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[[7, -8, -2, -2, 4, 9],\n [-8, 14, 5, -8, 0, -2],\n [-2, 5, -7, 2, -2, -6],\n [-2, -8, 2, -14, -8, -9],\n [4, 0, -2, -8, -3, 2],\n [9, -2, -6, -9, 2, 10]]\n\nP... | -1491 | 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, -2, -1, 4, 14, 0],\n [-2, -2, -8, 3, 5, 4],\n [-1, -8, 7, 5, -1, 8],\n [4, 3, 5, -1, 0, 6],\n [14, 5, -1, 0, -14, 4],\n [... | 41 | MATH |
[
{
"content": "Find the value at position (5, 5) of the inverse of matrix 1/180 * A where A =\n[[-5, 6, -14, 10, 13, 14],\n [0, -13, 15, -14, -9, -12],\n [-6, 13, -15, 9, -5, 0],\n [5, -9, -7, -10, -8, -14],\n [-15, -13, -13, -2, -14, 10],\n [0, -14, -11, 3, 2, 1]]\nRound your answer to the nearest integer.\n\nP... | -7 | 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, -7, -12, -9, 0, -9],\n [12, -13, 1, -1, 3, -15],\n [-5, -15, 5, 2, 8, 8],\n [1, 15, 8, -12, 0, 0],\n [9, 3, -3, 14, 10, -3],\n [10, 9, 2, -4, -1, -5]]\nRound your answer to the nearest ... | -39 | 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[[5, -2, -4, 6, 2, 0],\n [-2, -13, 0, -8, -5, -11],\n [-4, 0, -14, -10, 5, 5],\n [6, -8, -10, -2, 0, -6],\n [2, -5, 5, 0, -... | 265 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[10, -14, -1, 3, -2, 6],\n [-14, -2, 5, -8, 6, 6],\n [-1, 5, -13, 8, 8, 8],\n [3, -8, 8, 3, 3, 0],\n [-2, 6, 8, 3, -3, 4],\n [6, 6, 8, 0, 4, 11]]\nRound your answer to the nearest integer.\n\... | -15 | 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, -8, -3, 3, -6],\n [5, 0, -2, -4, 8, 4],\n [-8, -2, 13, -4, 10, 4],\n [-3, -4, -4, -4, 0, 12],\n [3, 8, 10, 0, -6, 8... | 24 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[8, -3, 2, 5, -4, 3],\n [-3, -8, 1, 12, -6, -6],\n [2, 1, -1, 6, 4, -1],\n [5, 12, 6, -6, 4, 3],\n [-4, -6, 4, 4, -12, 8],\n [3, -6, -1, 3, 8, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex f... | 100 | 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, 15, -12, -2, -3, -11],\n [0, 9, -2, -6, -6, 4],\n [0, 0, 1, 13, -12, 0],\n [0, 0, 0, 6, 0, -7],\n [0, 0, 0, 0, -3, 0],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answ... | 4713 | 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, 0, -1, 4, 9, -10],\n [0, -4, 4, -5, 0, 7],\n [-1, 4, 5, -8, 2, 4],\n [4, -5, -8, -5, 2, 10],\n [9, 0, 2, 2, 8, 6],\n [-10... | -20 | 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, -10, 5, 0, 8, 5],\n [-10, 12, -12, 0, -6, 6],\n [5, -12, -2, -2, -4, -2],\n [0, 0, -2, -10, -8, 8],... | 548 | 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, 4, -15, 3, 6, -6],\n [0, 2, 3, -12, 12, 6],\n [0, 0, -4, -3, 5, -9],\n [0, 0, 0, -4, -7, 8],\n [0, 0, 0, 0, -14, 7],\n [0, 0, 0, 0, 0,... | 4238 | 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[[10, -15, -2, -10, 11, 5],\n [0, 6, 7, -5, 9, -12],\n [0, 0, 5, 8, -8, 3],\n [0, 0, 0, 6, -13, 8],\n [0, 0, 0, 0, -15, 2],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex ... | -42 | 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[[-14, -1, -1, -7, 6, 1],\n [-1, -1, 8, -10, 6, -8],\n [-1, 8, 14, 6, -2, -4],\n [-7, -10, ... | 23 | 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, 3, -12, 10, -7, -4],\n [0, 15, -3, -4, -7, -8],\n [0, 0, 14, -5, 15, -9],\n [0, 0, 0, -9, -12, 13],\n [0, 0, 0, 0, -1... | 126 | 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[[-1, 8, -8, 7, 0, 2],\n [8, 9, 14, -2, 8, -1],\n [-8, 14, 3, -4, 5, -8],\n [7, -2, -4, -14, -10, 2],\n [0, 8, 5, -10, 7, 4],\n [2, -1, -8, 2, 4, -14]]\n\nPresent the answ... | 22 | 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[[-13, 2, -5, 2, -1, 3],\n [2, 2, -6, -2, -6, -4],\n [-5, -6, -8, -10, 12, 10],\n [2, -2, -10, -3, -6, -8],\n [-1, -6, 12, -6, -12, -2],\n [3, -4, 10, -8, -2, ... | -40 | 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, 11, 12, -2, -12, 9],\n [0, -10, 15, 3, 4, 5],\n [0, 0, 4, 12, -13, 9],\n [0, 0, 0, -9, 3, 6],\n [0, 0, 0... | 185 | 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[[-4, 9, -3, -5, -12, -10],\n [9, -13, 1, 0, 12, 2],\n [-3, 1, 9, -6, 3, 1],\n [-5, 0, -6, -11, 8, 4],\n [-12, 12, 3, 8, 8, 4],... | -19 | 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[[9, 12, 3, -5, 3, -2],\n [12, 2, -8, -12, -4, 10],\n [3, -8, -3, 0, 5, 0],\n [-5, -12, 0, ... | 157 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[15, -8, -14, 0, 15, -12],\n [0, 14, -2, 1, 4, 4],\n [0, 0, 2, 12, -5, 13],\n [0, 0, 0, 8, -4, 15],\n [0, 0, 0, 0, -3, 10],\n [0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the ans... | 59 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[3, 7, 1, 8, 3, 15],\n [7, -9, 6, 14, -3, -5],\n [14, 14, 10, -15, -7, 10],\n [-6, -10, 4, -3, 0, 11],\n [-13, -1, 3, -5, -12, 7],\n [-11, 15, 11, 3, 14, -8]]\nRound your answer to the nearest integer.\n\... | 129 | 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[[-3, -7, -4, -6, 4, 4],\n [-7, 11, 8, 2, 11, -5],\n [-4, 8, 7, 3, 8, 9],\n [-6, 2, 3, -8, -14, -6],\n [4, 11, 8, -14, 5, -8],\n [4, -5, 9, -6, -8, -14]]... | 7 | 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, -14, 4, 4, 4, 4],\n [-14, -15, 13, 0, 2, -4],\n [4, 13, 15, 1, -4, -6],\n [4, 0, 1, 12, -4, -10],\n [4, 2, -4, -4, -4, 7],\n [4, -4, -6, -10, 7, -11]]\n... | 148 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-13, -7, 10, 13, -7, -1],\n [0, -2, 12, -15, 12, -10],\n [0, 0, 14, 6, -8, 6],\n [0, 0, 0, 7, 13, 2],\n [0, 0, 0, 0, 13, 6],\n [0, 0, 0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex... | 203 | 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[[10, 13, -10, 8, 6, 8],\n [13, 0, 0, -2, 4, -1],\n [-10, 0, -13, -8, -9, 2],\n [8, -2, -8, -10, -7, 2],\n [6, 4, -9, -7, 14, -4],\n [8, -1, 2, 2, -4, 7]]\n\nPresent the a... | -273 | 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, -14, -10, 5, -3, 15],\n [1, 4, -5, -8, -6, -1],\n [-1, 6, 10, -14, -2, 5],\n [6, 2, -14, -4, -2, 13],\n [-9, -12, 3, 6, 9, -10],\n [-1, 3, 15, -3, 0, 7]]\nRound your answer to the neare... | -190 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 6) rounded to the nearest integer?\n[[-7, -9, -4, 12, 9, 14],\n [0, 11, 1, 3, -11, 0],\n [0, 0, -4, 13, 2, 7],\n [0, 0, 0, 11, 15, 15],\n [0, 0, 0, 0, -1, 11],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex f... | 132 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-12, -4, -2, 6, 2, -6],\n [-4, 5, 10, -2, -8, -2],\n [-2, 10, -13, -2, -4, -12],\n [6, -2, -2, -5, -6, -2],\n [2, -8, -4, -6, -7, 6],\n [-6, -2, -12, -2, 6, -14]]\nRound your answer to the nearest integer.\n\... | 9 | 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, -2, 0, -5, 4, 9],\n [-2, 3, -2, -1, 2, 10],\n [0, -2, 2, -12, 3, -2],\n [-5, -1, -12, -2, 11, 4],\n [4, 2, 3, 11, 11, -6],\n [9, 10, -2, 4, -6, 12]]\n\nPresent the ... | -229 | 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[[5, -11, 14, 4, 8, -9],\n [0, 10, -8, 4, 7, 3],\n [0, 0, 12, 4, -13, 11],\n [0, 0, 0, 3, -5, 12],\n [0, 0, 0, 0, -14, 10],\n [0, 0, 0, 0, 0, -9]]\n\nPresent t... | 11 | 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[[0, 5, 13, 7, 11, 4],\n [15, -2, 1, -9, -9, 14],\n [-10, 1, 14, 7, 4, -1],\n [10, -1, -2, 2, -3, -9],\n [13, 12, -7, 5, -14, -11],\n [1, 0, 7, 6, -12, -4]]\n\... | 1 | 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, 6, -2, -2, -12],\n [-2, 13, 3, -8, 10, -7],\n [6, 3, -15, -4, 2, 8],\n [-2, -8, -4... | 84 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 1) rounded to the nearest integer?\n[[10, -2, -2, -8, 4, 12],\n [-2, -3, -8, 2, 0, -2],\n [-2, -8, -7, -13, -6, 12],\n [-8, 2, -13, 13, -2, -12],\n [4, 0, -6, -2, 1, 2],\n [12, -2, 12, -12, 2, 11]]\n\nPresent the an... | 40 | 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, -15, -11, -9, 11, 13],\n [0, -7, 9, 2, -8, 3],\n [0, 0, -4, -11, 2, -5],\n [0, 0, 0, 10, 13, -6],\n [0, 0, 0, 0, -2, 14],\n [0, 0, 0, 0, 0, 13]]\n\nPresen... | -809 | 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[[5, -4, 6, -12, 6, 6],\n [4, -1, -8, 5, -5, -4],\n [0, 2, -8, -11, 2, 2],\n [12, 8, -3, 1, 8, -8],\n [7, -5, -11, -13, 6, -10]... | -22 | 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, -8, -7, -11, 8, -1],\n [0, 9, 4, 13, 6, -1],\n [0, 0, 7, -8, 5, -5],\n [0, 0, 0, 14, 2, -7],\n [0, 0, 0... | -51 | 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, -6, -7, -9, -10, 1],\n [7, 9, 6, -15, -4, -4],\n [0, 8, -8, 4, -4, 4],\n [-7, -13, 4, 9, -6, 12],\n [-10, 2, -13, 5, -7, -2],\n [13, 6, 2, 7, -13, 10]]\n\... | -17 | 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, 0, -9, 6, -2, 12],\n [0, -2, -2, 6, 6, 2],\n [-9, -2, -5, 2, 2, 4],\n [6, 6, 2, 13, -2, -2],\n [-2, 6, 2, -2, -15, -6],\n [12, 2, 4, -2, -6, 9]]\nRound your answer to the nearest integer.... | -163 | 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[[3, -4, -6, 12, 2, -7],\n [0, -9, 8, -10, 0, -12],\n [0, 0, -8, -9, -14, 4],\n [0, 0, 0, -10, 15, 13],\n [0, 0, 0, 0, -5, 4],\n [0, 0, 0, 0, 0, ... | -59 | 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[[-13, 6, 1, 2, -4, -3],\n [6, -9, 0, 8, 2, 0],\n [1, 0, -6, 0, 0, 2],\n [2, 8, 0, 8, -6, 7],\n [-4, 2, ... | 330 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-10, -4, 11, 8, 2, 2],\n [-4, -5, 6, 10, -2, 6],\n [11, 6, -9, -4, -10, 0],\n [8, 10, -4, -1, 8, 8],\n [2, -2, -10, 8, 0, 2],\n [2, 6, 0, 8, 2, -5]]\n\... | 23 | 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[[12, -9, -14, -1, -10, -3],\n [0, -4, 10, -7, 11, 11],\n [0, 0, 10, -3, 9, 7],\n [0, 0, 0, -14, -9, 10],\n [0, 0, 0, 0, -13, -1],\n [0, 0, 0, 0,... | -19 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-5, 11, -15, -9, 1, -15],\n [1, -1, 6, -13, -13, 10],\n [-13, 14, 8, 9, -6, -2],\n [11, -14, -7, -2, -11, 11],\n [12, 15, -5, 14, 13, -11],\n [14, -8, -8, -1, 6, -9]]\nRound your answer to the nearest in... | 197 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/180 * A where A =\n[[-1, 13, -14, -11, 3, 14],\n [0, 15, 12, 6, 12, 11],\n [0, 0, 13, -13, -11, 10],\n [0, 0, 0, 11, -6, 7],\n [0, 0, 0, 0, 13, 4],\n [0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer i... | -180 | 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[[-5, 3, -2, 12, -4, 0],\n [3, 10, -2, 0, 2, -6],\n [-2, -2, -14, -9, 0, 3],\n [12, 0, -9, -11, 6, 10],\n [-4, 2, 0, 6, 3, -10],\n [0, -6, 3, 10, -10, 7]]\n\nPresent the answer in... | -3 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[7, 8, -5, 12, 3, 9],\n [0, -8, -9, -4, 8, -10],\n [0, 0, -1, 9, 1, -11],\n [0, 0, 0, 2, -10, -1],\n [0, 0, 0, 0, 13, 1],\n [0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer ... | -37 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[15, -2, 6, 11, 9, 13],\n [0, -5, -9, 8, 12, 14],\n [0, 0, -11, 1, -1, 12],\n [0, 0, 0, -1, 11, -11],\n [0, 0, 0, 0, -1, -14],\n [0, 0, 0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex ... | -13021 | 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[[-11, -1, 0, 12, -6, -1],\n [0, 11, 6, 2, -1, -13],\n [0, 0, -13, 1, -5, 7],\n [0, 0, 0, 3, 9, -15],\n [0, 0, 0, 0, ... | 0 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 4) of the inverse. Round your answer to the nearest integer:\n[[-14, -4, 3, -4, 13, 13],\n [0, -14, -8, -7, -15, -6],\n [0, 0, 2, 3, 1, -14],\n [0, 0, 0, -10, 9, 14],\n [0, 0, 0, 0, -4, 1],\n [0, 0, 0, 0, 0, 9]]\n\n... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (2, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 9, 1, -14, -1, 10],\n [0, 5, 14, 11, -3, 14],\n [0, 0, 9, 7, 11, -12],\n [0, 0, 0, -5, -4, -8],\n [0, 0, 0, 0, 1... | 48 | 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[[10, 7, 3, 9, -6, 12],\n [5, -5, 0, 5, -5, -7],\n [9, 1, -13, 4, 14, -14],\n [8, 8, -14, -5, 3, -1],\n [8, 2, -3, 7, -13, 3],\n [6, -15, 12, 0, ... | 291 | MATH |
[
{
"content": "Find the value at position (4, 6) of the inverse of matrix 1/180 * A where A =\n[[-5, -7, 12, 6, -8, 5],\n [-6, 7, -9, -1, 9, -10],\n [14, 8, -12, -7, 14, 11],\n [6, 8, -8, -15, -1, 9],\n [8, -14, 4, 6, 11, 7],\n [14, -15, -1, -11, 1, -11]]\nRound your answer to the nearest integer.\n\nPresent the... | -13 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-8, 6, -11, 3, 1, -15],\n [0, -8, 4, 8, -11, 10],\n [0, 0, 5, -6, -13, -11],\n [0, 0, 0, -10, -9, -7],\n [0, 0, 0, 0, 9, 10],\n [0, 0, 0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent t... | 581 | 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[[12, -12, 7, 9, 15, -12],\n [-12, 11, 15, 8, 0, -12],\n [-7, 11, 6, 1, 14, -8],\n [-13, -5, 14, 12, -9, -9],\n [-10, -14, 6, 5... | 52 | 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[[-4, 12, 8, -1, 3, 12],\n [4, 8, -11, -7, -13, -2],\n [-14, -12, -2, -15, -3, -5],\n [-15, 1, -13, -1, -12, -13],\n [-12, -6, 11, 0, 12, -14],\n [-2, 5, 6, -5, -9, -... | 206 | 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, 2, 4, 14, 15, -1],\n [-6, 13, -1, -11, -13, -10],\n [-2, 8, 8, 10, 14, -4],\n [2, 12, -8, -7, -15, -6],... | 7 | 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[[-13, -8, 2, -1, 3, -2],\n [0, 7, 12, 5, -15, 4],\n [0, 0, 7, 4, -3, 5],\n [0, 0, 0, 1, 9,... | 439 | 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, 0, 8, 5, 12, -2],\n [0, 2, -6, 2, 3, 10],\n [8, -6, -13, -4, -6, 11],\n [5, 2, -4, -1, 4, 1],\n [12, 3, ... | 12 | 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, 1, -5, -6, -14, 12],\n [-3, 15, 1, 12, 14, -13],\n [6, -3, 14, -8, -7, -9],\n [-2, -10, 15, 0, -15, -4],\n [-2, -2, -1, -11, -12, 9],\n [3, -5, 14, 12, 6, -13]]\nRound your answer to the ... | 62 | 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, 10, 3, -6, 5, 12],\n [0, -3, 7, 9, 1, 5],\n [0, 0, -14, -5, -14, -11],\n [0, 0, 0, -1, -4, -1],\n [0, 0, 0, 0, 5, 1],\n [0, 0, 0, 0, 0, 5]]\n\nPres... | -1375 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-7, -5, -5, 1, 14, -1],\n [11, -14, -11, -3, 15, -1],\n [15, 12, -12, -10, 10, -11],\n [4, 14, -12, 2, -2, 7],\n [5, -13, 3, -12, 5, 5],\n [-8, -7, 9, -9, 13, 4]]\nRound your answer to the nearest integer.\n\nPresent the a... | -30 | 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[[11, 9, -6, 10, 4, 1],\n [9, -3, 5, 10, 8, -7],\n [-6, 5, 4, -3, 2, -4],\n [10, 10, -3, 11, -11, 4],\n ... | 199 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[13, 9, -4, -7, -9, 15],\n [0, 8, 12, 14, -9, -6],\n [0, 0, -7, 6, 11, 11],\n [0, 0, 0, 14, 8, 12],\n [0, 0, 0, 0, -10, 5],\n [0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n... | 48 | 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[[12, -10, 14, -8, 10, 4],\n [-13, -3, -5, 4, 8, 6],\n [-4, 2, -12, 0, -14, -7],\n [-6, -11, 4, 5, 2, -12],\n [6, 9, -5, 0, -3, -6],\n [9, 7, -9, 1, 1, 2... | -30 | 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, 8, 14, -12, 2, 3],\n [0, 8, -1, 2, 14, 1],\n [0, 0, -6, 12, 15, -12],\n [0, 0, 0, 6, -3, -11],\n [0, 0, 0, 0, -12, -7],\n [0, 0, 0, 0, 0, 2]]\nRound your answer to the nearest integer.\n... | -182 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-1, -7, -2, -10, -14, 14],\n [-9, 14, 5, 6, 14, -8],\n [-8, -5, 9, 5, 6, 3],\n [-12, -9, -13, -6, 12, 3],\n [12, -1, -15, -8, 8, 4],\n [-4, -5, -6, 6, 2, 14]]\nRound your answer to the nearest integer.\n\nPresent the answe... | 49 | 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[[-10, 7, 11, -3, 15, -14],\n [0, -1, 5, -6, -12, 8],\n [0, 0, 15, 5, -10, 15],\n [0, 0, 0, 7, -5, 8],\n [0, ... | -357 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[6, -5, 14, 2, -8, -2],\n [-5, -12, 0, 2, -2, -2],\n [14, 0, -4, -8, 2, 0],\n [2, 2, -8, 13, -4, -6],\n [-8, -2, 2, -4, -10, 0],\n [-2, -2, 0, -6, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in... | -56 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-4, -8, 0, 4, 6, -6],\n [2, 9, 4, -1, 3, 6],\n [-13, 11, 2, -4, 3, 9],\n [-9, -3, 2, -10, -13, 10],\n [-2, -6, -13, 10, -15, 2],\n [10, -1, 15, -6, 4, 0]]\nRound your answer to the nearest integer.\n\nPresent... | -65 | MATH |
[
{
"content": "Find the value at position (6, 1) of the inverse of matrix 1/180 * A where A =\n[[8, 12, -1, 0, -7, 6],\n [12, -8, 8, -3, -3, 6],\n [-1, 8, -13, 5, 5, -9],\n [0, -3, 5, -10, -9, 1],\n [-7, -3, 5, -9, 14, -6],\n [6, 6, -9, 1, -6, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer ... | -6 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[14, 6, 6, -11, 6, 0],\n [0, 3, 7, 15, 1, 2],\n [0, 0, -4, -8, 6, -3],\n [0, 0, 0, -12, -11, 14],\n [0, 0, 0, 0, -5, 11],\n [0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\n... | 127 | 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[[-1, 12, -12, 10, -3, -10],\n [-15, 11, 14, 14, -8, 2],\n [10, 13, 14, -5, 8, 2],\n [9, 7, -3, -6, 4, 0],\n [-1, -4, 11, 3, -15, -14],\n [-8, 12... | -34 | 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[[2, -7, -9, -11, 5, 8],\n [9, -14, 9, -6, -14, -9],\n [-15, 11, 13, -7, -13, -2],\n [3, -2, -4, 5, 12, -14],\n [-2, -2, -10, 11, -8, 3],\n [-13, 0, -15, -11, -5, 7]]... | 1334 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-3, -8, 5, -2, -3, 4],\n [0, 14, 14, -13, 7, 13],\n [0, 0, -10, -3, 6, 12],\n [0, 0, 0, 12, -5, -6],\n [0, 0, 0, 0, -11, 15],\n [0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTe... | -436 | 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[[-9, -7, -12, -2, 9, -4],\n [-8, -5, 1, -9, -7, 15],\n [12, -9, 11, -11, -3, -2],\n [-8, -5, -2, -6, -5, 13],\n [1, 7, -5, 0, -10, -11],\n [0, -11, -6, 4, -1, -11]]\n\nPresent th... | -1 | 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, 13, 7, 13, 6, -8],\n [-15, 8, 7, -11, -9, 3],\n [-10, -14, 1, 12, 9, -11],\n [-10, 14, 11, 0, 5, 0],\n [12, 6, -8, 10, -15, 9],\n [5, 1, -15, -8, -10, -11]]\nRound your answer to the nea... | -80 | 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[[-5, 10, 1, 0, -3, -13],\n [0, -10, 7, -5, -3, 2],\n [0, 0, 10, -5, -13, 9],\n [0, 0, 0, -14, -10, 12],\n [0, 0, 0, ... | 0 | 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[[8, -6, 12, -4, -9, -11],\n [1, -11, 7, 6, 0, 1],\n [-9, 2, -1, -3, 7, -15],\n [1, 7, 0, -10, 13, -15],\n [2, -12, -11, 15, 1, 8],\n [-5, 13, 5, -9, 14, 13]]\n\nPresent the answer in L... | -1917 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (2, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 9, 2, -10, 1, 14],\n [0, -7, -6, 11, 5, 0],\n [0, 0, -8, -7, -11, 0],\n [0, 0, 0, -4, -10, 2],\n [0, 0, 0, 0, ... | 235 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[4, 8, 4, 9, 0, -4],\n [8, -2, 2, 2, -2, -10],\n [4, 2, -1, 9, -4, -2],\n [9, 2, 9, 2, 11, 2],\n [0, -2, -4, 11, 7, 0],\n [-4, -10, -2, 2, 0, 2]]\n\nPre... | -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[[7, -11, 14, -6, 1, 0],\n [0, -14, 13, 11, -7, -3],\n [0, 0, -12, 0, 0, 12],\n [0, 0, 0, 1, 1, -9],\n [0, 0, 0, 0, -9, 5],\n [0, 0, 0, 0, 0... | 1803 | 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, 6, -4, -12, -4, 0],\n [6, 4, -10, -1, -3, -4],\n [-4, -10, 3, -4, 6, 4],\n [-12, -1, -4, -10, -8, -4],\n [-4, -3, 6, -8, -8, -2],\n [0, -4, 4, -4, -2, -... | -33 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-13, -4, 11, 8, -10, 4],\n [-4, 11, 8, 4, -7, -4],\n [11, 8, 12, 12, 1, -3],\n [8, 4, 12, -5, 11, -6],\n [-10, -7, 1, 11, 3, -2],\n [4, -4, -3, -6, -2, 1]]\nRound your answer to the nearest integer.\n\nP... | 275 | 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, 5, -9, -2, -12, -2],\n [5, -9, 3, 0, 2, 6],\n [-9, 3, -1, -2, 2, 6],\n [-2, 0, -2, -13, -6, -2],\n [-12, 2, 2, -6, -2, 0],\n [-2, 6, 6, -2, 0, 1]]\n\nPresent the answer in LaTex f... | 15 | 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[[-3, -5, -8, 14, -4, -5],\n [12, 9, -6, 11, 10, -13],\n [8, 13, 5, -2, 2, 13],\n [-1, -11, 4, 5, 11, -8],\n [7, -3, -13, 11, 4, -9],\n [-9, -3, ... | -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[[-2, 7, -10, -13, 9, -8],\n [-15, -4, 3, -13, -14, -13],\n [4, 3, 15, 3, 9, 6],\n [4, -13, 11, -5, -12, -12],\n [-8, -7, -8, 1, 2, 2],\n [1... | 148 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-11, 4, -1, 4, -13, -3],\n [-14, 12, -2, -1, 5, -2],\n [4, 2, -7, 10, -3, 11],\n [5, -13, 10, 14, 1, 10],\n [-1, -2, -14, -6, -4, -5],\n [2, 3, -10, -8, -2, -3]]\nRound your answer to the nearest integer... | 817 | 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, 6, -6, 13, -11, 13],\n [-4, 5, 5, -1, -9, 11],\n [-7, -2, 9, 11, 13, 11],\n [2, 3, -15, 3, -13, -9],\n [3, -14, -13, -4, ... | -21 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (5, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 4, -6, -2, -7, -6],\n [4, -1, -8, 4, 2, 2],\n [-6, -8, 0, 0, -2, -2],\n [-2, 4, 0, 9, -15, -2],\n [-7, 2, -2, -... | -10 | 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[[-9, 8, 15, -12, -4, -1],\n [0, -2, -14, 12, -12, -11],\n [0, 0, -2, 7, -8, 0],\n [0, 0, 0, 4, 6, -12],\n [0, 0, 0, 0, 2, 2],\n [0, 0, 0, 0, 0, -11]]\n\... | 4478 | 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, 1, -10, 4, 3, 6],\n [-15, 8, 7, -1, -11, -14],\n [-8, 5, -11, -5, 9, -10],\n [-13, 9, -4, 12, 11, 4],\n [-3, -3, 4, -15, 14, 13],\n [-10, 11, -15, 11, -10, 13]]\n\nPresent the an... | -11 | 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, -7, 2, 2, -8, -4],\n [-7, -6, 3, -2, -4, -5],\n [2, 3, -1, -14, -11, -2],\n [2, -2, -14, 2, -6, 6],\n [-8, -4, -11, -6, -4, 4],\n [-4,... | 369 | 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[[-7, -2, -13, 0, -8, -14],\n [0, 4, 11, 11, 4, 1],\n [0, 0, -9, -10, 5, -9],\n [0, 0, 0, 8, 7, 1],\n [0, 0, ... | 102 | 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[[0, 8, -7, -1, 5, 10],\n [8, -12, 0, 4, -14, -2],\n [-7, 0, 13, 10, -4, 11],\n [-1, 4, 10, 9, -8, -8],\n [5,... | 154 | 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[[2, 14, 8, 11, 4, 11],\n [0, -6, -11, 12, -8, 3],\n [0, 0, 12, 5, -12, -15],\n [0, 0, 0, -1, 9, 13],\n [0, 0, 0, 0, ... | -231 | 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[[-3, 0, -2, -2, 12, -2],\n [0, 4, -15, 4, -3, 0],\n [-2, -15, -12, 2, -4, 12],\n [-2, 4, 2, 0, 12, 0],\... | 428 | 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, -5, 13, -2, 7, 6],\n [0, 12, 8, -14, 1, 3],\n [0, 0, 2, 12, 14, 14],\n [0, 0, 0, -9, 5, 0],\n [0, 0, 0, 0, 6, 0],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer i... | 3003 | 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[[10, 3, 9, -6, 10, 7],\n [0, 4, 3, 10, 9, -2],\n [0, 0, 14, -14, 10, 4],\n [0, 0, 0, -8, -2, -6],\n [0, 0, 0, 0, -10, 8],\n [0... | 73 | MATH |
[
{
"content": "Find the value at position (6, 4) of the inverse of matrix 1/180 * A where A =\n[[6, -4, -14, 0, 15, -8],\n [0, -4, -15, -9, -13, -10],\n [0, 0, -5, 10, -2, -5],\n [0, 0, 0, -4, 15, -12],\n [0, 0, 0, 0, 7, 0],\n [0, 0, 0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer... | 0 | MATH |
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