messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -9, -12, 5, 1, 5, 4],\n [-9, 1, 2, 0, -4, 14, 2],\n [-12, 2, 4, 4, -2, -18, -5],\n [5, 0, 4, 1, 0, 4, 14],\n [1, -4, -2, 0, 7, -2, -12],\n [5, 14, -18, 4... | 188 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 3, -1, -1, 15, 17, 18],\n [0, 10, -7, -1, 12, -4, 11],\n [0, 0, -4, 14, -17, -11, 14],\n [0, 0, 0, 2, 9, 1, 1],\n [0, 0, 0, 0, 12, -12, -2]... | 185 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[16, -4, 0, 7, 16, 4, -9],\n [3, -8, 7, -18, 17, 2, -11],\n [1, -2, -4, 2, -18, -16, 12],\n [12, 2, 4, -2, 3, 3, 17],\n [-11, -11, -5, 5, 3, -4,... | 6 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 7) rounded to the nearest integer?\n[[-15, 13, 10, 11, -16, -14, 0],\n [-11, 18, 12, 8, -6, -13, -18],\n [11, -8, 12, -3, -4, -14, -4],\n [-18, -4, 17, -11, 3, 8, 15],\n [11, -7, -17, 3, -2, 16, 4],\n [10, 10, 0, -2... | -10 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[-17, -7, -7, 6, 18, 12, -2],\n [-7, 11, -17, -3, -18, 15, -18],\n [17, -16, 15, -7, 8, 18, 6],\n [-7, 14, -... | 6 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, 13, -10, -4, 2, 9, 8],\n [0, -2, 18, 5, 12, 16, -15],\n [0, 0, -9, 18, 2, 2, -3],\n [0, 0, 0, 14, 10, 12, 5],\n [0, 0, 0, 0, -5, -14, 17],\n [0, 0, 0, 0, 0, -12... | 5392 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[6, -9, -2, -16, -10, -1, 11],\n [0, 13, 8, 2, 5, -16, -3],\n [0, 0, -11, -15, 13, 16, 11],\n [0, 0, 0, 12, -2, -17,... | -29 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, 16, 13, -3, -13, -10, 3],\n [0, 13, 7, -1, 18, -7, 15],\n [0, 0, 5, -5, -2, 12, -15],\n [0, 0, 0, -7, 16, -17, 10],\n [0, 0, 0, 0, -5, 10, -4],\n [0, 0, 0, 0, 0, -7, 1],\n [0, 0, 0, 0, 0, 0, 12]]\nRound your answer to ... | 285 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, 16, -17, -16, -5, -2, 16],\n [-15, 11, -5, 8, -6, 1, 5],\n [-9, -12, -2, 3, -8, 4, 3],\n [-1, 7, 11, -6, -15, 8, -9],\n [9, 2, -8, 1, 17, 0, -9],\n [-4, -1, -12, 11, -5, 18, 11],\n... | -147 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[18, 11, 2, 1, 3, 17, 17],\n [2, 5, 2, -12, -11, 3, 3],\n [11, 15, 10, -9, -14, 15, -9],\n [-10, 13, -14, 16, -8, -3, 8],\n [1, -18, 7, -8, -4, -1, 5],\n [9, 6, 4, -8, 14, -3, 17],\n [4, -13, 5, -13, -9, 3, 4]]\nRound your ... | 16 | MATH |
[
{
"content": "Find the value at position (5, 4) of the inverse of matrix 1/252 * A where A =\n[[-14, 9, -10, 9, 6, 8, 5],\n [0, -17, -17, -14, 2, -9, -1],\n [0, 0, 17, 2, -17, 14, 4],\n [0, 0, 0, 18, -9, 13, 17],\n [0, 0, 0, 0, -6, 16, -17],\n [0, 0, 0, 0, 0, 7, 9],\n [0, 0, 0, 0, 0, 0, 9]]\nRound your answer t... | 0 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 6, -10, -8, 18, 2, -17],\n [15, -6, -14, -8, 10, 9, 9],\n [-14, 1, 18, -9, 13, 10, -17],\n [-18, 1, -18, -15, -4, 11, -13],\n [-18, -12, -14, -12, 17, -16, -7],\n [-4... | 25 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[14, 2, -6, 7, 13, 2, -1],\n [2, 18, -16, -12, -4, 2, 6],\n [-6, -16, -8, 8, 8, 2, 10],\n [7, -12, 8, -3, -6, -12, -4],\n [13, -4, 8, -6, 0, -6, -7],\n [2, 2, 2, -12, -6, -5, 12],\n [-1, 6, 10, -4, -7, 12... | 691 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -15, -9, 16, -3, 8, 1],\n [0, 14, -12, 3, -2, -10, -9],\n [0, 0, 12, -14, -1, -13, 9],\n [0, 0, 0, -16, -1, -15, 13],\n [0, 0, 0, 0, -17, -8, 14],... | 79 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (6, 4) of the inverse. Round your answer to the nearest integer:\n[[13, -4, 2, -5, -3, -18, -1],\n [15, 7, 17, 2, -18, 8, -8],\n [-5, 9, 8, 3, 2, 5, 0],\n [5, 7, 6, 10, -9, -8, 5],\n [5, -7, -12, -2, 16, -13, -7],\n [-4... | 11 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[2, 4, 5, -9, -13, 2, 18],\n [0, 2, 3, 16, -14, -4, 0],\n [0, 0, -15, 2, 5, 7, -17],\n [0, 0, 0, -5, 1, -17,... | 475 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -14, 8, -8, 11, 18, 15],\n [0, -3, 11, 5, -16, 10, -7],\n [0, 0, -17, 10, -10, 9, 18],\n [0, 0, 0, 13, 9, -4, 5],\n [0, 0, 0, 0, 17, 9, 13],\n [0, 0, 0, ... | -828 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, 12, 8, -13, 2, 0, -9],\n [12, -17, 4, -13, 0, -2, -11],\n [8, 4, 12, 8, 10, 4, 2],\n [-13, -13, 8, 15, 2, 5, 8],\n [2, 0, 10, 2, -2, 8, 4],\n [0, -2, 4, 5, 8, 1... | 427 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, 2, 7, -4, 16, -8, -10],\n [0, -15, 11, 9, 6, 3, 6],\n [0, 0, 13, 7, 9, 1, -17],\n [0, 0, 0, 3, -8, 11, 9],\n [0, 0, 0, 0, 17, 6, 5],\n [0, 0, 0, 0, 0, -11, -14],... | 848 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, -3, -4, 12, 2, 11, -5],\n [-3, -1, -5, 6, -8, -8, -2],\n [-4, -5, 4, 10, -2, 10, -10],\n [12, 6, 10, -7, 4, -11, 14],\n [2, -8, -2, 4, 2, 5... | 21 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-13, 5, 2, 4, -14, -12, -16],\n [-6, -7, -13, 15, -4, -1, -16],\n [3, 16, 9, -7, -18, 17, 11],\n [4, 18, 9, -14, 17, -9, -14],\n [-5, 5, 9, 2, -7, 1, 13],\n [2, -2, -18, 9, -17, -2, -5],\n [-5, -1, 15, -18, -1, 15, 4]]\nRo... | -112 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-3, -6, 6, -8, 12, 6, 1],\n [-6, -3, 3, 1, 0, 1, 1],\n [6, 3, 5, -1, -4, -8, 0],\n [-8, 1, -1, -12, 10, 8, -12],\n [12, 0, -4, 10, 13, 4, -6],\n [6, 1, -8, 8, 4, -12, 0],\n [1, 1, 0, -12, -6, 0, -17]]\nRound ... | 1 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, -9, 13, -2, -9, 3, -13],\n [8, 1, -18, -2, -18, 18, -4],\n [-18, -2, -17, -1, -7, 10, 4],\n [-10, -11, -3, 4, 10, -9, -7],\n [-7, 11, -... | 375 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -10, -12, 8, 2, 16, 5],\n [13, -7, 4, 17, 10, -16, -11],\n [15, -5, 17, 13, -12, -9, -7],\n [4, -8, -6, -7, -12, -9, -12],\n [8, -12, 5, 4, 6, 17,... | 39 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[-14, 11, -7, 8, -6, -9, 17],\n [0, -3, 17, 7, 1, 15, 18],\n [0, 0, 10, 12, -17, 6, -16],\n [0, 0, 0, -10, -10, -7, -15],\n [0, 0, 0, 0, -2, -7, -8],\n ... | 0 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-10, -12, 8, -16, 3, -3, -11],\n [-14, 11, 9, 8, 3, 11, 18],\n [-12, 11, -6, 3, -8, -14, 3],\n [-4, 18, 12, 10, -2, -13, -2],\n [15, 4, 11, -6, 11, 1, -13],\n [12, 0, -13, 15, 9, -6, -9],\n [-12, -1, 3, -5, 17, -11, -7]]\n... | -43 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[14, 5, -5, -14, 0, -16, -18],\n [0, 14, -2, -10, 12, 16, -16],\n [0, 0, -5, -13, 10, -10, 17],\n [0, 0, 0, 6, 18, 4, -8],\n [0, 0, 0, 0, -3, -6, 18],\n [0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 13]]\nRound your answer to... | -3564 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[11, -2, 15, -5, 8, 8, -8],\n [-2, 2, 5, 15, 8, 4, -3],\n [15, 5, 7, 6, -2, 11, -10],\n [-5, 15, 6, -9, 10, -1, -13],\n [8, 8, -2, 10, -18, 4, 7],\n [8, 4, 11, -1, 4, 13, 4],\n [-8, -3, -10, -13, 7, 4, -11]]\nRound your ans... | -81 | MATH |
[
{
"content": "Find the inverse of 1/252 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, 4, 8, -10, 2, 2, -14],\n [4, -18, 4, 4, 1, -7, -12],\n [8, 4, -2, 8, -1, -10, 2],\n [-10, 4, 8, -15, -6, -8, 0],\n [2, 1, ... | -94 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[-9, -8, 9, 8, -1, 11, -6],\n [0, -17, 1, -7, 10, -11, 1],\n [0, 0, -3, 4, 15, 13, -2],\n [0, 0, 0, -11, 4, 2, 0],\n... | -32 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -7, 17, -17, 1, -16, 15],\n [0, -9, 5, -1, 14, -12, 10],\n [0, 0, -2, 18, -16, 5, -1]... | -758848 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[17, 4, -7, 4, 14, 9, 4],\n [-12, -17, -18, -15, -11, 10, -1],\n [18, 12, -13, 5, -4, -7, -5],\n [8, 18, -6, -16, -3, -7, -5],\n [15, 12, -14, -7, 7, -2, -8],\n [14, -15, 13, 12, -8, -2, 8],\n [-11, 2, 14, -14... | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[8, 2, -2, 1, -7, -8, -4],\n [2, -16, 12, -1, 13, -5, 15],\n [-2, 12, -7, 2, 0, 8, 9],\n [... | 29 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[13, -8, -17, 13, -14, 12, -6],\n [3, 16, 0, 10, 4, 0, -3],\n [12, -3, 7, -16, 4, -10, 5],\n [14, -5, 9, 5, -12, 6, -17],\n [-18, 4, -1, -11, 15, -11, 10],\n [-6, -1... | 394 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-9, -16, -10, 8, -6, -12, 4],\n [-16, -1, 5, 6, 12, -4, -9],\n [-10, 5, -15, -10, 12, -4, 2],\n [8, 6, -10, -10, 12, 3, 8],\n [-6, 12, 12, 12, 7, -2, -2],\n [-12, -4, -4, 3, -2, -6, -6],\n [... | -387 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[11, 4, -3, -8, 0, 0, -4],\n [4, 2, -10, 4, 7, 2, 4],\n [-3, -10, -5, 7, -6, 5, 8],\n [-8, 4, 7, 1, -9, -10, 3],\n [0, 7, -6, -9, -16, 0, -12],\n [0, 2, 5, -10, 0, -2, 4],\n [-4, 4, 8, 3, -12, 4, -10]]\nRound your answer to... | 172 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[13, 12, -8, -3, 4, 0, -2],\n [12, 13, -12, 16, -14, -17, -1],\n [-8, -12, -17, -8, 2, -8, -6],\n [-3, 16, -8, 13, 8, 3, -12],\n [4, -14, 2, 8, -13, -14, -8],\n [0, ... | 354 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-7, 11, 8, -14, 1, 2, -16],\n [0, 5, -12, 5, -8, -17, -13],\n [0, 0, -10, 9, 0, -15, -15],\n [0, 0, 0, -17, -13, -7, 18],\n [0, 0, 0, 0, -15, 15, 3],\n... | -17 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, -9, 18, -7, 0, -17, -4],\n [-11, 16, 11, -10, 11, 0, 10],\n [-17, 9, -11, 6, -9, 3, 16],\n [5, 7, 12, 4, -17, 14, 5],\n [-7, 18, -10, -16, 4... | -71 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -10, -2, -2, -4, 5, -12],\n [-10, -11, 8, -6, 5, 2, -4],\n [-2, 8, 1, -12, -4, -2, -2],\n [-2, -6, -12, 14, 8, 14, 11],\n [-4, 5, -4, 8, 14, -3, 0],\n [5, 2, -2, 14, ... | 1324 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[8, -6, 12, 6, 4, -2, -6],\n [-6, -13, 11, 4, 2, -2, 1],\n [12, 11, -1, 3, 0, 3, 0],\n [6, 4, 3, 12, 2, -6, -8],\n [4, 2, 0, 2, 8, -12, 0],\n [-2, -2, 3, -6, -12, 0, 10],\n [-6, 1, 0, -8, 0, ... | 32 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/252 * A where A =\n[[1, -1, 0, -14, 0, 6, 6],\n [-1, 8, 13, 10, 0, -2, -3],\n [0, 13, 13, -13, 4, -8, 10],\n [-14, 10, -13, 1, -4, -16, 0],\n [0, 0, 4, -4, 6, -8, 4],\n [6, -2, -8, -16, -8, 9, 9],\n [6, -3, 10, 0, 4, 9, -15]]\nRound your... | 59 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 14, -18, -14, 13, -18, 16],\n [0, 10, -2, 11, 16, -18, -15],\n [0, 0, -14, -5, 7, 4, 3],\n [0, 0, 0, -15, 13, -10, -17],\n [0, 0, 0, 0, 10, 18, -14],\n [0, 0, ... | 1131 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, 4, 4, 9, -6, -8, 6],\n [4, -5, 4, 10, -2, -7, -9],\n [4, 4, 10, -9, 0, -7, 0],\n [9, 10, -9, -5, -8, 7, 15],\n [-6, -2, 0, -8, -6, 12, 0],\n [-8, -7, -7, 7, 12, ... | 479 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, 4, 6, 0, 0, -4, -12],\n [4, -6, 6, -10, -8, 2, 6],\n [6, 6, 14, 11, 2, 5, -12],\n [0, -10, 11, 13, 0, 12, 9],\n [0, -8, 2, 0, -14, 2, 2],\n [-4, 2, 5, 12, 2, -14, 8]... | -38 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[17, 14, -2, -14, 1, 4, -15],\n [0, 11, 10, 15, -9, 1, 5],\n [0, 0, -6, 4, -9, 3, -5],\n [0, 0, 0, 9, -11, -14, 2],\n [0, 0, 0, 0, -12, 6, 17],\n [0, 0, 0, 0, 0, -7, 1],\n [0, 0, 0, 0, 0, 0, 16]]\nRound y... | 1046 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -2, -4, -2, 10, 9, 0],\n [-2, -5, 0, 8, 4, -16, 8],\n [-4, 0, 6, -2, 14, -2, -4],\n [-2, 8, -2, 18, -5, 8, -14],\n [10, 4, 14, -5, -18, -2, -2],\n [9, -16, -2, 8, -2... | 200 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 10, 8, -1, -2, 1, -2],\n [10, 16, -6, 2, 0, 10, -9],\n [8, -6, 0, -6, 8, -2, -11],\n [-1, 2, -6, -3, 12, -8, -6],\n [... | 1766 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 6) of the inverse. Round your answer to the nearest integer:\n[[3, -15, -16, -9, 18, 0, -1],\n [0, 12, -2, 5, -18, -14, 13],\n [0, 0, 3, 15, -5, -3, -14],\n [0, 0, 0, 8, -13, -8, 2],\n [0, 0, 0, 0, 4, -18, -15],\n [... | 38 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -18, -11, -3, -4, 0, 6],\n [0, -17, 6, 12, -15, -15, -7],\n [0, 0, 10, 3, 17, -3, -4]... | -5770 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-17, -9, -3, -3, 0, 14, 0],\n [-9, 5, 9, -14, 10, -2, 0],\n [-3, 9, 9, 2, 13, 8, -9],\n [-3, -14, 2, -9, -6, -4, -4],\n [0, 10, 13, -6, -9, -8,... | -30 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -2, 12, 10, -6, 2, -2],\n [-2, 11, 3, -2, 2, 12, 12],\n [12, 3, -16, 0, 13, 12, 1],\... | -69 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[2, -5, 14, 6, 0, -10, 18],\n [0, 17, -4, -14, -2, 11, -12],\n [0, 0, -9, -13, -6, -5, -18],\n [0, 0, 0, 18,... | 56 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, 2, 0, 0, 8, 10, 11],\n [2, -1, -2, -10, 8, -1, 4],\n [0, -2, -5, 0, 8, -10, 5],\n [0, -10, 0, -2, 8, -6, 3],\n [8, 8, 8, 8, 16, 16, -7],\n [10, -1, -10, -6, 16, ... | 711 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-17, 8, 4, -4, -6, 3, -9],\n [8, -1, -6, -1, 1, 2, 2],\n [4, -6, -5, 0, -3, -6, -1],\n [-4, -1, 0, -6, -6, 4, 4],\n [-6, 1, -3, -6, 7, -1, -4],\n [3, 2, -6, 4, -1, 7, 9],\n [-9, 2, -1... | -103 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, -14, -16, -2, -6, -16, 9],\n [0, -1, 16, -5, -3, -7, -8],\n [0, 0, -6, 11, 7, -1, -6],\n [0, 0, 0, -2, -13, -14, 14],\n [0, 0, 0, 0, 16, 8, -7],\n ... | 28719 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 6) rounded to the nearest integer?\n[[5, 11, -9, -8, 3, -16, 4],\n [0, -6, 17, -16, 3, 6, 1],\n [0, 0, 3, 18, -1, 1, -14],\n [0, 0, 0, -7, 7, 14, 14],\n [0, 0, 0, 0, -2, 5, 3],\n [0, 0, 0, 0, 0, 16, -14],\n [0, 0, 0... | 0 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[1, -3, -2, -2, 15, -8, 16],\n [0, 17, -11, 0, 14, 4, -17],\n [0, 0, -12, 10, 12, 11, 16],\n [0, 0, 0, -9, -18, -1, 0],\n [0, 0, 0, 0, -18, 16, -2],\n [0, 0, 0, 0, 0, -7, -15],\n [0, 0, 0, 0, 0, 0, -17]]\nRound your answer ... | 415 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[-14, 9, -7, 17, -6, 2, 13],\n [0, 18, -10, 18, -17, -16, -9],\n [0, 0, 13, 2, 15, 6, 13],\n [0, 0, 0, -18, 17, 2, -3],\n [0, 0, 0, 0, -5, 4, 5],\n [0, ... | 11 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[2, 0, -15, 3, -4, -13, -8],\n [11, 5, 3, 11, -15, -13, 7],\n [0, -17, -15, -14, 16, 10, -3],\n [-7, 2, -10, -8, -11, 7, 13],\n [-15, 15, 9, 6, 16, 0, 16],\n [10, -5, 2, 17, -5, -4, 11],\n [-7, -14, 8, -4... | 311 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[-6, 14, 15, -15, -6, -9, -18],\n [-8, -10, 4, -6, -14, 6, -9],\n [-14, 3, 6, 18, 1, 9, 2],\n [-8, 10, -14, 18, -14, 14, 17],\n [-11, -13, -4, -4, -10, -14, 7],\n [4, -3, 16, -9,... | -4 | MATH |
[
{
"content": "Find the inverse of 1/252 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, 4, -8, 8, 16, 0, 6],\n [4, -2, 4, 8, 4, 4, 6],\n [-8, 4, 5, 0, 16, 4, -10],\n [8, 8, 0, -11, 6, 0, -4],\n [16, 4, 16, 6, -... | -50 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, 8, 2, -18, 13, -5, -5],\n [14, 17, -7, 6, -4, 1, 15],\n [-5, 11, -6, -5, 10, 7, -16],\n [6, 8, -3, -8, 10, 5, 10],\n [15, -8, 1, 1, -10, 4, 17],\n [8, 5, 6, 6, 14, 12, -9],\n [-4, -18, -3, 2, -17, -16, -4]]\nRound your... | -37 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 8, 17, 16, 5, -11, -12],\n [-15, 11, -9, 6, 13, 13, 13],\n [-9, -10, 6, 6, -3, -3, 11],\n [-14, -12, -6, -11, 1... | 21 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, 2, -9, 0, 7, 3, 1],\n [2, 2, -2, -11, 1, -2, -4],\n [-9, -2, -14, -2, 8, -12, 3],\n [0, -11, -2, 0, -4, -4, 6],\n [7, 1, 8, -4, 15, -4, -10],\n [3, -2, -12, -4, -4, ... | 5 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -4, 4, -3, -14, 7, 4],\n [-4, -6, 0, -4, -4, 3, -7],\n [4, 0, -18, -6, -6, 8, -6],\n [-3, -4, -6, -16, -11, 0,... | -13 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[8, -9, 12, -4, -2, 4, -2],\n [-9, -7, 3, 10, -1, 2, -4],\n [12, 3, 17, -1, 12, -6, 13],\n [-4, 10, -1, -15, 2, -4, -6],\n [-2, -1, 12, 2, -13, 7, 12],\n [4, 2, -6, -4, 7, -4, -4],\n [... | -16886 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, -17, -12, 2, 12, 4, 6],\n [16, 16, -12, -14, 13, -14, 6],\n [12, 1, 3, -6, -17, 3, -10],\n [-17, 13, -11, -3, 14, -8, 13],\n [-11, 13, 2, 6, 1, -18, 2],\n [-12, 6, -... | 20 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, 13, 16, -2, -9, 16],\n [-3, -13, -15, -10, 10, -12, -3],\n [-13, -16, -5, -5, -10, 17, 4],\n [-4, -12, 1, 0, -13,... | 122 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[10, -2, 0, 8, 6, -6, -4],\n [-2, 6, 1, 0, 0, 4, 2],\n [0, 1, -14, 0, 2, -8, 16],\n [8, 0, 0, 11, 2, 0, -7],\n [6, 0, 2, 2, 12, 6, -4],\n [-6, 4, -8, 0, 6, -4, -3],\n [-4, 2, 16, -7, -4, -3, 6]]\nRound your an... | 276 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[10, -4, 2, -4, 0, -13, -2],\n [-4, -4, 0, -14, 0, 6, -4],\n [2, 0, 17, 8, -9, -16, -6],\n [-4, -14, 8, 0, 0, -17, 2],\n [0, 0, -9, 0, 17, -4, -12],\n [-13, 6, -16, ... | 265 | MATH |
[
{
"content": "Find the inverse of 1/252 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, 4, 1, 10, 0, -4, -1],\n [4, -7, 2, 16, 14, 9, 14],\n [1, 2, 1, -6, -8, -6, -7],\n [10, 16, -6, 16, 2, 1, -6],\n [0, 14, -... | 830 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-3, 2, 14, -2, -10, 0, -12],\n [2, 17, 1, 2, -4, -7, 2],\n [14, 1, -5, -16, -9, 1, 4],\n [-2, 2, -16, -14, 9, -12, -10],\n [-10, -4, -9, 9, -14, -4, 2],\n [0, -7, 1, -12, -4, -1, 6],\n [-12,... | -33 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, 18, 17, 1, -3, -11, 3],\n [-14, -14, -8, 0, -2, 18, -1],\n [-10, -2, 14, 1, -1, 5, -6],\n [9, -16, 17, -8, 2, 18, -17],\n [-13, -14, 13, 1... | -33 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 5, 15, 2, -17, -3, 2],\n [0, -11, -5, 3, -1, -14, 11],\n [0, 0, 12, 12, -10, 18, -13],\n [0, 0, 0, 14, 11, 5, 9],\n [0, 0, 0, 0, -10, -8, -13],\n [0, 0, 0... | 280 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, 10, -1, 16, -6, -2, -7],\n [10, -7, -4, 3, -4, -6, 0],\n [-1, -4, 2, -4, 0, 2, 2],\n [16, 3, -4, 12, 5, -8, 0],\n [-6... | 111 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, 12, 14, 2, 16, 2, -4],\n [0, -17, 11, 9, -2, 1, 10],\n [0, 0, -9, 0, -18, 15, -5],\n [0, 0, 0, -3... | 6392 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, -1, -18, -4, -14, 8, -2],\n [0, 7, -17, 9, 4, 1, 17],\n [0, 0, 9, 3, -2, 12, -8],\n [0, 0, 0, 4, 10, 4, 17],\n [0, 0, 0, 0, 7, 13, 2],\n [0, 0, 0, 0, 0, 16, -5],\n [0, 0, 0, 0, 0, 0, -10]]\nRound you... | 4732 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -12, 9, -17, -18, 18, 5],\n [0, -12, 10, -18, 11, 13, -9],\n [0, 0, 18, 8, -9, 3, 5],\n [0, 0, 0, -14, -13, 13, 1],\n [0, 0, 0, 0, -18, 16, 0],\n [... | 71 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -10, 9, -9, 16, -12, 6],\n [11, 7, -7, -6, -15, -18, -13],\n [-17, 8, -1, 10, 14, -1... | 86 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[16, -12, -4, -15, 18, 9, -10],\n [16, 6, -10, 14, -2, -7, -10],\n [-14, 7, 0, 16, -17, -12, -10],\n [3, 14, -3, 5, -11, 11, 7],\n [16, -2, -9, -2, -12,... | -3256 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-5, -16, -12, -8, 14, 0, 4],\n [4, 10, -13, -14, 13, 7, -5],\n [-1, 2, 6, 1, 5, -16, 3],\n [-11, 10, -12, -13, -13, -7, 3],\n [7, 6, 0, 17, 16, -6, 6],\n [13, 11, 2, -11, -12, -... | -3 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 2, 0, 14, -2, -2, -6],\n [2, 1, -15, -1, 4, 10, 14],\n [0, -15, -16, -4, -10, -10, -7],\n [14, -1, -4, -11, 5, -4, -2... | -7 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[16, -7, -9, 18, -17, -16, -5],\n [1, -15, 7, -4, -10, -16, -17],\n [11, 18, -2, -16, -10, -11, -10],\n [-2, 5, -11, -5, -3, -1, 5],\n [8, 9, -1... | -16 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -17, 4, 10, 0, 1, -7],\n [0, 16, -12, 4, -2, -17, -14],\n [0, 0, -8, 5, 14, 8, 16],\n [0, 0, 0, 13, -8, -16, 2],\n [0... | 9 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[16, 0, 0, 0, 0, -6, -6],\n [0, -17, -4, -11, -8, 2, -12],\n [0, -4, 0, 8, 2, -4, -10],\n [0, -11, 8, 10, 0,... | 278 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-9, 8, -9, 8, -8, -4, 8],\n [8, -13, 12, -12, 4, -6, -15],\n [-9, 12, 5, 12, 3, 6, 12],\n [8, -12, 12, 18, 9, 6, 2],\n [-8, 4, 3, 9, 17, 2, -6],\n [-4, -6, 6, 6, 2, 1, -7],\n [8, -15, 12, 2, -6, -7, -16]]\nRound your answe... | -44 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-10, -17, 9, 15, -9, 0, 10],\n [0, -13, -12, 17, -11, 0, -9],\n [0, 0, 8, 10, 0, -1, 4],\n [0, 0, 0, -12, 7, -3, 13],\n [0, 0, 0, 0, 14, 6, -2],\n [0, 0, 0, 0, 0, 15, 6],\n [0, 0, 0, 0, 0, 0... | 89 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -11, 0, -1, -2, -1, 0],\n [0, -8, -12, 8, 18, -14, -11],\n [0, 0, 7, -4, -3, 10, 9],\n [0, 0, 0, 14, -1, -7, -9],\n [0, 0, 0, 0, 7, -4, 2],\n [0, ... | 111 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-4, 5, 2, 4, 12, 15, 9],\n [0, 3, -16, -10, -13, -18, 3],\n [0, 0, 18, 0, -18, 5, -2],\n [0, 0, 0, 13, 14, 11, 15],\n [0, 0, 0, 0, -18, 3, 14],\n [0, 0, 0, 0, 0, -13, 1],\n [0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the... | -150 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -12, 4, -3, 6, 6, -10],\n [-12, -9, -4, 12, 8, -3, 6],\n [4, -4, 6, 4, -2, 10, 2],\n [... | 58 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[10, 16, -7, -11, 6, 8, -13],\n [0, -8, -13, -14, -12, 0, -13],\n [0, 0, 1, 6, -11, 18, -17],\n [0, 0, 0, -18, 14, 5, -14],\n [0, 0, 0, 0, -1, 6... | 48 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, -11, 11, 9, 7, 15, 13],\n [0, 1, -5, 4, -16, 0, -5],\n [0, 0, -18, 0, -4, 6, -18],\n [0, 0, 0, 1, -14, -4, -17],\n [0, 0, 0, 0, -10, 8, 9],\n [0, 0, 0, 0, 0, -13, 11],\n [0, 0, 0, 0, 0, 0, -9]]\nRou... | 18044 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, -4, 4, 17, 12, -11, 11],\n [15, 14, -18, -3, -8, 8, 3],\n [0, -13, 1, -16, -18, 4, -16],\n [15, -2, 8, 4, -8, -4, 7],\n [-8, -12, -11, -14, -2, 4, -17],\n [8, 2, -12, 7, 11, -7, -8],\n [-2, -9, -3, ... | 673 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[13, 3, 16, -5, 11, 12, -9],\n [-13, 8, -8, 17, -9, -3, 5],\n [2, 17, 4, 2, 13, -2, -2],\n [2, -15, 4, 6, 13, -13, -5],\n [-3, 13, -3, 0, 18, 2, -4],\n [7, 11, -4, -6, 8, 4, 15],\n [15, 4, 1, -10, 1, -5, ... | 604 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, 15, 10, 13, -14, -15, 4],\n [0, 14, 5, -3, 13, 0, 7],\n [0, 0, -1, -12, 13, 5, -3],\n [0, 0, 0, 15, 0, -5, -6],\n [0, 0, 0, 0, -7, -5, 17],\n [0, 0, 0, 0, 0, 9, ... | 3060 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[-16, -8, -9, -7, -8, -18, 13],\n [-8, -3, -8, 7, 6, 6, -14],\n [-9, -8, -11, -1, -1, 6, 0],\n [-7, 7, -1, 18, -12, 2, 4],\n [-8, 6, -1, -12, -2, 0, 0],\n [-18, 6, 6, 2, 0, 15, 0... | -36 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[16, -10, -10, -2, -4, -14, 1],\n [-10, 0, 2, -12, -3, -2, 3],\n [-10, 2, 13, -4, 2, -12, 1],\n [-2, -12, -4, -15, -2, -7, -8],\n [-4, -3, 2, -2, 3, 2, -1],\n [-14, ... | 575 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -16, 17, -6, -18, -8, 5],\n [0, -17, -2, -2, 1, -4, -15],\n [0, 0, -18, -15, -17, 8, 15],\n [0, 0, 0, -14, 10,... | -42 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 18, 18, -12, 14, 3, 8],\n [0, -3, 2, -8, 2, -10, 8],\n [0, 0, 4, 10, -3, -16, -3],\n [0, 0, 0, 16, -12, -11, 16],\n [0, 0, 0, 0, -18, 6, -7],\n [0, 0, 0, 0, 0, ... | 4825 | MATH |
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