messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"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, 4, 13, -1, -5, -8],\n [0, 5, -9, 10, 3, 7],\n [0, 0, 8, 5, -12, -8],\n [0, 0, 0, 5, -14, 8],\n [0, 0, 0, 0, 12, 5],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the... | -798 | 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, 1, 11, 11, 15, -6],\n [0, 12, 0, -1, 14, 14],\n [0, 0, 3, -4, 7, 4],\n [0, 0, 0, 3, -9, 5],\n [0, 0, 0, ... | 211 | 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, 4, 12, -1, 12, -9],\n [-4, 13, -8, -1, -13, -2],\n [1, -12, 2, -8, -12, -14],\n [14, -10, 6, -6, -12, 6],\n [13, 15, 2, 10, -4, -14],... | 157 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[-1, -8, -2, 7, 12, 9],\n [0, -8, 5, 0, -3, 2],\n [0, 0, 8, 10, 9, 12],\n [0, 0, 0, -7, 13, -1],\n [0, 0, 0, 0, -7, 8],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex form... | -1340 | 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, -8, -13, -13, -15],\n [11, -11, -6, -9, 10, -7],\n [12, -9, -7, -8, -4, -14],\n [-15, 0, 7, 7, 14, 8],\n [-11, -13, -4, -8, 6, 11],\n [-13, -15, -13, -... | -29 | 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, -15, -11, 10, 7, 15],\n [-2, -9, 11, -7, -1, -1],\n [10, -6, 12, -3, 3, 15],\n [-9, 1, 4, 13, -12, 14],\n [-11, 7, -9, -3, -1, -5],\n... | 290 | 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, 12, -14, -6, -3, 14],\n [0, 5, -10, 12, 12, -4],\n [0, 0, 14, 14, -5, 10],\n [0, 0, 0, -9, 14, -15],\n [0, 0, 0, 0, 9, 4],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the ... | 1907 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[11, -7, 14, -11, -15, 3],\n [-6, -4, 8, -1, 11, 6],\n [8, -7, 4, 1, 14, 1],\n [10, 4, -4, 14, -9, -14],\n [-13, 1, -11, 1, 8, 1],\n [11, 1, -14, -14, 12, 6]]\nRound your answer to the neares... | -289 | 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[[7, -11, -15, -15, 3, 14],\n [-14, 5, -4, 10, -10, 7],\n [-12, 7, -5, 8, 11, 1],\n [15, -10, 8, -11, 4, -14],\n [-10, 6, -5, 15, 0, 0],\n [-15, -7, 12, 11, -10, 0]]\... | 343 | 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, -5, -2, 7, 10, -12],\n [-5, 10, -4, 4, 2, -2],\n [-2, -4, -7, -15, 0, 2],\n [7, 4, -15, -5, 14, 4],\n [... | 220 | 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, 4, 12, 1, -14, -15],\n [0, 14, -4, -11, -11, 11],\n [7, -7, -7, -13, 3, 0],\n [0, -13, 4, 8, 6, 8],\n [-15, 8, 4, -5, 1, -8],\n [-12, -10, -... | -16 | 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[[0, 14, 9, -13, 9, 13],\n [2, -2, 2, -14, 6, -13],\n [0, 13, -7, -12, -15, -12],\n [-15, -2, 5, 0, 4, 8],\n [-8, -9, -13, 1, -... | -23 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-2, 10, 2, 1, -1, 0],\n [10, -8, -2, 12, -6, 5],\n [2, -2, 12, 0, -10, -10],\n [1, 12, 0, 3, 0, -13],\n [-1, -6, -10, 0, 14, 12],\n [0, 5, -10, -13, 12, -7]]\nRound your answer to the nearest integer.\n\nPres... | 117 | 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[[-11, 8, 13, 1, -2, 5],\n [15, -13, 12, -15, 4, 15],\n [13, 5, 7, -15, -13, 2],\n [9, -6, 15, 6, 10, -13],\n [-8, -2, 8, 2, -1... | -167 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[10, 4, 1, -2, -2, -4],\n [4, 0, -11, 12, -10, 5],\n [1, -11, 2, 0, 0, 2],\n [-2, 12, 0, 9, -7, -2],\n [-2, -10, 0, -7, 0, 5],\n [-4, 5, 2, -2, 5, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in La... | -161 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[-14, 7, 15, 6, 3, 9],\n [0, 15, 14, 13, 6, 10],\n [0, 0, 1, 4, -6, -10],\n [0, 0, 0, 12, -11, -15],\n [0, 0, 0, 0, ... | -105 | 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[[-1, -13, 7, -8, 4, 0],\n [0, 2, 12, -6, 14, 3],\n [0, 0, 15, 3, 12, 10],\n [0, 0, 0, 10, 5, 14],\n [0, 0, 0, 0, 5, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent th... | 3323 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[4, 8, -4, 2, -13, 12],\n [0, -15, 13, 3, -5, -11],\n [0, 0, -15, -15, -8, -6],\n [0, 0, 0, -3, -4, 15],\n [0, 0, 0, 0, 2, -13],\n [0, 0, 0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresen... | 1746 | 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[[-6, 10, 14, -14, 3, -7],\n [-9, -12, 10, 5, 2, -3],\n [-5, 13, 8, -12, 9, 5],\n [13, 9, -12, -6, -11, -7],\n [8, -13, 1, -13, 0, -12],\n [... | 3235 | 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[[-11, 2, 8, 9, -5, 2],\n [2, -13, -2, 8, 2, 8],\n [8, -2, 0, 5, 1, 0],\n [9, 8, 5, -12, -6, 8],\n [-5, 2, 1, -6, -9, 11],\n [2, 8, 0, 8, 11, -1]]\n\nPresent the answer in... | -55 | 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[[1, 13, -10, -9, -2, -3],\n [0, -6, -7, 2, 11, 10],\n [0, 0, 13, -11, -10, 3],\n [0, 0, 0, -15, 6, 4],\n [0,... | 106 | 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[[-4, 4, -4, 2, -10, 11],\n [4, -9, 13, 0, -3, -1],\n [-4, 13, 14, 12, 8, 10],\n [2, 0, 12, -7, 2, -4],\n [-1... | -139 | 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[[5, -10, 10, -4, -3, -3],\n [0, -1, 5, 0, 6, 5],\n [0, 0, -11, -12, -13, 3],\n [0, 0, 0, -1, -7, 1],\n [0, 0, 0, 0, 5, 6],\n [0, 0, 0, 0, 0, -5]... | -340 | 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[[-4, -6, 0, -8, -10, -4],\n [0, 12, 5, -8, 10, 12],\n [0, 0, -8, 10, 12, 2],\n [0, 0, 0, -7, -12, 11],\... | 796 | 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[[-2, -13, 13, -10, 2, 3],\n [-11, -1, 9, -14, -6, 8],\n [14, 2, 11, -3, -11, 7],\n [8, -15, 6, -15, 2, -1],\n [1, -5, 5, 10, 15, 9],\n [6, 11, 11, 1, -3... | -21 | MATH |
[
{
"content": "Find the value at position (2, 6) of the inverse of matrix 1/180 * A where A =\n[[-14, -4, 1, 2, -7, 4],\n [-4, 7, -10, 8, 3, -7],\n [1, -10, -10, -12, 2, 2],\n [2, 8, -12, -6, -6, -4],\n [-7, 3, 2, -6, -2, 0],\n [4, -7, 2, -4, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the ans... | -4 | 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[[1, -8, -14, 12, 15, -8],\n [-9, 10, 10, -14, 6, 6],\n [-13, 11, 2, -4, -15, 6],\n [-4, -11, 14, 14, 11, 9],\n [1, 0, 15, -1, 7, -1],\n [-1... | 246 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-9, -12, 14, -3, -4, 5],\n [-12, 2, 0, -1, 6, 2],\n [14, 0, 4, 10, -10, -10],\n [-3, -1, 10, 14, 10, -2],\n [-4, 6, -10, 10, -12, 3],\n [5, 2, -10, -2, 3, 4]]\nRound your answer to the neare... | -96 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[8, -11, -14, -10, 5, -14],\n [-3, 14, -5, -5, 0, -5],\n [3, -1, 9, 7, 7, 0],\n [15, -5, 6, 0, -8, -12],\n [-8, -12, 8, 9, -13, -13],\n [11, 13, 2, 13, 10, 3]]\nRound your answer to the nearest integer.\n... | 178 | 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[[3, 5, -11, 2, 12, -6],\n [13, 6, 5, -10, -15, -11],\n [-7, -4, 10, -2, -14, 1],\n [-2, 10, -3, 11, -7, 10],\n [9, -1, 9, 6, -1, 8],\n [14, -5, 15, 0, 1... | 44 | 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, -12, -15, -8, 1, -13],\n [0, 4, -1, -1, 15, 8],\n [0, 0, 10, 12, 7, -2],\n [0, 0, 0, ... | -3787 | 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[[10, -2, -6, 6, -4, -2],\n [-2, -11, 2, -2, -11, 4],\n [-6, 2, 6, 4, 4, 1],\n [6, -2, 4, 4, 3, -13],\n ... | 943 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-8, 1, -4, 3, -6, -7],\n [0, -10, 4, 10, -14, 11],\n [0, 0, -3, -10, -11, 9],\n [0, 0, 0, 5, -10, -10],\n [0, 0, 0, 0, -5, 14],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in L... | 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[[7, -13, 3, 15, -8, -11],\n [0, 8, 15, -10, -14, 4],\n [0, 0, -12, -1, -10, 6],\n [0, 0, 0, -10, 3, 14],\n [0, 0, 0, 0, -8, 10],\n [0, 0, 0, 0, 0, 10]]\nRound your answer to the nearest integ... | -176 | 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, -12, 3, 4, -15, 4],\n [1, -4, -1, -15, 10, -2],\n [-10, -11, 14, -5, 15, -12],\n [-3, -5, -13, -15, -10, 2],\n [8, -6, -11, 7, -6, -4],\n [-14, -3, -8, -14, 4, -... | 515 | 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[[15, -11, -7, 1, -7, -5],\n [-1, 8, -10, 7, -13, 14],\n [15, 1, -11, 14, 12, -4],\n [2, -2, 5, 8, -5, -7],\n [-14, -4, -13, -13, -15, -8],\n [6, 12, 13, -8, -... | -10 | 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[[-11, -2, 12, 14, -13, 5],\n [-11, -11, 3, 11, -2, 10],\n [14, -12, 9, -3, -6, 9],\n [2, -8, -8, -9, -8, -2],\n [3, 13, -10, -15, 7, 15],\n [-1, -15, 9, 1, -15, -1]]... | 307 | 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, -14, -2, 5, -8, -8],\n [0, -9, 3, -10, -10, -13],\n [0, 0, -8, -6, 4, -1],\n [0, 0, 0, 4, 14, -9],\n [0, 0, 0, 0, 9, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex for... | 219 | MATH |
[
{
"content": "Find the value at position (4, 5) of the inverse of matrix 1/180 * A where A =\n[[-12, 0, -8, -4, -12, 7],\n [0, -15, -3, 2, -4, 9],\n [-8, -3, -3, 0, 0, -2],\n [-4, 2, 0, -11, 0, -6],\n [-12, -4, 0, 0, 11, 12],\n [7, 9, -2, -6, 12, -5]]\nRound your answer to the nearest integer.\n\nPresent the an... | -2 | 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[[11, -11, 4, -5, 14, -6],\n [0, -10, -10, -8, 7, -1],\n [0, 0, -5, -4, 10, -3],\n [0, 0, 0, 9, -15, -1],\n [0, 0, 0, 0, -4, -12],\n [0, 0, 0, 0, 0, -8]]\n\nPr... | -3 | MATH |
[
{
"content": "Find the value at position (3, 6) of the inverse of matrix 1/180 * A where A =\n[[15, -6, 1, 12, 15, 10],\n [0, 6, 3, 13, -2, -8],\n [0, 0, -5, 7, -15, -2],\n [0, 0, 0, -2, -12, 6],\n [0, 0, 0, 0, 6, 7],\n [0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaT... | -440 | 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[[5, -7, -6, 4, 9, 5],\n [10, -7, -13, 15, 4, 9],\n [10, -5, -10, -14, -9, 2],\n [11, -14, 11, 1, -5, 11],\n [-4, 11, 3, 6, 8, 9],\n [-9, 4, -10, 5, 8, -15]]\n\nPresent th... | -119 | 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, 13, 15, -5, 6, 10],\n [12, 2, 5, 1, -9, 1],\n [4, -7, 1, 4, 6, 6],\n [12, 15, 13, -8, 1, -9],\n [-15, -3, 14, 7, 3, 11],\n... | -21 | 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[[-3, 13, 14, 0, -8, 3],\n [0, -15, -2, 3, -1, 2],\n [0, 0, 12, 1, 2, 14],\n [0, 0, 0, -12, -15, -8],\n [0, 0... | -76 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[7, 12, 2, -9, 13, -8],\n [0, 9, 7, -13, 8, 7],\n [0, 0, 13, -8, 6, 9],\n [0, 0, 0, 3, -15, 12],\n [0, 0, 0, 0, 8, -2],\n [0, 0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format:... | 183 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (5, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 6, 5, -2, 15, 7],\n [0, 2, -9, -6, -9, -15],\n [0, 0, 3, 0, 13, 3],\n [0, 0, 0, 2, -14, -15],\n [0, 0, 0, 0, -... | 0 | 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[[-11, -3, -7, 12, -3, -2],\n [-3, -4, -2, 1, 4, -2],\n [-7, -2, 1, 0, 4, 0],\n [12, 1, 0, 1, -3, 4],\n [-3, 4, 4, -3, -14, 2],\n [-2, -2, 0... | 535 | 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, -12, 10, 10, 13, -3],\n [0, 7, -11, -5, -10, 2],\n [0, 0, -12, -7, -10, -14],\n [0, 0, 0, -10, 10, -4],\n [0, 0, 0, 0, 5, 11],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the... | -74 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, -3, 9, 5, -9, -6],\n [-3, 1, 10, 5, 12, 14],\n [10, -2, -14, 12, 6, -5],\n [-15, 3, 5, -12, 3, 10],\n [13, 5, -5, -8, -5, -12],\n [1, 11, -9, -8, -13, 6]]\nRound your answer to the nearest integer.\n\nPresent the answe... | 124 | 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, -2, 2, 11, 8, 4],\n [-2, 8, -6, 10, -13, -8],\n [2, -6, -13, 0, 0, 5],\n [11, 10, 0, -5, -10, 3],\n [8, -13, 0, -10, -7, -6],\n [4, -... | 322 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[-6, 9, -9, -13, -13, 2],\n [-11, -4, -4, 3, 14, -10],\n [-14, -4, 3, -11, -4, 11],\n [11, 1, 13, 1, -6, 9],\n [7, 1, -1, -4, 14, 0],\n [8, 3, -8, 15, 5, 1]]\n\nPresent the answe... | -8 | 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[[7, -11, 6, 0, -10, -8],\n [9, 2, 9, -4, -1, 11],\n [10, -7, -3, 10, -1, -6],\n [0, -9, 1, 7, 10, 5],\n [6, 10, -9, -2, -1, 5],\n [-9, -7, 3, 0, -8, 2]]\n\nPresent the answer in ... | 7 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[11, 7, 13, 2, 15, 14],\n [0, -9, -13, 2, 11, -6],\n [0, 0, -2, 15, 8, -13],\n [0, 0, 0, -14, -13, -11],\n [0, 0, 0, 0, 7, -4],\n [0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent... | 1399 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[6, 9, -3, 2, -15, 0],\n [0, -6, -4, 14, -14, 7],\n [0, 0, -14, 14, 11, 7],\n [0, 0, 0, -13, 11, -9],\n [0, 0, 0, 0,... | 0 | 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[[-4, -1, 9, -6, 14, 9],\n [0, -9, 4, -11, -15, 14],\n [0, 0, -3, -2, 8, 14],\n [0, 0, 0, 14, -11, 9],\n [0, 0, 0, 0, -1, -7],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer... | -337 | 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[[11, 10, -11, 13, -11, -5],\n [0, -10, -9, 8, 15, -2],\n [0, 0, 14, -3, -14, 9],\n [0, 0, 0, 11, -8, 4],\n [0, 0, 0, 0, 3, -3],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answ... | 106 | 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, 1, 10, -13, 8, -10],\n [0, -11, 6, -1, 7, 1],\n [0, 0, 4, 10, 1, 13],\n [0, 0, 0, 2, 2, 14],\n [0, 0, 0, 0, -10, -3],\n [... | -507 | 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[[-2, -11, -14, -5, -7, 8],\n [-13, 11, 12, 13, -7, -13],\n [9, -14, -4, -6, -7, -1],\n [-8, 9, -11, -5, 11, -14],\n [8, 12, -1, -10, -8, 11... | 201 | 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[[12, 0, 0, 2, -2, 4],\n [0, 2, 1, 4, 8, 12],\n [0, 1, -13, 2, -4, -7],\n [2, 4, 2, -3, -12, -8],\n [-2, 8, -4, -12, 12, -9... | 177 | 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[[-3, 9, 5, -6, -12, 15],\n [0, -10, 12, -9, -11, -5],\n [0, 0, 9, 3, 15, 7],\n [0, 0, 0, 5, 14, -9],\n [0, 0, 0, 0, -2, -3],\n [0, 0, 0, 0,... | 3817 | 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[[11, 1, -7, 1, -8, 15],\n [-14, 12, 8, -3, -13, 0],\n [-10, 3, 14, -9, -6, -7],\n [-14, 15, 12, 12, -1, 14],\n [-11, 13, 6... | -51 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[1, -6, 6, -15, 6, 10],\n [8, 11, 2, 2, -2, -1],\n [13, -4, -12, 11, -13, 4],\n [13, -4, -9, 13, -5, -15],\n [-10, -1, -1, 3, -5, 10],\n [7, 10, -14, -2, -14, 13]]\nRound your answer to the nearest integer.\n\nPresent the a... | -792 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-12, 1, -13, -3, -7, -9],\n [-1, 7, 13, 13, -5, 4],\n [-14, -1, -2, 4, 6, -5],\n [11, -13, 1, 14, -4, 8],\n [12, 13, 5, -1, 0, -11],\n [11, 4, -10, 3, 9, -11]]\n\nPresent the an... | -13 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[-13, 11, -15, 10, 12, -10],\n [-1, -14, 13, -13, 1, 9],\n [8, -4, 2, -1, -4, 0],\n [11, -8, 12, -2, 9, 1],\n [13, 5, -8, -1, 11, -2],\n [2, 4, -9, -13, 13, -4]]\n\nPresent the a... | 8 | 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[[5, 8, 12, 10, -13, 4],\n [-2, -1, 9, 14, -2, -9],\n [1, 14, -4, 4, -12, -7],\n [-10, 0, 9, 12, 15, 6],\n [6, 5, 5, -14, 8, -8],\n [-5, -3, 1, -8, 5, 2]... | -24 | 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[[14, 2, -2, -1, 15, -10],\n [-5, -3, 9, -15, 12, -10],\n [-7, -8, -5, 6, 3, 8],\n [-7, 1, -4, 9, -2, -1],\n [0, 6, 6, 12, 4, -15],\n [-6, -8, 2, 12, -15, -14]... | -37 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-15, -15, -7, -3, 14, -15],\n [0, 4, 10, 6, -9, -14],\n [0, 0, 10, -2, 10, 2],\n [0, 0, 0, 7, -4, 1],\n [0, 0, 0, 0, 11, -10],\n [0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest intege... | -195 | 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[[2, 5, -8, 1, -2, 9],\n [5, 4, 4, 2, 12, 6],\n [-8, 4, 4, 5, -9, -2],\n [1, 2, 5, 15, -8, 6],\n [-2, 12, -9, -8, -5, 0],\n [9, 6, -2, 6, 0, 9]]\n\nPrese... | 162 | 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, 3, 10, 3, 7, -2],\n [0, -3, -8, 13, 7, 5],\n [0, 0, -4, 2, -10, 2],\n [0, 0, 0, 8, -7, 11],\n [0, 0, 0, 0, -13, 13],\n [0, 0, 0, 0, 0, -9]]\n\nPresent th... | -346 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-4, 1, 14, 5, 15, 10],\n [13, 8, 4, -11, -12, 12],\n [-4, 14, 4, 12, 8, 2],\n [1, 3, -7, -12, 10, 5],\n [-14, -12, -14, -1, -14, -12],\n [-10, -9, -6, 3, 3, 10]]\nRound your answer to the ne... | -15 | 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, 13, -4, -13, -3, 2],\n [-8, 5, -1, -15, -13, 10],\n [-8, -12, 0, 14, 7, -6],\n [-4, -2, -2, -14, 7,... | 387 | 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[[9, 4, -14, -9, -10, 1],\n [11, 9, 9, 12, -14, -13],\n [-11, -11, 15, -15, -8, -4],\n [8, -12, -3, 7, -1, 15],\n [-5, -6, -13, 6, -2, 0],\n [-6, 13, -6, -4, 14, -7]]\n\nPresent t... | -3 | 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[[-15, -11, 4, -8, -5, -4],\n [-15, 9, 6, 4, 12, 9],\n [-5, -11, -1, -11, -4, -11],\n [1, 1, 8, -4, 8, 12],\n [-1, -1, -10, -4, 11, 13],\n [4, 2, -2, -14, -7, 15]]\n\nPres... | 11 | 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[[-11, 4, 10, 13, -15, 7],\n [-13, -10, -11, 5, 11, -11],\n [-15, 1, 3, -2, -4, -6],\n [4, 5, 2, 8, 11, -5],\n [14, -14, 9, 2, 13, 9],\n [-9, 15, 8, -1, -5, 2]]\n\nPresent the answer in... | 25 | 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[[7, -4, -10, 4, 7, 14],\n [0, 4, 0, 2, -6, 12],\n [0, 0, 2, 5, -15, 7],\n [0, 0, 0, -11, -1, 6],\n [0, 0, 0, 0, 7, 10],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the a... | -7666 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -8, -1, -8, 1, -4],\n [0, -8, 9, -2, -12, -15],\n [0, 0, 15, 0, -2, 5],\n [0, 0, 0, 10, 14, 12],\n [0, 0, 0, 0,... | 18 | 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[[-3, 15, -7, -5, -12, -14],\n [13, -10, -2, -12, -10, 3],\n [-10, -14, 2, -3, -7, 7],\n [3, -3, -5, -15, 8, 14],\n [6, -9, 9, 5, -1, -15],\n [-4, 10, -9... | -39 | 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, 0, -11, -6, 5],\n [0, -4, -6, -2, -8, -8],\n [0, -6, -2, 0, -1, -6],\n [-11, -2, 0, 10, -2, -7],\n [-6, -8, -1, -2, 13, 5],\n [5, -8, -6, -7, 5, -11]]\n\nPre... | 1121 | 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[[-1, -4, -12, -1, -5, 0],\n [7, -10, -2, 2, -4, 11],\n [-5, -3, 5, 7, -5, 7],\n [0, -1, 5, 12, -1, 9],\n [-12, -5, 3, -1, -12, 5],\n [-3, 6, 3, -14, -2, 13]]\n\nPres... | 1969 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-12, 0, 5, 4, -2, 11],\n [13, -1, 12, -13, -8, 0],\n [-6, -12, 14, 2, -14, 1],\n [-3, -12, 10, 9, 14, -5],\n [-9, 15, -4, -6, -9, -3],\n [15, -9, 15, 8, 1, -6]]\nRound your answer to the nea... | 12 | 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[[13, 0, 2, -3, 7, -2],\n [0, -9, 0, -4, -6, 10],\n [2, 0, -1, 8, -2, 0],\n [-3, -4, 8, 6, 3, -8],\n [7, -6, -2, 3, 8, 9],\n [-2, 10, 0, -8, 9, 0]]\n\nPresent the answer i... | 103 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 6) rounded to the nearest integer?\n[[1, 10, 11, -11, -12, 2],\n [0, 3, -12, 12, -9, -6],\n [0, 0, 3, -12, -6, -15],\n [0, 0, 0, -1, 1, -13],\n [0, 0, 0, 0, 5, 1],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaT... | 15 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-9, -5, -6, -7, -2, -3],\n [13, 9, 14, 9, -14, -13],\n [-9, 5, 2, -13, -6, 6],\n [13, -9, -7, 1, -5, -9],\n [8, 12, -2, 3, -12, 10],\n [-10, -6, -9, -3, -2, -12]]\nRound your answer to the nearest intege... | 659 | 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[[-8, -11, -15, -12, -13, -7],\n [-8, -15, 11, -10, -7, -9],\n [-12, -3, 1, 12, -14, 12],\n [-11, -4, 11, 5, -8, -10],\n [-8, 2, -13, 6, -4, 13],\n [10, -13, 6... | -14 | 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[[14, -3, 7, 12, 3, -8],\n [0, -11, 4, -8, 8, -4],\n [0, 0, 14, 5, 4, -10],\n [0, 0, 0, -9, -15, 5],\n [0, 0, 0, 0, -14, 13],\n [0, 0, 0, 0, 0, -... | -84 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (4, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -7, 5, -14, 11, 9],\n [-7, -15, -5, -13, 4, 14],\n [7, 10, -12, 2, 7, -10],\n [-13, 6, -5, -1, 6, 12],\n [-11,... | 14 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[8, -6, 14, -2, -10, -13],\n [0, -9, 4, -2, -7, -1],\n [5, -13, -14, 11, -14, -13],\n [2, -2, 4, 2, -6, 9],\n [-14, 9, 13, 6, -15, -12],\n [15, -2, -15,... | -12 | 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[[-2, 13, 4, -13, -13, -7],\n [0, 9, -3, 5, -14, -8],\n [0, 0, -12, 9, -1, -12],\n [0, 0, 0, 12, -3, 15],\n [0, 0, 0, 0, 12... | -38 | 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, -6, 8, 5, 0, 2],\n [-6, -6, 11, -6, 14, 4],\n [8, 11, 15, 0, -2, -11],\n [5, -6, 0, -13, 4, -10],\n [0, 14, -2, 4, -9,... | -621 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 5) of the inverse. Round your answer to the nearest integer:\n[[-8, 1, -11, -9, 12, 4],\n [0, 4, -12, 12, -10, -9],\n [0, 0, -11, 4, 15, 14],\n [0, 0, 0, 11, 12, 6],\n [0, 0, 0, 0, 6, -11],\n [0, 0, 0, 0, 0, 5]]\n\n... | 74 | MATH |
[
{
"content": "Find the value at position (5, 5) of the inverse of matrix 1/180 * A where A =\n[[6, 0, 2, 4, -2, 7],\n [0, 8, 0, -11, -2, 1],\n [2, 0, 2, -3, 0, 8],\n [4, -11, -3, -12, 8, 0],\n [-2, -2, 0, 8, 5, -4],\n [7, 1, 8, 0, -4, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaT... | 34 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[4, -4, 8, 5, -4, 0],\n [-4, 13, -1, 3, 2, -7],\n [8, -1, -3, -3, -11, 3],\n [5, 3, -3, -15, -10, 12],\n [-4, 2, -11, -10, 2, 2],\n [0, -7, 3, 12, 2, 7]]\nRound your answer to the nearest integer.\n\nPres... | 761 | 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[[-14, -8, 11, 6, -8, 1],\n [-1, 1, 12, 7, 8, -3],\n [3, -11, -4, -15, 7, -11],\n [-8, -3, -8, 9, 7, -5],\n [-15, -3, 3, 8, -13, 8],\n [1, -11, 4, 5, -8, 10]]\n\nPresent t... | 91 | 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[[15, -2, -12, -5, 4, -1],\n [3, -9, 3, 12, 3, -5],\n [10, -11, -11, 14, 6, -8],\n [-6, -10, -1, 0, 12, 1],\n [15, -8, -8, 9, -7, -14],\n [-1, 2, -13, 1, -12, 14]]\n\nPres... | -26 | 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, 2, -10, -5, 2, 8],\n [2, 14, 6, 4, -6, -1],\n [-10, 6, 11, 4, -8, 8],\n [-5, 4, 4, 0, 6, -11],\n [2, -6, -8, 6, -8, 6],\n [8, -1, 8, -11, 6, -2]]\n\nPre... | -578 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[12, 12, 5, 4, 4, -2],\n [12, 4, 6, -6, 4, -2],\n [5, 6, 5, -6, 4, 3],\n [4, -6, -6, -4, 4, -2],\n [4, 4, 4, 4, 5, 2],\n [-2, -2, 3, -2, 2, 7]]\n\nPrese... | -30 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, -5, 6, 6, -5, 9],\n [0, 12, 13, -3, 2, -14],\n [0, 0, -1, 4, 11, 2],\n [0, 0, 0, 7, 8, -4],\n [0, 0, 0, 0, 13, -15],\n [0, 0, 0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the an... | 3474 | 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[[13, 14, -9, -4, -1, 9],\n [-11, -1, -8, -6, 10, 0],\n [-8, -15, -4, -11, -13, -15],\n [-12, -8, -13, -6, -14, -5],\n [9, -6, 5, -2, -9, 11],\n ... | 13 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[4, -12, 6, -6, 10, 10],\n [6, -4, 1, -2, -2, 9],\n [-14, 5, 9, 4, -5, 0],\n [3, 15, 7, -10, 8, 3],\n [-11, 10, -12, -1, 13, -12],\n [4, -6, 8, 6, -13, 10]]\nRound your answer to the nearest integer.\n\nPresen... | 40 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-11, -10, 5, 6, -8, -9],\n [5, -6, -10, -2, -12, 12],\n [9, -3, 4, 1, 7, -9],\n [-12, 13, -2, -13, 8, -11],\n [0, 10, 7, 4, -12, 8],\n [14, 8, -14, 14, 2, 3]]\nRound your answer to the neare... | 14 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.