0, 0... | -5 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[8, 11, 4, 3, -11, 1],\n [0, -5, 15, -9, -9, 3],\n [0, 0, -14, 2, -6, -6],\n [0, 0, 0, 7, 11, 12],\n [0, 0, 0, 0, -4, -10],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex... | -36 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[5, -7, 4, 0, 2, -6],\n [-7, 5, -11, 6, -3, -4],\n [4, -11, 9, -4, -9, -4],\n [0, 6, -4, -4, 9, 14],\n [2, -... | -920 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -8, 8, 6, -5, -6],\n [-8, -7, -6, -2, 13, -1],\n [8, -6, 15, 1, -8, 3],\n [6, -2, 1, 6, 2, 2],\n [-5, 13, -8, 2, 11, -6],\n [-6, -1, 3, 2, -6, -2]]\n\nPresent the answer in LaTex ... | 182 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 6, -2, 10, -13, 3],\n [0, 11, -7, -4, -15, 1],\n [0, 0, -11, 1, 15, -13],\n [0, 0, 0, -12, 14, 7],\n [0, 0, 0, 0, 9, 3],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the ... | 518 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-15, -7, -15, -7, -11, 6],\n [-7, 4, 10, -4, 8, -14],\n [-10, 12, 15, 13, 5, 0],\n [6, 12, -7, -15, -1, -6],\n [-5, -1, 14, 13, 5, 3],\n [1, 13, 0, 13,... | 65 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[8, 0, -11, 0, 0, -8],\n [0, 3, -10, 0, 2, -5],\n [-11, -10, -8, -2, -8, -1],\n [0, 0, -2, -2, -6, -8],\n [0, 2, -8, -6, 2, 10],\n [-8, -5, -1, -8, 10, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in... | -51 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, 8, 1, -3, 3, 5],\n [8, -6, 10, 4, -2, -6],\n [1, 10, 3, 4, 10, 5],\n [-3, 4, 4, 10, -3, -2],\n [3, -2, 10, -3, -5, -6],\n [5, -6, 5, -2, -6, 11]]\n\nPresent the ans... | -45 | MATH |
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