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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[13, 12, 8, -14, 2, 6, 6],\n [12, -12, 0, -2, 0, 12, 6],\n [8, 0, -18, -10, -12, 2, -9],\n [-14, -2, -10, 11, 4, -11, 11],\n [... | -77 | 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, 11, -16, -5, -8, 4, 13],\n [0, -18, -10, -10, -7, -18, -3],\n [0, 0, -9, 14, 3, -3, 0],\n [0, 0, 0, 7, 1, 1, -14],\n... | -361 | 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[[-1, 8, 8, 6, -10, 0, -8],\n [8, 1, 6, -14, 2, 14, -2],\n [8, 6, 12, 8, 4, 3, 2],\n [6, -14, 8, -6, -10, -6, -10],\n [-10, 2, 4, -10, 5, -14, 2],\n [0, ... | -15 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[6, 1, 2, 6, 2, 8, -10],\n [1, 3, -4, 8, 0, 8, 0],\n [2, -4, -16, -12, 10, -6, 0],\n [6, 8, -12, 14, -3, 10, 2],\n [2, 0, 10, -3, -16, -8, -8],\n [8, 8, -6, 10, -8, 3, -6],\n [-10, 0, 0, 2, -8, -6, 15]]\n... | 1634 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-7, 9, 15, -13, 0, -7, 6],\n [0, -2, -7, -16, 5, -11, 17],\n [0, 0, 13, 13, -18, -16, -18],\n [0, 0, 0, -4, 18, 2, 4],\n [0, 0, 0, 0, 7, 3, 17],\n [0, 0, 0, 0, 0, 8, -15],\n [0, 0, 0, 0, 0, 0, -9]]\nRoun... | 9884 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-3, -9, -9, 17, 2, -5, -11],\n [0, -3, 7, -13, -17, -10, -14],\n [0, 0, -14, -14, -2, -10, 15],\n [0, 0, 0, -4, -18, -12, 4],\n [0, 0, 0, 0, -6, -6, -17],\n [0, 0, 0, 0, 0, 15, -3],\n [0, 0, 0, 0, 0, 0, -14]]... | -292 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[0, -6, -2, 2, 5, -1, -1],\n [-6, 11, -2, 12, 0, 7, -10],\n [-2, -2, 18, -8, -8, 6, 10],\n [2, 12, -8, -1, 3, 0, 0],\n [5, 0, -8, 3, 16, 6, 11],\n [-1, 7, 6, 0, 6, -16, -6],\n [-1, -10, 10, 0, 11, -6, -1]... | 1695 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -1, -14, -14, -11, -10, 13],\n [0, -6, -1, -15, 3, 1, -4],\n [0, 0, 15, 11, -14, -18, 12],\n [0, 0, 0, -9, 10, ... | 21 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-15, -1, 0, 0, 15, 4, 6],\n [-1, 2, -6, -2, -8, -12, -4],\n [0, -6, -7, 2, -4, -10, 3],\n [0, -2, 2, 9, -1, 2, 13],\n [15, -8, -4, -1, -1, -12, 2],\n [4, -12, -10, 2, -12, 11, 10],\n [6, -4, 3, 13, 2, 10, 16]]\nRound your ... | 49 | 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[[-8, -6, 4, 12, -3, 7, -1],\n [-6, -6, -4, -11, -4, 2, 3],\n [4, -4, 9, -14, -13, -14, 6],\n [12, -11, ... | 362 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[10, 6, -1, -16, -1, -12, 9],\n [-2, 6, -1, -16, 6, -12, -9],\n [0, -4, 2, 2, 18, 9, 13],\n [8, 4, -9, -13, 5, -1, -9],\n [-4, 15, -11, 16, 8, 6, -16],\n [2, 13, 2, -10, -18, -15, -15],\n [7, 15, 8, -4, 13, -12, -5]]\nRound... | 68 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -18, 9, 1, -8, -4, 14],\n [-18, 13, -12, -2, 0, 12, -2],\n [9, -12, -4, -8, -1, -1, -1],\n [1, -2, -8, -11, 2, 2... | 17 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[10, -2, 0, 4, 2, 10, -8],\n [-2, -7, 0, 0, 14, 0, -6],\n [0, 0, 3, 9, 8, -9, 0],\n [4, 0, 9, -13, 9, 4, 12],\n [2, ... | 17 | 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[[-5, -2, 6, 11, 10, 10, -1],\n [12, 0, -2, -13, -7, -16, 16],\n [14, 10, -16, -14, -5, 17, 9],\n [13, -1, -6, -17, 6, 1, -12],\n [-8, -14, 10, -1, -11, ... | -16 | 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, -14, 6, 0, -8, -2, -8],\n [-14, -6, -7, 3, -18, 10, 10],\n [6, -7, 13, 0, -15, 0, 12],\n [0, 3, 0, -11, -16, 8, 3],\n [-8, -18, -15, -16, -16, -1, 2],\n [-2, 10, 0, 8... | -44 | 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[[6, 18, 6, 10, 12, -17, -7],\n [-14, 8, 15, -5, -12, 18, 17],\n [-9, 10, -3, 2, 14, 10, -2],\n [-6, -13, -17, -11, 13, 17, -10],\n [4, -12, 12, 2, -18, -17, -8],\n [18, -1, 5, 0, -14, ... | -119 | 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, -11, 18, -17, -2, -6, -5],\n [0, 8, 1, -7, 3, 18, 12],\n [0, 0, -10, -9, 10, 11, -17... | -662 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-16, -4, -9, 3, 4, -8, -3],\n [-3, -5, -13, -2, 12, -9, 1],\n [-10, -4, -17, -15, 5, -1, -8],\n [18, 7, -11, 3, -14, -17, -14],\n [16, 13, 0, -15, 4, 0... | 16 | 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, -10, -2, 5, 14, 12, 0],\n [-10, -12, -8, -4, 3, -18, -2],\n [-2, -8, -14, 12, -4, 3, 4],\n [5, -4, 12, 13, -2, -5, 8],\n [14, 3, -4, -2, -5, -8, 4... | -42 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 7) of the inverse. Round your answer to the nearest integer:\n[[-1, 8, 14, 4, 10, 2, -5],\n [8, 0, 2, -6, -6, -3, -12],\n [14, 2, -9, -2, -1, 12, 4],\n [4, -6, -2, -7, 10, 3, -4],\n [10, -6, -1, 10, -10, -12, -6],\n... | 5 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-17, -4, 5, -10, 0, -6, -6],\n [-4, -9, -2, 6, 7, -10, 4],\n [5, -2, -3, -7, 2, 4, 8],\n [-10, 6, -7, -2, 9, -4, 16],\n [0, 7, 2, 9, -17, -2, -18],\n [-6, -10, 4, -4, -2, -14, 8],\n [-6, 4, 8, 16, -18, 8... | 480 | 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[[-18, -8, -1, 8, -9, 17, 2],\n [0, -18, -5, 1, -10, 8, -15],\n [0, 0, 12, -9, -10, 9, 9],\n [0, 0, 0, -11, 4, -14, -12],\n [0, 0, 0, 0, 14, 2, -2],\n [0, 0, 0, 0, 0, -16,... | 14 | 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, 7, -6, 0, 6, 2],\n [-8, -4, 1, -12, 6, -2, 2],\n [7, 1, -9, 5, -2, -16, 5],\n [-6, -12, 5, 0, -11, -12, 3],\n [0, 6, -2, -11, -4, 2, -14],\n [6, -2, -16, -12, 2, 14, -13],\n [... | -737 | MATH |
[
{
"content": "Find the value at position (5, 2) of the inverse of matrix 1/252 * A where A =\n[[-16, -16, -13, -9, -6, -7, 8],\n [-11, -14, 17, 11, 18, 10, 3],\n [-5, -9, -8, 16, 4, -11, 2],\n [18, 9, 12, 9, 8, 2, -10],\n [10, -4, 14, 18, 17, 9, -9],\n [4, 9, 15, -14, -1, -13, 4],\n [9, -6, 6, -12, -17, -3, -17... | 241 | 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, -17, -9, -5, 8, -4, 2],\n [0, 14, 3, -1, -17, 10, -12],\n [0, 0, -10, -11, 14, -14, -5],\n [0, 0, 0, 4, 8, -4, 11],\n [0, 0, 0, 0, -11, 10,... | 107 | MATH |
[
{
"content": "Find the value at position (4, 7) of the inverse of matrix 1/252 * A where A =\n[[-18, -4, 1, 8, 6, 3, 0],\n [-4, -15, -12, 1, 0, 0, -16],\n [1, -12, -5, 10, -12, 3, 8],\n [8, 1, 10, -5, -8, 5, 6],\n [6, 0, -12, -8, 0, -1, 2],\n [3, 0, 3, 5, -1, 11, 0],\n [0, -16, 8, 6, 2, 0, 3]]\nRound your answe... | 1 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[4, 2, 17, 11, 2, 4, 2],\n [0, -6, 3, -12, 5, -14, 7],\n [0, 0, -8, 11, -15, -17, -6],\n [0, 0, 0, -6, 10, -3, -16],\n [0, 0, 0, 0, -13, 9, 17],\n [0, 0... | 21 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-11, 5, 12, 0, -9, -2, 2],\n [5, 9, -1, 0, -5, -8, -2],\n [12, -1, -13, 10, 1, -2, 2],\n [0, 0, 10, -10, 1, -7, 6],\n [-9, -5, 1, 1, 5, 14, 6],\n [-2, -8, -2, -7, 14, 5, 3],\n [2, -2, 2, 6, 6, 3, -11]]\nRound... | -15 | 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[[-7, 13, 6, -16, 7, 17, -2],\n [0, 3, 16, -12, -16, -13, -6],\n [0, 0, 14, -4, -5, 0, 9],\n [0, 0, 0, -9, -1... | 166 | 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[[-12, -15, 18, -14, -17, -14, -16],\n [-11, 7, -9, 15, 17, -7, 1],\n [10, -5, -14, 8, -15, 10, -16],\n [14, 11, 17, -10, -18, 4, -16],\n [13, 5, -13, -6... | 5 | 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[[3, -2, 1, 5, 12, -11, -14],\n [-17, -15, 16, 15, -16, 1, -10],\n [-13, -14, 16, 12, -6, 7, 3],\n [13, -4, -8, -3, -13, -8... | -110 | 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[[6, 1, -10, -3, 9, 17, 5],\n [0, -5, 15, 5, -8, 17, -18],\n [0, 0, -10, -16, -3, -15, 7],\n [0, 0, 0, 8, -17, -9, 6],\n [0, 0, 0, 0, -2, -3, -1],\n [0, 0, 0, 0, 0, -4, 10... | -163 | 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, 15, -5, 6, -7, 1, -12],\n [0, -10, -15, 12, 4, -13, 9],\n [0, 0, 5, 15, 0, 5, 1],\n [... | 2193 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/252 * A where A =\n[[-12, -4, -2, -10, -6, 13, -17],\n [0, 1, 0, 8, 17, 11, -8],\n [0, 0, 11, -17, 15, 3, 12],\n [0, 0, 0, 7, -1, -4, 15],\n [0, 0, 0, 0, 16, -6, -6],\n [0, 0, 0, 0, 0, -3, 11],\n [0, 0, 0, 0, 0, 0, -4]]\nRound your answe... | 0 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[0, -2, -16, -16, 9, 12, -11],\n [-2, 16, 17, 8, 14, -8, 2],\n [-13, 2, 9, -2, -1, -8, 6],\n [11, 6, -12, 18, 8, 7, -6],\n [5, -7, -5, -10, 12, -15, 0],\n [-18, 10, -13, -18, 6, 8, 3],\n [-2,... | -57 | 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[[14, 3, -15, -6, 4, -6, 1],\n [0, 15, 10, 13, -8, -1, 2],\n [0, 0, -12, 8, -12, -17, 14],\n [0, 0, 0, -7, -6, -16, -11],\n [0, 0, 0, 0, 13, -13, 8],\n [0, 0, 0, 0, 0, -7,... | -16 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[-14, -15, -11, -3, -18, -4, 5],\n [0, -13, -17, -14, 15, 13, 10],\n [0, 0, 12, 5, -4, -7, 1],\n [0, 0, 0, 4, -12, -7, -4],\n [0, 0, 0, 0, -12, 11, -1],... | -26 | 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[[-12, 1, -12, 4, -4, -4, -5],\n [1, 15, 8, -1, -6, 0, 10],\n [-12, 8, -10, -16, 8, 4, 2],\n [4, -1, -16, -4, 2, 8, -8],\n [-4, -6, 8, 2, -3, -6,... | 42 | 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[[13, -1, -8, -8, 0, 4, -12],\n [-1, 11, -8, 0, -2, 3, -4],\n [-8, -8, 11, 2, 2, 2, 1],\n [-8, 0, 2, -11, 12, 0, -14],\n [0, -2, 2, 12, 3, 14, -12],\n [4... | -9 | 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, -7, 16, -2, -16, -8, -13],\n [0, -2, 3, -18, -16, -3, 16],\n [0, 0, 7, 12, 5, 0, 18],\n [0, 0, 0, -1, -18, 10, -6],\n [0, 0, 0, 0, -3, 6, -9],\n [0, 0, 0, 0, 0, -7, -11],\n [0, 0, 0, 0, 0... | -39889 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 2) of the inverse. Round your answer to the nearest integer:\n[[-16, -17, 10, 15, -5, 14, -1],\n [0, -17, -8, 12, -6, 7, 15],\n [0, 0, 3, 12, 0, 5, 6],\n [0, 0, 0, 3, 9, -7, 14],\n [0, 0, 0, 0, 7, -6, 4],\n [0, 0, 0... | 0 | 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[[18, -9, -17, 17, -17, -4, 1],\n [0, 11, 5, -17, 3, 10, -5],\n [0, 0, 7, -17, 15, 4, 16],\... | -14706 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 7) rounded to the nearest integer?\n[[7, -5, 6, 7, 6, 6, 8],\n [0, 1, -3, 6, 8, -1, -9],\n [0, 0, -15, 4, -12, 11, 7],\n [0, 0, 0, 7, -2, 12, -11],\n [0, 0, 0, 0, -12, 8, 16],\n [0, 0, 0, 0, 0, 11, -12],\n [0, 0, 0,... | 252 | 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, 0, -6, -3, -4, -8, -7],\n [3, 6, -16, 5, 6, -10, 9],\n [11, -12, -8, -9, -16, 0, -17],\n [-2, 10, -17, -3, -9, -15, 7],\n [5, -7, 2, -3... | 540 | 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[[-2, 1, -12, -15, -9, 2, -5],\n [0, -2, 9, -5, -6, 15, -16],\n [0, 0, 1, -11, -14, -17, 9],\n [0, 0, 0, -18, 17, -17, 7],\... | -1579 | 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, 12, -5, 6, 7, 3, -10],\n [14, 4, 16, 1, 14, 16, 11],\n [11, 3, -18, -4, 6, 1, -12],\n [-3, 4, 2, -18, 1, 0, -13],\n [13, -18, 11, -3, 8, -1, -6],\n [9, -9, -5, 10, -8, 8, -2],\n [-16, 12... | -251 | 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, -4, 6, 12, -14, -10, 2],\n [-4, 5, 10, 15, -10, 5, -4],\n [6, 10, -17, -3, 0, 5, -3],\n [12, 15, -3, 12, 14, 3, 1],\n [-14, -10, 0, 14, 17, 0, 0],\n [-10, 5, 5, ... | 423 | 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, -8, -12, -7, -11, 9, -3],\n [0, 18, 13, 2, -1, -8, -11],\n [0, 0, 3, -10, -5, -4, -8],\n [0, 0, 0, 18, -13, 18, 14],\n [0, 0, 0, 0, 12, 7, -8],\n [0, 0, 0, 0, 0... | 1223 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 7) of the inverse. Round your answer to the nearest integer:\n[[-3, 6, -1, -3, 0, -3, -14],\n [0, -13, 15, -3, 4, 13, 4],\n [0, 0, 10, -11, 10, -1, -14],\n [0, 0, 0, -2, 13, -15, 12],\n [0, 0, 0, 0, 13, 1, -6],\n [0... | -311 | 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[[-4, -14, 18, -15, 1, 3, 5],\n [0, -13, 8, -9, -9, 7, 18],\n [0, 0, 9, 17, 6, 17, -6],\n [0, 0, 0, 9, 1... | 3183 | 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, 0, 1, 8, 10, -1],\n [0, 6, 1, -13, 17, -4, -1],\n [0, 0, 3, -7, 14, 10, -17],\n [0, 0, 0, 11, 0, -9, 6],\n [0, 0, 0, 0, -11, -17, -1],\n [0, 0, 0, 0, 0, -17, 17... | 52 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-12, 2, 10, 18, -5, 18, -15],\n [0, -8, 15, -3, -10, -3, -3],\n [0, 0, -6, -14, -1, 1, -17],\n [0, 0, 0, 10, -3, 9, -2],\n [0, 0, 0, 0, 17, 7, -8],\n [0, 0, 0, 0, 0, -13, -7],\n [0, 0, 0, 0,... | -213 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[5, 18, 0, -14, 11, 6, 11],\n [6, -10, 8, 5, -4, 7, 11],\n [-8, 10, -4, -10, 10, -4, -2],\n [-3, 3, -8, 6, 11, -17, -18],\n [18, -10, -14, 5, 8, 11, -4],\n [-10, 18, 11, -4, 1, 6, -10],\n [3,... | 34 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-7, 16, -18, -18, 1, 15, 15],\n [0, 9, -8, -11, 16, -3, -3],\n [0, 0, -8, -11, 1, 13, 14],\n [0, 0, 0, -5, -16, -17, 3],\n [0, 0, 0, 0, -13, -11, 5],\n [0, 0, 0, 0, 0, 6, -6],\n [0, 0, 0, 0, 0, 0, 12]]\nRound... | -46 | 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, 18, 4, 7, -7, -18, 15],\n [0, 4, -12, -12, -18, -1, -11],\n [0, 0, 4, 10, -18, -4, -4... | -4408 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-3, -1, 6, 15, -15, -14, -5],\n [-18, 3, 2, -6, 17, 10, -10],\n [14, 3, -2, 4, 17, -13, 10],\n [8, -14, -10, 5, 0, 14, 11],\n [-15, 13, -18, 15, 2, 12, -5],\n [7, 3, 15, 14, -6, 13, -11],\n [3, 1, 2, 15, 11, ... | 6 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[8, 1, -5, -9, -4, -16, -4],\n [12, -8, 0, -4, 1, 3, -12],\n [-5, -15, -10, 6, 16, 18, 8],\n [9, 5, 14, 14, -3, 4, -8],\n [0, 15, 4, -9, 18, -18, -17],\n [3, -2, 5, 2, 10, -5, -11],\n [11, 3, 4, -6, 9, 11, -14... | 70 | 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[[-9, -10, -5, -9, 14, -8, -13],\n [0, 17, -13, -9, -14, 0, -12],\n [0, 0, -8, -16, 11, -13, 16],\n [0, 0, 0, 8, 10, -11, 4],\n [0, 0, 0, 0, -11, 14, -14],\n [0, 0, 0... | 1055 | 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, -12, 0, -2, 12, -10, -15],\n [-12, 12, -15, 0, 9, -5, -12],\n [0, -15, -4, -10, -8, -9, 4],\n [-2, 0, -10, -6, -4, -4, -4],\n [12, 9, -8, -4, 16, -10, 6],\n [-10, -5, -9, -4, -10, -9, 1... | 684 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[13, -10, -2, 16, -3, -17, 12],\n [0, 14, 2, -2, 16, -12, 10],\n [0, 0, -1, -3, -13, -17, -9],\n [0, 0, 0, 5, -14, 16, -15],\n [0, 0, 0, 0, -18, -8, 7],\n [0, 0, 0, 0, 0, 11, -13],\n [0, 0, 0, 0, 0, 0, 13]]\nR... | -136 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 5) rounded to the nearest integer?\n[[-7, -15, 13, 16, -3, -4, -17],\n [-13, -5, 10, 7, -1, -15, 18],\n [6, 10, 15, -3, 18, 11, 4],\n [17, 9, -18, -11, -4, 15, 0],\n [11, -9, 8, 1, 6, -10, 15],\n [2, 5, -12, -15, -1... | -22 | 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[[11, 5, 12, 4, 4, -11, 4],\n [5, -2, -11, 6, -6, 12, -10],\n [12, -11, -15, 4, 2, 0, 16],\n [4, 6, 4, -14, -... | 105 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[1, -6, 5, -16, 8, -8, 0],\n [-6, -5, -7, -8, 8, -6, -8],\n [5, -7, 7, -14, 0, -13, 2],\n [-16, -8, -14, 17, 0, 3, -6],\n [8, 8, 0, 0, 18, 1, 6],\n [-8, -6, -13, 3, 1, -12, -10],\n [0, -8, 2, -6, 6, -10, 11]]\nRound your an... | 8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-9, 13, -18, 5, 10, -12, 12],\n [0, 11, 6, 9, 17, -12, 16],\n [0, 0, 11, -18, 6, 15, -11],\n [0, 0, 0, 2, 8, -9, 4],\n [0, 0, 0, 0, -15, 4, -14],\n [0, 0, 0, 0, 0, 4, 4],\n [0, 0, 0, 0, 0, 0, 14]]\nRound your answer to the... | -1448 | 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[[10, 2, -11, 2, 0, -4, -5],\n [2, 8, -3, 4, 3, 2, -12],\n [-11, -3, 0, 0, 10, 2, -9],\n [2, 4, 0, 9, 3, 10, -10],\n [0, 3, 10, 3, -9, -10, 0],\n [-4, 2, 2, 10, -10, 8, 0]... | -662 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[3, 4, -14, 18, -12, 18, 7],\n [9, -15, 13, -10, 17, 7, -8],\n [1, -4, 16, -10, 14, -8, 3],\n [-13, 18, 2, -7, -12, -17, 5],\n [7, 6, 1, -17, 16, 14, -2],\n [3, -18, 18, 11, -13, -5, 17],\n [14, -13, 7, 5... | 1148 | 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[[15, 2, -10, -9, -9, 11, 14],\n [0, 13, -2, 9, -2, -5, -9],\n [0, 0, -2, 18, 3, -1, 16],\n [0, 0, 0, -13, -4... | -223 | 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[[9, 18, -14, 13, 12, -4, -16],\n [-4, -1, 2, -9, 2, 7, -16],\n [-18, 2, -8, -3, 16, 2, -8],\n [12, -18, 13, -16, 13,... | -36 | 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[[-12, 0, 14, -17, -16, 9, -5],\n [-4, 2, -5, -1, 1, -18, -10],\n [-10, 10, -4, 1, 11, 7, -13],\n [-2, -13, 9, -10, 8, 16, ... | -5 | 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[[1, -2, 16, 18, 4, -1, 17],\n [0, -12, 17, -18, 18, 16, -16],\n [0, 0, -10, 18, 6, -7, -12],\n [0, 0, 0, -9, 4, 7, 4],\n [0, 0, 0, 0, -13, ... | 3733 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-5, 10, -13, 15, -11, -17, 7],\n [-2, 5, 12, -3, 2, 7, -2],\n [-15, -15, 0, 6, -11, -1, -1],\n [-12, -2, -16, 3, -4, 12, 17],\n [7, -5, -2, -10, -12, 8, 9],\n [-7, -2, -10, -11, 8, -7, 18],\... | -478 | 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[[10, 4, 16, -3, -11, 8, -7],\n [0, 6, -13, -16, 5, 2, -13],\n [0, 0, 14, -16, -17, 5, 2],\n [0, 0, 0, -8, -16, 4, -18],\n [0, ... | -1522 | 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[[-6, -2, 7, -13, -2, -15, 6],\n [0, -2, 3, 9, -13, 11, -9],\n [0, 0, 7, -9, -17, -16, -8],\n [0, 0, 0, 11, -6, 11, -8],\n [0, 0, 0, 0, 7, 6... | 1264 | 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, -17, -5, -1, -10, -15],\n [0, -8, 11, 8, 10, 13, 11],\n [0, 0, -9, -7, 14, 15, -1],\n [0, 0, 0, 9, -1, -10, 3],\n [0, 0, 0, 0, -6, 6, 10],\n [0, 0, 0, 0, 0,... | 1583 | 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[[-17, 15, 1, -17, 9, -1, 16],\n [0, -16, 0, 4, 0, -1, 11],\n [0, 0, -6, 15, 5, -1, -15],\n [0, 0, 0, 17, -6, 3, 10],\n [0, 0, 0, 0, 18, -16, -15],\n [0,... | -42 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, 16, 3, 13, 7, -13, -8],\n [0, 2, 3, -18, 2, 1, -10],\n [0, 0, 14, -18, -16, 13, 1],\n [0, 0, 0, 10, 13, -6, 12],\n [0, 0, 0, 0, 18, 14, 18],\n [0, 0, 0, 0, 0, 18, -7],\n [0, 0, 0, 0, 0, 0, 18]]\nRou... | 2372 | 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[[-2, -3, 0, -10, -3, 10, 4],\n [-3, 13, 5, -6, 12, 4, 8],\n [0, 5, 11, 8, 6, -8, 1],\n [-10, -6, 8, -15, 15, 5, 11],\n [-3, 12, 6, 15, -11, -14,... | 131 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[-11, -4, -11, 10, 16, -5, 13],\n [-12, 14, 16, 8, -18, -13, -17],\n [-12, -11, 10, -3, 10, 12, 3],\n [-9, -15, 6, -6, -2, -11, 4],\n [-12, 13, 5, -18, ... | 28 | 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[[18, 7, -2, 16, -11, -8, 5],\n [-11, 11, -18, 15, 1, 17, 15],\n [15, -6, -13, 17, 6, 8, 12... | 16 | 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, 10, 18, 17, 2, -7],\n [4, -5, -9, 8, -17, -5, -12],\n [-2, 1, -11, 1, 17, -14, -6],\n [-2, -13, 0, 6, -16, 9, 7],\n [-11, -4, -18, 4, 17, -3,... | 23 | 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, 15, 7, -13, 14, 8, -7],\n [-11, -10, -18, -14, -12, -1, 5],\n [7, -9, -7, 3, 8, -16, -1],\n [-14, -5, 6, 12, 2, 1, -5],\n [1, 18, 11, 1, -1... | -34 | 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[[3, -9, 2, 6, -13, 11, 10],\n [-8, -8, 8, 0, 3, 9, -15],\n [18, 0, -2, 17, 4, 9, -8],\n [-5, -6, 5, -3, 9, 11, 8],\n [-2, 7, -12, 16, -4, -3, 2]... | 6 | 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, -2, 9, -12, -2, 0, 14],\n [-2, -5, -2, 0, 8, 6, 4],\n [9, -2, -7, 12, -9, 8, 5],\n [-12, 0, 12, -18, -8, 8, -4],\n [-2, 8, -9, -8, -10, -9, 9],\n [0, 6, 8, 8, -9, -... | 98 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -5, 0, 7, -9, -2, 15],\n [0, 7, 15, 0, 5, 12, -13],\n [0, 0, 3, -12, 14, -13, -3],\n [0, 0, 0, -5, 17, -4, -14],... | 0 | 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, -17, 12, 9, -3, -18, 3],\n [0, 12, 3, 15, -7, 4, 9],\n [0, 0, 4, -18, -17, 12, -17],\n [0, 0, 0, -13, 0, -2, -13],\n [0, 0, 0, 0, 4, -14, -9],\n [0, 0, 0, 0, 0, -14, -6],\n [0, 0, 0, 0, ... | 393 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[7, -9, -10, -18, -3, -6, -5],\n [4, -1, 9, 1, -18, -7, 8],\n [-6, -15, 6, -13, 3, 17, -16],\n [-4, -8, 15, 8, 4, -2, 4],\n [15, 2, 14, -14, -2, -18, -12],\n [-16, 7, -3, -3, -5, 7, 8],\n [-2, -15, -2, 14, 11, 2, -2]]\nRoun... | -177 | 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, 11, -1, 1, 15, 9, -10],\n [12, -3, 12, 10, -6, 4, -5],\n [-17, -7, 9, 13, 5, 18, 10],\n [-1, -16, -6, -6, 10, -17, 9],\n [-15, -14, -14, -11, 15, 6, 8],\n [-12, 17, 13, 2, -1, -17, -14],... | -41 | 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[[4, 3, 17, -9, 9, 16, 10],\n [0, -15, -4, 11, 7, 4, 10],\n [0, 0, -1, 16, 14, -12, 15],\n [0, 0, 0, 8, -13, -11, 2],\n [0, 0, 0, 0, 9, -13,... | 25478 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-15, -17, 9, -5, 10, -17, 15],\n [0, 1, 11, 7, 1, -18, -18],\n [0, 0, 4, -8, -4, -5, -18],\n [0, 0, 0, 7, -16, -13, 6],\n [0, 0, 0, 0, 4, -3, 13],\n [0, 0, 0, 0, 0, -1, 2],\n [0, 0, 0, 0, 0, 0, -2]]\nRound yo... | 19 | 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[[-17, 2, -12, 1, -16, 17, 0],\n [0, -8, -6, 14, -17, 4, 1],\n [0, 0, -17, 11, 6, -15, -18],\n [0, 0, 0,... | 1315 | 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[[7, 16, 9, 14, -1, -5, -10],\n [0, -16, 15, 14, 8, -10, -6],\n [0, 0, 7, -14, 8, -4, 9],\n [0, 0, 0, -13, -8, -3, 14],\n [0, 0, 0, 0, -9, -6, -18],\n [0... | 633 | 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, -15, 17, 2, 14, 7, -8],\n [0, 3, 18, -12, -6, 1, -4],\n [0, 0, 6, 10, 9, -5, -15],\n [0, 0, 0, 10, -2, 17, 0],\n [0, 0, 0, 0, 4, -1, 7],\n... | 255 | 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[[0, 6, 6, 4, -1, 7, -6],\n [6, 7, -11, 7, 11, -6, 7],\n [6, -11, 10, -3, -1, 4, -4],\n [4, 7, -3, 8, -4, -3, 0],\n [-1, 11... | 42 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[18, -8, 4, -10, -1, 17, 17],\n [9, 0, 11, -4, -7, -17, -10],\n [16, -18, 12, 9, 18, -12, -3],\n [-5, 14, -13, 2, -9, 13, -13],\n [-17, 8, -5, 4, 2, 11, 6],\n [5, -8, 16, -15, 18, 17, -6],\n ... | 33 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[2, 7, -16, 16, -12, 8, 14],\n [-15, 7, -11, 1, -2, -14, -10],\n [-11, -12, 18, 17, -16, -11, -14],\n [-14, -2, 8, -7, 9, -15, 9],\n [6, 17, -16, 12, 18, -7, 18],\n [18, -15, 11, 8, 3, -18, 1],\n [-1, -13, -7, -2, 3, -1, -9... | -31 | 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[[5, -1, 2, -1, 1, 12, 6],\n [-1, -14, -2, -4, -10, -4, 2],\n [2, -2, -9, -1, -2, 2, -4],\n [-1, -4, -1, 12, -8, -6, 6],\n [1, -10, -2, -8, -4, -3, -5],\n [12, -4, 2,... | 920 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[11, -14, 1, 8, 10, -8, -2],\n [-14, 9, -4, -5, -10, 0, 9],\n [1, -4, -17, 6, -13, 3, 14],\n [8, -5, 6, -5, -12, -6, 4],\n [10, -10, -13, -12, 5, 0, 5],\n [-8, 0, 3, -6, 0, -1, 0],\n [-2, 9, 14, 4, 5, 0, 3]]\n... | 84 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/252 * A where A =\n[[16, -15, -1, 5, 8, 14, 6],\n [0, -1, 1, 16, -13, 8, 9],\n [0, 0, 9, 0, 2, 12, -12],\n [0, 0, 0, 17, -2, 7, 9],\n [0, 0, 0, 0, 15, 4, 11],\n [0, 0, 0, 0, 0, 18, -15],\n [0, 0, 0, 0, 0, 0, -14]]\nRound your answer to t... | 28 | 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, 6, 5, 18, 12, 15, -5],\n [0, -15, 4, -14, 8, -5, -12],\n [0, 0, -17, 1, 10, 7, -18],\n [0, 0, 0, -10, 11, 0, -11],\n [0, 0, 0, 0, 13,... | 2442 | 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, -10, -16, -2, 15, 13, -10],\n [0, 1, -14, 2, -14, -15, -11],\n [0, 0, 18, 13, -2, 9, -13],\n [0, 0, 0, -18, -16, -6, 12],\n [0, 0, 0, 0, -18, 18, 13],\n [0, 0, 0, 0, 0, 18, -17],\n... | -1648 | MATH |
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