messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[15, -13, 9, 12, 16, 4, -13],\n [0, -17, 5, -2, -18, -13, -14],\n [0, 0, -16, -18, 8, 5, 0],\n [0, 0, 0, 11, 13, -18, -6],\n [0, 0, 0, 0, -2, -2, -15],\n [0, 0, 0, 0, 0, 7, 10],\n [0, 0, 0, 0, 0, 0, 5]]\nRound... | -30 | 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[[-16, 12, 18, -17, -17, 15, 1],\n [14, -15, -8, -14, 6, 18, 15],\n [-10, -13, -1, -5, 0, -5, -2],\n [16, 10, -2, -11, -18, 17, -12],\n [-14, 5, 9, -2, 1... | 0 | 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[[-14, -6, -18, 6, -15, 17, -9],\n [9, -13, 8, -7, -16, 14, -9],\n [12, -4, -12, 17, -5, -5, -16],\n [-16, 3, 0, 16, -7, -14, -9],\n [14, -6, 16,... | -9 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-11, -14, -12, -3, -5, 18, -15],\n [0, -2, 17, -13, -3, 10, 17],\n [0, 0, 17, 10, -5, -15, 17],\n [0, 0, 0, 2, -3, -4, -14],\n [0, 0, 0, 0, 14, 17, 14],\n [0, 0, 0, 0, 0, 18, 13],\n [0, 0, 0, 0, 0, 0, -15]]\nRound your ans... | 214 | 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[[18, 13, -8, -18, 6, 5, -2],\n [0, 8, -1, 8, 3, -3, -17],\n [0, 0, -16, 8, -2, -3, -13],\n [0, 0, 0, 14, 8, 10, 18],\n [0, 0, 0, 0, -17, -13, -15],\n [0... | -76 | 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[[9, -10, 3, -11, 8, 0, 6],\n [0, 5, 5, 0, -17, -5, 13],\n [0, 0, -6, -7, -11, -4, 7],\n [0, 0, 0, 17, 8, -10, -18],\n [0, 0, 0, 0, -11, -3,... | 1581 | 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[[8, -16, 9, -2, 12, -9, 3],\n [0, 2, 17, 4, -7, 6, 1],\n [0, 0, 10, -6, -16, -17, -3],\n [0, 0, 0, -14, -12, 15, 13],\n [0, 0, 0, 0, 2, 9, ... | 10435 | 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, 7, -5, 17, -11, 3, 3],\n [0, 8, -9, 6, 12, 2, 8],\n [0, 0, 12, 7, 2, 17, -18],\n [0, 0, 0, -15, -10, 11, -15],\n [0, 0, 0, 0, 18, -11, 14],... | 60 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[4, -2, -12, -3, 17, 1, 5],\n [0, -13, 9, -14, -17, 2, 18],\n [0, 0, -2, 18, -4, -12, -5],\n [0, 0, 0, 12, -6, -1, -2],\n [0, 0, 0, 0, 10, 15, -2],\n [0, 0, 0, 0, 0, -7, 9],\n [0, 0, 0, 0, 0, 0, -8]]\nRound your answer to t... | 3398 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[14, -8, -10, -5, -10, -16, 10],\n [0, 17, 13, -12, 9, -1, -14],\n [0, 0, 7, -7, 0, -18, -16],\n [0, 0, 0, -17, -14, 10, 14],\n [0, 0, 0, 0, -4, 1, -11],\n [0, 0, 0, 0, 0, 7, 14],\n [0, 0, 0,... | -141 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (6, 3) of the inverse. Round your answer to the nearest integer:\n[[-17, -18, 12, -3, 3, -1, -2],\n [11, -9, 16, 2, -3, -13, -16],\n [2, -6, -1, 5, 8, -15, 3],\n [5, -9, -17, -13, -1, -2, 4],\n [11, 2, -9, -6, -7, -10, ... | -9 | 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[[5, 9, 14, -11, 12, -7, 14],\n [9, 0, -11, -6, -2, 0, -6],\n [14, -11, -4, -16, -8, 7, -8],\n [-11, -6, -16, -6, -8, 2, -2],\n... | 58 | 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[[-16, -16, -2, 2, -4, -4, 6],\n [-16, 5, 2, -2, 10, 4, -6],\n [-2, 2, 0, 2, 2, -11, -6],\n [2, -2, 2, -17, 2, 8, -2],\n [-4, 10, 2, 2, -2, -4, 0],\n [-4, 4, -11, 8, -4, -... | -110 | 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[[-1, -3, 4, 18, -10, -16, -11],\n [0, -7, 12, 6, -3, -5, -6],\n [0, 0, 18, -15, -17, 16, -16],\n [0, 0, 0, -9, -18, -2, -3],\n [0, 0, 0, 0, -4, -17, -8],\n [0, 0, 0,... | 9584 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[-2, 18, -10, 1, 9, 1, 17],\n [8, -11, 13, -18, -2, -10, 1],\n [13, -17, 13, -10, 11, 1, -18],\n [-14, 16, 17, -18, -5, -10, 11],\n [5, -15, -5, 6, -15, 6, -9],\n [16, -12, -6, -... | 8 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[6, -3, 2, -6, 7, -7, 4],\n [-3, -9, -8, 7, -2, 6, -9],\n [2, -8, -17, -5, 1, -6, -12],\n [-6, 7, -5, -18, -10, -2, 0],\n [7, -2, 1, -10, -2, -2, 3],\n [-7, 6, -6, -2, -2, -4, 10],\n [4, -9, ... | -50 | 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[[-13, 0, 6, -11, 6, -2, -8],\n [0, 9, 2, 6, 10, 6, -5],\n [6, 2, 6, 4, 2, 6, 7],\n [-11, 6, 4, 15, 4, -8, -4],\n [6, 10, 2, 4, -7, -4, 8],\... | 1685 | 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[[-7, 6, -6, 2, 9, 10, 7],\n [6, -3, -6, 8, 12, 13, 4],\n [-6, -6, -4, 5, 4, 4, 10],\n [2, ... | 115 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 6) rounded to the nearest integer?\n[[15, 9, -9, 10, 12, 10, 0],\n [9, 1, 0, -13, -4, 11, 0],\n [-9, 0, -13, -12, -8, 2, 12],\n [10, -13, -12, -8, 3, -16, 4],\n [12, -4, -8, 3, 16, 10, 10],\n [10, 11, 2, -16, 10, 1,... | 0 | 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[[10, 0, -6, -2, 3, 10, 16],\n [0, 17, 8, -8, 0, -2, 10],\n [-6, 8, 0, 0, 0, -2, -16],\n [-2, -8, 0, -8, 10, -2, 8],\n [3, 0, 0, 10, -11, -9, -2],\n [10, -2, -2, -2, -9, 8, 6],\n [16, 1... | -896 | 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[[-14, -1, -7, 8, -2, 0, 0],\n [-1, 7, 4, 3, -6, 8, -2],\n [-7, 4, -6, 8, -12, 6, -2],\n [8, 3, 8, 15, 4, 0, -14],\n [-2, -6, -12, 4, -4, -12, 0],\n [0, 8, 6, 0, -12,... | 1894 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[8, -12, -16, 14, -17, -3, 6],\n [-4, 5, -4, 12, -5, -5, -13],\n [-5, -2, -1, 1, -2, -3, 13],\n [-10, 8, 14, -9, -2, 17, -2],\n [-1, 4, 15, -11, -6, 4, 1],\n [3, 4, 16, -16, 15, 14, -2],\n [0, 11, 4, -4, -5, -... | 68 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-13, 5, 0, 10, 1, -16, 8],\n [5, 3, 6, -6, 2, 6, -8],\n [0, 6, 17, -14, 6, 2, -1],\n [10, -6, -14, 7, -6, -8, 1],\n [1, 2, 6, -6, 13, 6, 2],\n [-16, 6, 2, -8, 6, -11, 0],\n [8, -8, -1, 1, 2, 0, 16]]\nRound yo... | -3876 | 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[[10, -1, -7, 0, 3, -4, -18],\n [0, -11, 3, 6, -17, -10, -10],\n [0, 0, 11, -4, -4, -12, -8],\n [0, 0, 0, -12, -15, 16, 17]... | 6050 | 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, -12, -17, 11, -6, 4, 10],\n [18, 1, 14, 10, -4, 4, -16],\n [18, 10, -11, 3, 10, -17, -18],\n [1, 2, 18, -11, 8, 16, -13],\n [0, -1, -18, 6, 8, -12, 10],\n [12,... | 1733 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 2) rounded to the nearest integer?\n[[14, -2, -2, -8, -4, 4, 4],\n [-2, -2, 4, 2, -2, -2, 2],\n [-2, 4, -13, 5, 12, 12, -4],\n [-8, 2, 5, 8, 4, -6, -14],\n [-4, -2, 12, 4, 2, -6, 6],\n [4, -2, 12, -6, -6, -6, 12],\n... | -13 | 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[[4, -8, 12, -13, -8, -6, -7],\n [0, 16, 17, -2, 9, 9, 3],\n [0, 0, 13, -8, 5, -16, 11],\n [0, 0, 0, -1, 12, -6, 7],\n [0, 0, 0, 0, 5, 15, -11],\n [0, 0,... | 3528 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-6, 5, 11, -17, 0, 6, -5],\n [-13, -7, 1, 4, 11, 11, 11],\n [11, 17, 15, -3, 5, -5, 7],\n [-11, -5, 12, -17, -15, -18, 1],\n [-5, 6, 6, -16, -14, 7, -15],\n [-12, 11, 11, 0, 16, 14, 14],\n [-5, -9, 9, -5, 17, -3, 2]]\nRoun... | 66 | 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[[9, 14, -13, -4, -16, 16, -5],\n [-17, 10, -15, 7, -7, -17, -2],\n [16, -9, 3, 2, -4, 16, ... | 36 | MATH |
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/252 * A where A =\n[[-17, -2, -4, -2, 6, 12, 4],\n [-2, 16, 1, 14, -6, 0, 2],\n [-4, 1, -15, 16, 5, 7, 0],\n [-2, 14, 16, 3, -9, 6, 6],\n [6, -6, 5, -9, 15, -8, 1],\n [12, 0, 7, 6, -8, 6, 7],\n [4, 2, 0, 6, 1, 7, -9]]\nRound your answer ... | 325 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[15, 6, 5, -5, 2, 8, 0],\n [6, -10, 2, -4, 2, 16, -14],\n [5, 2, -5, 0, 0, -9, 6],\n [-5, -4, 0, 14, -9, 9, -12],\n [2, 2, 0, -9, 7, -2, 3],\n [8, 16, -9, 9, -2, 15, 2],\n [0, -1... | -51 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[6, -2, -1, -10, 6, -13, -12],\n [-2, -13, -3, 0, 10, -2, -6],\n [-1, -3, -8, 5, 6, -6, 8],\n [-10, 0, 5, 11, 0, -8, 0],\n [6, 10, 6, 0, -1, 1, 0],\n [-13, -2, -6, -8, 1, 2, 6],\n [-12, -6, 8, 0, 0, 6, 17]]\nR... | 56 | 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, 8, 15, 14, 9, 12, 13],\n [1, 16, 12, 12, 3, -10, -10],\n [-4, -6, 3, -3, 13, -17, 7],\n [-5, 15, -11, 17, 2, 9, -13],... | -117 | 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, 6, -4, 11, -8, -11, 0],\n [6, -4, 6, 12, 10, -4, -4],\n [-4, 6, 8, 4, 4, 10, -2],\n [11, 12, 4, -1, 6, 10, -16],\n [-... | 105 | 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[[17, -18, 10, -18, -11, -3, 9],\n [3, -1, 3, -7, 0, 6, -14],\n [15, -9, -12, 18, -4, 5, 7],\n [7, 7, -9, -2, -5, -17, -6],\n [8, -10, -12, -9, -10, 3, 4],\n [-12, -1... | 326 | MATH |
[
{
"content": "Find the value at position (7, 5) of the inverse of matrix 1/252 * A where A =\n[[6, -4, 8, -9, 10, 5, -8],\n [-4, 5, -4, -18, 2, 0, -12],\n [8, -4, 9, 2, -4, 12, 9],\n [-9, -18, 2, -12, -4, -8, 3],\n [10, 2, -4, -4, 7, -4, -7],\n [5, 0, 12, -8, -4, 13, 2],\n [-8, -12, 9, 3, -7, 2, 15]]\nRound you... | 42 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[9, 8, -18, 14, -15, -12, -10],\n [-3, -14, 15, 4, 6, -6, 5],\n [-8, -2, 18, -6, 8, 1, 14],\n [13, -11, 10, 0, -13, 2, 3],\n [-9, -9, 10, -3, -18, -2, 11],\n [7, 0, 2, -2, 2, 0, -12],\n [-2, -18, 18, -13,... | 301 | 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[[-14, 18, 12, -7, 16, 11, -13],\n [-4, -4, -3, 1, -6, 12, 15],\n [10, -16, -10, -8, -8, 6, 3],\n [-10, 1, 2,... | 40 | 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[[16, 8, 10, -1, -9, 14, 6],\n [8, -11, -4, 8, -14, -10, -14],\n [10, -4, -3, 2, 0, -1, -6],\n [-1, 8, 2, -16, 2, -8, -11],... | 13 | 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[[-14, 4, -4, 2, 4, -14, 7],\n [4, -4, -1, 0, 3, -4, -1],\n [-4, -1, -9, 4, -8, -8, 14],\n [2, 0, 4, -3, 0, -6, -4],\n [4, 3, -8, 0, -16, 5, 0],\n [-14, -4, -8... | -309 | 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, 17, 13, 17, 9, -5],\n [0, -13, -10, 2, -7, 11, 12],\n [0, 0, 8, 6, -14, -13, -14],\n [0, 0, 0, -4, 1... | -140 | 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, -9, 2, 10, 13, -9, -6],\n [0, 4, 12, -15, -16, 2, -17],\n [0, 0, -4, 14, -13, -12, 0],\n [0, 0, 0, -7, 3, -6, 9],\n [0, 0... | -1612 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[4, -14, 15, 5, -2, 12, -12],\n [-2, 9, 3, -4, 18, -4, 6],\n [2, -17, 8, 13, 2, -15, 0],\n [-17, 7, 15, -5, -4, 1, 15],\n [17, 0, -10, -12, 11, -6, 8],\n [16, -6, -4, -10, 4, 17,... | 8 | 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[[-4, -10, 6, -2, -12, 2, -12],\n [-10, -3, -2, 10, -10, 14, -16],\n [6, -2, 10, -10, -7, -7, 1],\n [-2, 10, ... | 183 | 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[[15, -8, -16, -13, -13, 1, 2],\n [-17, 7, 12, 7, 13, -9, 4],\n [-13, 4, 9, 11, -5, 18, 13],\n [15, 3, 12, -12, 2, -3, 1],\n [0, 13, -4, -14, -8, -4, 10],\n [-15, 17, 4, -... | -56 | 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[[5, -7, -9, 12, -8, -3, -10],\n [-5, 0, 12, -10, 17, 7, -11],\n [5, -11, 0, 11, 3, -10, -15],\n [18, -11, -18, 9, -13, 17, -8],\n [-14, 5, -1, 1, 9, -6, -14],\n [11, -18, 3, -1, -14, 1... | 89 | 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[[-1, 0, -4, -5, -2, 1, 2],\n [0, -2, 4, 7, 2, 9, -6],\n [-4, 4, 10, -6, 0, 0, -2],\n [-5, 7, -6, 18, -2, -7, 7],\n [-2, 2, 0, -2, -14, -4, 6],\n [1, 9, 0, -7,... | -670 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[13, -11, -14, 11, -11, 0, 11],\n [-4, 17, 8, -6, -5, 18, 11],\n [-6, -3, -12, 8, 16, -4, 9],\n [16, -12, 1, 13, 13, 7, 1],\n [-1, -4, 3, 3, 2, -17, -1],\n [4, -6, -10, -12, -18, -17, -15],\n [-5, 13, 17,... | 573 | 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[[-11, 9, 2, 4, 13, -11, 12],\n [18, -3, 8, -1, 16, -4, 8],\n [-2, -17, 12, 18, 15, 15, -16],\n [-2, -5, -5, 16, -18, 10, -15],\n [14, -2, 9... | 344 | 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[[11, -10, 18, -18, -15, -4, 8],\n [0, 4, -4, 8, 12, -11, 11],\n [0, 0, 3, -16, -4, 16, 14]... | 379 | 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, -17, 0, -7, -9, 12],\n [0, 4, 4, -4, 7, -16, 4],\n [0, 0, -1, -13, 8, 17, -4],\n [0, 0, 0, -12, 1, -9, 7],\n [0, 0, 0, 0, -2, 5, 8],\n [0, 0, 0... | -2390 | 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[[-15, -4, 6, 1, -4, 2, 4],\n [-4, -18, -9, 2, 7, 14, 7],\n [6, -9, 15, -5, 1, 0, 9],\n [1, 2, -5, -16, -7, 12, 0],\n [-4, 7, 1, -7, 18, -6, -3],\n [2, 14, 0, 12, -6, 12, ... | -27 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[4, 2, -6, -9, -2, 3, 0],\n [2, -4, -5, 7, -1, 4, -2],\n [-6, -5, 17, 12, 0, -6, 12],\n [-9, 7, 12, 8, -4, 7, 8],\n [-2, -1, 0, -4, -9, -2, 8],\n [3, 4,... | -22 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[10, -16, -12, 17, 10, 18, 17],\n [4, -3, 12, 15, -18, -1, -4],\n [-2, -9, 1, -13, -11, 15, 13],\n [-15, 1, 5, 5, 7, 6, 17],\n [-12, -9, -7, -18, 6, -3, -14],\n [0, -15, -13, 7, -10, -5, -10],\n [-4, 18, ... | 338 | 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[[10, 12, -13, -15, 10, -16, -18],\n [0, 2, 12, -12, -2, 0, -16],\n [0, 0, 10, -5, 16, 9, 11],\n [0, 0, 0, -14, 16, -5, 17]... | -4 | 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[[-14, 3, 12, -16, 11, 2, 16],\n [-13, 9, 13, 18, 6, 13, 16],\n [3, 5, 11, 13, 12, 4, 14],\n [6, 17, 5, 12, -6, -9, 4],\n [-1, 13, 14, 17, 9... | 603 | 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, 17, 6, -9, 0, -4, -3],\n [-17, 10, -15, 10, 12, -2, -9],\n [8, -4, 12, 2, 7, 17, -2],\n [-16, -5, -6, 8, -18, -2, 15],\n [-5, -2, -16, 15, 6, -17, 15],\n [7, 12, -10, 11, 1, 2, 10... | 78 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-7, 8, 12, 8, 2, -2, -2],\n [8, 0, -6, -1, 12, 2, -2],\n [12, -6, 3, -12, 10, 5, 9],\n [8, -1, -12, -1, 1, -2, 12],\n [2, 12, 10, 1, 9, 5, 0],\n [-2, 2... | -1 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-1, 8, 12, 8, -18, -13, -8],\n [15, 1, 2, 2, -1, 2, 0],\n [-15, -6, -1, 10, 6, -6, 8],\n [0, -18, 0, -18, -2, 2, 3],\n [-4, 13, -15, 13, -15, -18, 14],\n [-12, -10, -18, -3, -1, -13, -17],\n [-10, -15, 4, -11... | -18 | 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[[-2, -1, 8, -4, -2, -14, -3],\n [0, 15, 0, -11, -9, -14, 7],\n [0, 0, -6, -10, 1, 9, 18],\n [0, 0, 0, 11, -10, -2, 17],\n [0, ... | 422 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[10, 17, 16, -13, 4, -11, -17],\n [0, 2, 12, 17, 8, 17, 4],\n [0, 0, 18, 7, -12, 3, 4],\n [0, 0, 0, -9, 11, 7, -12],\n [0, 0, 0, 0, -6, 6, -11],\n [0, 0, 0, 0, 0, 1, -4],\n [0, 0, 0, 0, 0, 0, -4]]\nRound ... | 38423 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -6, 5, -5, 9, -8, -13],\n [0, -18, 6, -17, 13, -6, 14],\n [0, 0, 8, -15, 5, 4, 10],\n [0, 0, 0, 7, 1, -3, -16],... | -14 | 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[[8, 0, -4, -2, 13, 0, 0],\n [0, 2, 0, -8, -6, -6, 2],\n [-4, 0, -8, -1, -8, 16, -6],\n [-2, -8, -1, 3, 18, 8, -9],\n [13, ... | 83 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[6, -2, 13, 5, -12, -6, 8],\n [0, 17, 7, 12, -9, 7, 3],\n [0, 0, 8, 14, 1, -6, -5],\n [0, 0, 0, -3, 16, 15, -16],\n [0, 0, 0, 0, 13, 12, -17],\n [0, 0, 0, 0, 0, 4, 14],\n [0, 0, 0, 0, 0, 0, -17]]\nRound y... | 2295 | 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[[12, 6, -15, -8, -2, -17, -13],\n [-10, -14, 1, 10, 2, -10, 9],\n [-11, 12, 1, 8, -11, 2, 9],\n [4, -13, -16, -14, -10, -12, -15],\n [-14, -8, -4, 15, -6, -12... | -30 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-6, -18, 3, -4, 7, -1, -10],\n [-18, -10, 4, -17, -5, -1, -3],\n [10, -8, -13, -16, -5, -17, 13],\n [12, -8, 3, -16, 12, 14, 5],\n [-18, -4, 18, 8, 8, -7, -16],\n [11, 13, 4, -17, -12, 15, 13],\n [13, -5, -16... | 15 | 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, 8, 0, -5, 3, -10, 14],\n [8, 7, -4, -4, 6, 0, -6],\n [0, -4, 16, 2, -4, -1, -12],\n [-5, -4, 2, -13, 2, -7, -10],\n [3, 6, -4, 2, -10, 5, -8],\n [-10, 0, -1, -7, 5, 9, 8],\n [14, ... | 32 | 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[[-17, -11, 14, 9, -9, -18, 15],\n [0, -10, -14, -9, -7, -1, 2],\n [0, 0, -16, -14, 6, -11, -2],\n [0, 0, 0, 2, -12, -12, 8],\n [0, 0, 0, 0, -17, -12, -1],\n [0, 0, 0, 0, ... | -37 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 4) rounded to the nearest integer?\n[[7, -17, -12, -13, 6, 8, 12],\n [-17, 0, -15, 14, -5, 13, -7],\n [-12, -15, -13, 8, 2, -10, -2],\n [-13, 14, 8, 18, 2, 0, 5],\n [6, -5, 2, 2, 4, -13, -6],\n [8, 13, -10, 0, -13, ... | 11 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/252 * A where A =\n[[-18, -16, -2, -11, -2, 6, -7],\n [10, 6, 17, 6, 10, -8, -15],\n [-5, -2, -17, -11, 17, -9, -12],\n [17, -3, -5, -3, 6, -15, 10],\n [-13, -18, -18, -16, -18, -18, 2],\n [11, 13, 14, 3, 11, -15, 4],\n [6, -7, -2, -4, -... | 2 | 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[[8, 1, 13, -15, -14, -11, 3],\n [0, 3, 11, 18, -3, -4, -14],\n [0, 0, -9, -14, 4, -4, -1],\n [0, 0, 0, 2, -17, 3, -11],\n [0, 0, 0, 0, 11, 0, 4]... | 305 | 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[[-14, 4, 0, -18, 14, 14, 13],\n [9, 18, -7, -10, -8, 14, 0],\n [15, -12, 12, -17, 0, 13, -9],\n [-11, 7, 11, -8, 1, 1, -10],\n [-11, -4, 15... | 2225 | 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, -17, 5, 9, -18, -18, 9],\n [0, 1, -11, -18, 7, 6, -9],\n [0, 0, -7, -2, -14, -5, 15],\n [0, 0, 0, 17, -4, 0, -14],\n [0, 0, 0, 0, -7, 17, ... | 220 | 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[[-8, 5, 5, -12, 2, 1, -9],\n [6, 17, -4, -13, 18, -17, -7],\n [-15, 4, -6, -2, 12, -3, 7],\n [9, -18, -7, 18, 1, -17, 17],\n [-4, 3, 13, 1, 17, 14, -4],... | 46 | 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, 0, 0, 2, -3, 8, 8],\n [0, 0, -6, -17, -2, -8, 4],\n [0, -6, -1, 4, -1, 5, 10],\n [2, -17, 4, -17, 16, -4, -11],\n [-3, -2, -1, 16, 1, -6, -2],\n [8, -8, 5, -4, ... | 1878 | 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[[2, -15, 14, -5, 0, -14, 17],\n [0, -1, 12, 11, 2, 11, -15],\n [0, 0, 8, -3, 11, -6, 17],\n [0, 0, 0, 1, -14, 13, -13],\n [0, ... | 38471 | 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[[11, 4, 2, -1, -2, -6, -8],\n [4, -5, 0, -3, -10, -6, -8],\n [2, 0, 0, 6, 12, 10, -6],\n [-1, -3, 6, 7, 2, -10, 12],\n [-2, -10, 12, 2, -11, 4, -16],\n [-6, -6, 10, -10, ... | 308 | 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, -4, 2, 2, 8, 7, 4],\n [-4, 8, -12, -2, -4, -8, 4],\n [2, -12, 10, -8, -6, 3, 0],\n [2, -2, -8, 16, 4, 17, -2],\n [8, -4, -6, 4, 18, 9, -4]... | -99 | 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[[-15, -11, 13, -5, -6, 2, 5],\n [-1, 7, 13, 14, 12, -1, 16],\n [-7, 6, 12, -9, 15, -16, -11],\n [13, 10, 3, 1, -13, 10, -2],\n [12, 15, 18, -15, -17, -7, 16],\n [-13, -11... | -10 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-4, 3, 9, -10, 15, 17, -10],\n [0, 1, -11, 9, 0, -3, -8],\n [0, 0, -9, -1, 16, -16, 8],\n [0, 0, 0, -12, -9, -4, 12],\n [0, 0, 0, 0, 7, -7, 6],\n [0, 0, 0, 0, 0, 7, -2],\n [0, 0, 0, 0, 0, 0,... | -1092 | 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[[13, 4, 15, 0, -17, -17, -4],\n [0, 16, -14, 8, 5, -12, -13],\n [0, 0, 11, -11, -12, -13, -15],\n [0, 0, 0, 6, 14, 16, -14],\n... | -106 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, 4, -16, 5, -2, 12, -3],\n [4, 4, 2, 11, -8, 0, 4],\n [-16, 2, 2, -16, -5, -4, 4],\n [5, 11, -16, -13, -3, 3, 16],\n [-2, -8, -5, -3, -12, -6, 2],\n [12, 0, -4, 3, -6, 5, 14],\n [-3, 4, 4, 16, 2, 14, -16]]\nRound your ... | -15 | 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, -8, -2, -2, -10, 14, -4],\n [-8, 1, 4, -3, -16, -14, 8],\n [-2, 4, -16, 2, -14, 2, 4],\n [-2, -3, 2, 0, 1, -16, -3],\n [-10, -16, -14, 1, -... | 53 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 1) rounded to the nearest integer?\n[[8, 8, -1, 8, 10, -8, -17],\n [8, 8, 10, -6, 2, 10, -4],\n [-1, 10, -18, -7, -12, -1, -4],\n [8, -6, -7, -11, 6, 2, -6],\n [10, 2, -12, 6, -9, -10, 7],\n [-8, 10, -1, 2, -10, 9, ... | 8 | 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[[4, 1, -6, -11, -5, -1, 0],\n [1, -11, -4, 1, -1, 0, -2],\n [-6, -4, 7, 13, 4, 10, -2],\n [-11, 1, 13, -14, 2, -7, 10],\n ... | -281 | 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[[17, -13, 13, 2, -12, 7, -4],\n [0, -4, -3, 13, 18, -1, 1],\n [0, 0, 11, -16, -18, 3, 10],\n [0, 0, 0, 13, -13, -18, 2],\n [0, 0, 0, 0, 15, 0, 1],\n [0, 0, 0, 0, 0, -4, 1... | -66 | 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[[15, 0, 5, -15, 17, -6, 13],\n [0, -3, -16, 1, -9, 3, -16],\n [0, 0, -11, -10, -4, 13, -16],\n [0, 0, 0, 2, 0, 3, 1],\n [0, 0,... | -4945 | 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[[14, -15, 4, -8, -10, 11, -11],\n [-14, -7, -18, -4, 6, -1, 7],\n [-16, 3, 7, 0, 17, 2, 7],\n [-6, 17, 5, 7,... | 20 | 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[[-4, 2, -11, -10, 2, 2, -4],\n [2, -5, 0, 7, 2, -1, 16],\n [-11, 0, 10, -17, -16, -11, -8],\n [-10, 7, -17, 16, -4, 6, -11],\n [2, 2, -16, -4, -18, -9, ... | 30 | 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[[-4, -1, 5, 4, -7, 4, 2],\n [7, -11, 11, 15, -17, -14, 12],\n [14, -15, -13, 4, 0, -11, -6],\n [-18, -13, -12, 8, -4, 15, ... | -132 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, -6, 5, 10, -14, 16, 0],\n [0, -14, -5, 3, -10, 7, -14],\n [0, 0, -16, 9, -5, -5, -8],\n [0, 0, 0, 6, -3, -4, 15],\n [0, 0, 0, 0, -2, -18, -12],\n [0, 0, 0, 0, 0, 1, 7],\n [0, 0, 0, 0, 0, 0, 15]]\nRou... | 11047 | 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[[-1, -7, -4, 9, 12, -10, -11],\n [0, -11, 15, -15, 12, -16, 16],\n [0, 0, -9, -7, 11, 11, -1],\n [0, 0, 0, 5, 7, -16, 4],\n [0, 0, 0, 0, 10, -6, 7],\n [0, 0, 0, 0, 0, -11, -6],\n [0, 0... | -1772 | 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, -11, -3, 2, -9, 6, 3],\n [-15, -15, 11, -17, 10, 17, 2],\n [2, 2, -15, -18, 7, -17, -10],\n [-1, -8, 6, 7, 17, 16, -16],\n [16, 3, -11... | 475 | 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, -8, 18, 4, 0, 5],\n [-2, -6, -2, 4, 14, -10, -4],\n [-8, -2, -1, -12, -2, -2, 2],\n [18, 4, -12, 1, -8, 2, 0],\n ... | 40 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[12, -3, -8, 14, -10, -10, 4],\n [-3, -9, 4, -4, 6, -10, 4],\n [-8, 4, -15, 12, -18, 0, -6],\n [14, -4, 12, 17, -14, 11, -8],\n [-10, 6, -18, -14, 7, -8, 0],\n [-10, -10, 0, 11, -8, -6, -10],\n [4, 4, -6, -8, ... | -72 | 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[[-11, 6, 8, 8, 3, 12, -2],\n [6, -10, 2, 4, 0, 2, -8],\n [8, 2, 2, 6, -2, -1, -4],\n [8, 4, 6, -6, 5, 2, -4],\n [3, 0, -2, 5, -11, 7, 0],\n [12, 2, -1, ... | -37 | 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[[-6, 12, 6, -9, 5, -18, 6],\n [9, 17, -1, -13, -17, -16, -11],\n [12, 0, -13, -5, -16, -18... | -11 | 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[[2, -4, 1, 0, -1, -4, 0],\n [-4, 0, -1, 2, -8, -3, -10],\n [1, -1, -10, 12, 8, 6, 9],\n [0, 2, 12, 17, ... | 530 | 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, 3, 8, 18, 13, 0, 9],\n [9, -9, 1, 6, 2, -5, 3],\n [7, -8, -12, -2, -1, -12, 1],\n [-8, -3, 8, -8, -3, 4, -7],\n [-16, -17, 5, 10, 15, 1, -1],\n [-5, -1, -17, -18, 1,... | 838 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 7) of the inverse. Round your answer to the nearest integer:\n[[-18, -4, -8, -3, 16, -5, 11],\n [-4, 10, -3, -9, 0, 2, 10],\n [-8, -3, 2, -4, -5, 4, -9],\n [-3, -9, -4, -7, 1, -5, 2],\n [16, 0, -5, 1, -12, -10, 2],\... | -15 | MATH |
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