messages listlengths 1 1 | ground_truth stringlengths 1 9 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-35, 29, 21, -3, 8, 12, -35, -19, 9, 9, 19, 16],\n [-31, -9, 7, 5, 31, -16, 23, 23, -12, -10, -31, -7],\n [-10, 12, -4, 25, 0, 4, -17, -33, 25, -20, 24, -25],\n [-3, -28, 35, -20, 25, -10, -20, -8, 19, -10, -32, -15],\n [1... | -187 | MATH |
[
{
"content": "Find the value at position (10, 7) of the inverse of matrix 1/839 * A where A =\n[[-19, 8, 2, 5, 4, -30, 1, 23, 13, 22, -21, 4],\n [0, 16, 31, 33, 7, -30, -12, 8, -25, 28, -3, -12],\n [0, 0, 3, 16, -30, 17, -1, -26, -34, -28, 11, 31],\n [0, 0, 0, 17, -35, -16, 30, -28, 26, 15, 4, 26],\n [0, 0, 0, ... | 0 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[18, -35, -16, 5, -23, 8, 1, 24, -27, 27, 18, 14],\n [-4, 26, -24, 5, 8, 14, 24, -17, 16, -16, -35, -6],\n [35, -14, 12, 27, 33, -34, 0, -5, -22, 5, 25, 24],\n [-23, -32,... | 34 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[28, -24, 21, 12, -16, 6, 24, -7, 3, 14, 20, 14],\n [-24, -10, -22, -25, -20, -16, -1, 2, 5, 4, -8, 3],\n [21, -22, -1, 15, -12, 14, 0, -2, -22, 10, 20, -12],\n [12, -25, 15, 8, -18, -14, -12, 11, -2, 10,... | 5458 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[31, -24, -32, -25, 30, 22, -19, -17, -20, -17, 30, 14],\n [0, -1, -26, -1, 14, 15, 23, 4, 4, -7, -23, 24],\n [0, 0, 10, 34, -12, -14, 14, -4, 19, -14, ... | -5290 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 7) of the inverse. Round your answer to the nearest integer:\n[[25, -14, 14, -24, -17, -30, 20, -32, -11, -17, 18, -26],\n [-18, -33, 1, 26, 31, -2, -29, -11, 33, -16, -35, -20],\n [-7, 23, -11, -21, -1, 34, -3, -5... | -2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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, -35, -19, 2, 5, -25, 20, 29, 9, -24, 24, -24],\n [0, -29, -30, -1, -35, 4, 4, -11, -29, 20, -3, -35],\n... | 190 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[31, 34, 18, 14, 27, 6, -27, 27, -3, -30, 26, -22],\n [0, 20, 7, -32, 31, -19, -3, 18, 33, -7, -8, -25],\n [0, 0, -1, 9, 34, 28, 33, -32, 15, 26, -9, 26],\n [... | 500 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 6, 22, 2, -9, -7, -3, -4, 18, -21, -17, 8],\n [6, -3, -11, 19, 28, -28, 9, -14, -32, 12, -16, -18],\n [22, -11, -35, 19, 15, -7, -12, 6, 2, -10, -3, -6],\n [2,... | 1521 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, -18, 3, 29, -28, 3, -6, -7, 29, 15, 24, -34],\n [0, 26, 16, 2, 22, 3, 0, 27, -4, 21, -9, -26],\n [0, 0, 19, 14, 20, 1, 23, -20, 28, -35, 3, 6],\n [0, 0, 0, -7, -... | 11372 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, -20, 15, -10, 4, 11, 17, -2, -14, 24, -6, -6],\n [-20, -9, 5, 12, 13, -4, 20, 2, -2, 8, 2, -16],\n [15, 5, 27, 7, -7, -1, -3, -25, -4, 25, ... | 18 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-6, 27, 18, -25, -4, 22, 8, 12, 23, -21, 10, -34],\n [13, -31, -11, 12, 13, 17, 29, 2, 14, -33, -32, 32],\n [-6, -35, -14, 33, -19, -4, 17, 15, -21, 27, -21, -20],\n [-34, -10, 17, -3, 3, 10, 32, 33, -28, -14, -20, -3],\n ... | -335 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-23, -20, -24, 6, 4, -4, -30, -12, 28, 9, -8, 8],\n [-20, 31, 18, -8, 17, 6, -10, -26, 16, -23, 4, -22],\n [-24, 18, -32, -19, -18, -1, -6, 1, -12, 13, 15, -7],\n [6, -8, -19, -35, -21, 6, -6, -17, -12, -22, ... | 3536 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 13, 7, -19, 28, -2, -33, 30, 13, 0, -5, -19],\n [14, -4, 31, 2, 35, 12, 34, 18, 9, -26, -34, -17],\n [23, 34, -13, 21, -7, -20, -19, -... | 4618 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-32, 0, 3, 4, 33, -22, -19, 18, 31, 34, -5, -2],\n [-30, -20, -33, 4, 14, 25, -7, -5, 4, 34, 7, -22],\n [-5, -10, -12, 29, -26, 22, 27, -28, 16, -17, 5... | -40 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[19, 31, 2, 21, 13, -34, 17, -28, 27, -31, 27, -6],\n [0, 29, 34, -16, -26, -3, -32, -20, -5, -26, 23, 29],\n [0, 0, -15, -8, -27, -15, 27, 28, -29, 13,... | 0 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-12, -9, 15, 6, -10, 9, 17, 19, -22, 0, 14, 28],\n [-22, -34, -3, 12, 27, -35, 1, 12, -34, -22, -8, 5],\n [-18, 22, -25, -1, 12, -4, 23, 8, 15, -24, -18, 2],\n [34, -23, -29, 35, -1, -34, 31, -9, -25, -29, -34, 22],\n [21,... | 400 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-30, 6, 23, -22, 10, -18, 35, 31, 6, -33, -25, -25],\n [0, -22, 16, 15, 34, -22, 7, 29, -20, -17, 33, -25],\n [0, 0, 3, -25, -25, 19, 26, -31, -12, 27, 31, 14],\n [0, 0, 0, -27, 31, -35, -35, 11, -26, 29, -13, 1],\n [0, 0,... | -97274 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-2, -14, 22, -6, 13, 12, 4, 8, 23, 20, -8, 1],\n [-14, 17, -28, -2, -6, 27, -8, -14, -16, 8, -13, -10],\n [22, -28, 5, 14, 13, 14, 10, -4, 10, 10, -2, -2],\n [-6, -2, 14, -14, 14, 8, 9, 11, 20, -9, 0, 6],\n [13, -6, 13, 14... | 498 | MATH |
[
{
"content": "Find the inverse of 1/839 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[[34, 3, 8, 27, -34, -14, 27, 4, 0, -8, 17, 12],\n [3, -21, -10, 4, 7, -2, -12, 6, -11, -18, -20, 21],\n [8, -10, 4, -20, 32, 2... | 43 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 8, 33, -21, -26, 6, -24, 32, 2, 19, -16, -27],\n [0, -28, -23, -26, 19, 23, -6, 24, -9, -30, 32, 4],\n [0, 0, ... | -4983 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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, 17, 7, 1, -5, -16, 16, 6, 35, 15, 2, 35],\n [0, 14, -28, 18, 4, 11, -32, 12, -12, 22, ... | -100114 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-3, -1, -31, 21, 12, 1, 5, -4, 34, -20, -32, 9],\n [-27, 15, -9, 8, -26, 28, 9, -18, 34, -18, 30, 15],\n [11, -21, -34, -28, -21, -16, -30, 11, -15, -32, -15, -31],\n [-30, -30, 29, -4, 24, -2, 1, -8, 34, -25... | 55 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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[[25, 22, -12, 12, 17, -17, -30, -2, 14, 10, 2, 10],\n [22, 20, -6, -2, 12, -1, 0, 11, 8, -... | 455 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[19, 10, 35, 4, -17, 3, 31, 13, -16, 5, 11, 33],\n [-32, -32, 25, 2, 22, 33, -13, -25, -10, -27, 25, -15],\n [-27, 1, -10, 22, -5, 2, 18, 28, -9, 7, -35, 28],\n [5, ... | 941 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[10, -28, -12, 16, -6, 24, 0, -28, -20, -28, 28, -16],\n [-28, 23, -18, -14, 9, -10, -18, 31, -12, 16, -12, -8],\n [-12, -18, -4, 18, 22, -12, 25, -10, -10, 28, -22, -11],\n [16, -14, 18, 22,... | 19 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-7, 6, -8, 2, -6, 4, -14, 2, -6, 0, 22, 1],\n [6, -27, -17, -9, -1, -24, -6, 8, -24, 26, 19, 5],\n [-8, -17, 27, -6, 18, 16, -2, 10, 10, 6, 12, -30],\n [2, -9, -6, 11, 4, -14, -14, -3, -2, 14, -18, -14],\n [-6, -1, 18, 4, ... | -37 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 2, 8, 6, 10, -3, -14, 6, -12, 2, -6, -2],\n [2, 29, 0, 10, 6, 8, 0, 21, -17, 13, -2, -20],\n [8, 0, 23, 22, -3, 0, 0, 2, -8, 32, -16, -6],\n [6, 10, 22, 31, -9, ... | 2216 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (4, 8) of the inverse. Round your answer to the nearest integer:\n[[-35, -24, -16, -3, -8, 6, -21, 14, -13, 28, -3, -3],\n [0, -33, 4, -15, 30, 14, -18, 21, -4, 12, 3, -7],\n [0, 0, 30, 5, -22, 20, -13, -25, 34, 22, 13,... | -128 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, 30, -23, 15, 26, -7, -28, -16, -6, 22, 15, -16],\n [2, -28, 29, -30, 8, -35, 29, 9, -24, -32, 7, -11],\n [-24, 2, 20, -34, -24, 29, 11, 6, 2... | -61 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, -6, -14, -2, -19, 6, 10, -16, 2, 0, 0, 16],\n [-6, -21, 18, 7, -10, -11, 2, 20, 4, -12, -2, -2],\n [-14, 18, 15, -18, -22, -9, -8, 13, -5, 0, -4, -13],\n [-2, 7, -18,... | -536 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-1, 6, -8, 12, 12, 10, 14, 8, 16, 12, -9, 34],\n [6, 16, 2, 24, -4, 11, 28, 8, 14, -2, 10, 3],\n [-8, 2, 20, -18, -27, 6, -11, -10, 2, 14, -19, -20],\n [12, 24, -18, -14, -7, 1, -34, -10, -9... | 41 | MATH |
[
{
"content": "Find the value at position (3, 5) of the inverse of matrix 1/839 * A where A =\n[[20, 6, -10, 6, 22, -8, 14, -12, -10, -4, 0, 10],\n [6, -32, 9, 26, 3, 20, 0, -23, -10, -14, -22, -16],\n [-10, 9, 5, 22, 10, -15, 0, -4, 4, 6, -28, -13],\n [6, 26, 22, 2, 18, -5, 20, 12, -11, 8, 22, 0],\n [22, 3, 10,... | 18 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-23, 8, 30, -17, 32, 30, -8, 32, 5, -24, 35, -5],\n [0, 8, 15, 0, -19, 23, 18, 14, 32, 22, 21, -20],\n [0, 0, 21, 11, 26, 7, 28, 6, 1, -13, 15, 28],\n [0, 0, 0, 21,... | 21005 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-34, -10, 8, -10, -25, -6, -4, 1, -5, -10, -10, -18],\n [-10, -25, -10, -22, 0, -2, -16, -2, 8, 12, 16, -14],\n [8, -10, 26, -4, 14, 5, -16, 18, -12, -26, 10, 4],\n... | 1623 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, -5, 1, 18, 13, 2, -5, 17, -4, -32, -12, 5],\n [-5, -11, 8, 1, -6, 1, 1, -2, 0, -8, 0, -4],\n [1, 8, -32, -17, -2, -15, -6, -26, 21, -5, -2, -15],\n [18, 1, -17, -9,... | 348 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[29, 30, -26, -23, 35, -21, 13, 20, 20, 8, -17, 9],\n [0, 24, 6, -2, 29, 11, -33, -2, 10, -17, 21, -25],\n [0, 0, 5, 20, -21, -27, -30, -8, -1, 16, 27, -28],\n [0, 0, 0, -17, -31, 23, 21, 3, -33, 5, 35, 2... | 1044882 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, 0, 8, -6, 7, 4, -12, 2, -22, -8, 5, 4],\n [0, -10, 16, 2, 2, 18, 6, 6, -4, 8, 12, -16],\n [8, 16, 20, 0, -4, 4, 7, -13, -8, -2, -11, 32],\n [-6, 2, 0, 16, 21, 6, 0, ... | 872 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-24, 14, 2, 10, 2, 20, 16, 0, -9, -17, 0, 8],\n [14, 16, 27, -28, -13, 6, -15, 9, -6, 16, 21, -1],\n [2, 27, 16, 25, -6, ... | -107 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (3, 11) of the inverse. Round your answer to the nearest integer:\n[[-35, 12, 2, -15, -11, -23, 20, -12, 0, 14, 0, -25],\n [0, -26, 2, 0, -16, -2, 24, 0, 8, 23, 11, -16],\n [0, 0, 32, 31, 4, -2, -12, 21, 30, -6, 17, 3],... | -156 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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, -12, 5, -3, -10, -24, 19, 35, -12, -25, 33],\n [0, -35, -9, -12, 33, 13, 6, 14, -... | -726 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-26, 18, -2, -22, -1, -6, -14, 6, -29, -24, -22, -3],\n [18, 27, -8, -16, 6, -7, -20, 22, 9, 18, -2, -1],\n [-2, -8, 9, -7, -4, -26, -3, -5, 21... | -167 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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[[-20, -16, -24, 22, 22, -14, 6, -6, -16, 3, 0, 14],\n [-16, 20, 3, -10, -14, 4, -10, 16, -... | 136 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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[[34, 32, 0, 1, -35, -10, 6, 4, 17, 26, 8, 0],\n [0, -15, -19, -20, 5, 19, 21, 30, 2, 20, 1, 14],\n [0, 0, 29... | 27 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, -4, -13, -2, 4, -4, -2, 20, -3, -6, -21, 27],\n [-4, 34, 8, 26, 28, -1, 4, -1, 6, -30, 0, 20],\n [-13, 8, -35, 2, 0, -8, 1, -21, 0, -4, -8, -16],\n [-2, 26, 2, -... | 1306 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[28, -26, 21, 2, 4, -8, 2, 32, -18, -1, 16, 0],\n [-26, -2, -4, 14, -2, 25, -18, 15, -2, 8, 3, 10],\n [21, -4, -4, 7, -14, 28, 30, -26, -5, 18, -21, -24],\n [2, 14, 7, 10, 25, -10, 9, ... | 62 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[29, 28, 3, 1, -10, -2, 0, 10, 28, -10, -26, -5],\n [0, -8, -1, 21, -16, 0, 27, 34, 8, -23, -3, 14],\n [0, 0, 14, 16, 11, 7, -26, 12, 32, 19, 6, -5],\n ... | -32189 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (12, 7) of the inverse. Round your answer to the nearest integer:\n[[35, -28, -26, 34, 12, 18, 14, 11, -7, -27, 30, 33],\n [0, -20, -28, -14, -21, -8, -7, -4, -20, -3, 0, 3],\n [0, 0, -22, 3, 35, -16, 14, 3, -28, -6, -1... | 0 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 11) of the inverse. Round your answer to the nearest integer:\n[[-33, -9, 12, -21, -14, 5, -34, -3, -14, -4, -4, 2],\n [-9, -29, -6, 30, -25, -12, -14, 20, -26, -20, -2, 12],\n [12, -6, 4, -2, 10, -10, -8, -2, -2, ... | 178 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-34, 20, -20, 9, 11, 5, 8, 35, 22, 19, -11, -24],\n [-18, 29, 18, 28, 27, -21, 33, -30, -7, -10, -35, -7],\n [-21, 10, 28, 1, 19, 20, -19, 21, -14, -29, -33, 18],\n [20, 28, -27, 14, 35, 21, -28, 17, -1,... | 932 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (1, 10) rounded to the nearest integer?\n[[12, -30, 31, 34, -2, -33, 1, 18, -14, -34, -30, 2],\n [32, 21, -30, -2, 16, -30, 28, 23, 4, -20, 30, -26],\n [-6, -3, 32, 3, -32, 28, -11, -21, -30, 33, 7, 15],\n [-21, 19, -33... | -40 | MATH |
[
{
"content": "Find the inverse of 1/839 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[[-33, -8, 1, 0, -6, 8, 0, 10, -20, 2, -12, -2],\n [-8, -25, -6, 8, -4, -28, -1, 4, -12, -25, -12, -16],\n [1, -6, -6, -16, -17... | -145 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[31, 22, -10, 14, -29, -17, 32, 22, -9, 1, -28, -35],\n [35, 33, -32, 29, -4, -13, -18, -30, 23, 26, -24, 10],\n [-12, -23, 3, -34, -25, 35, 19, -12, 34, -28, 14, 33],\n [-11, -32, 31, -29, 8, -14, 22, -19, -28, 21, -4, 6],... | -83 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -24, -9, -31, 11, -27, -13, 27, -29, 17, 19, -6],\n [15, -27, -5, -31, 25, 16, -3, 22, 5, -19, 16, -25],\n [1... | -5 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-33, 6, -8, 15, -24, -3, 17, 10, 27, 16, 16, 10],\n [6, -26, 6, 18, 30, -16, 3, 19, 24, -20, 28, 4],\n [-8, 6, 32, 29, -16, -2, 32, 0, -4, -12, 18, 16],\n [15, 18, 29, -... | -539 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[32, 14, -2, -2, -3, 18, 12, -13, -6, 2, 10, -14],\n [14, -26, -9, 4, 8, -3, 30, -9, -6, 24, 10, 6],\n [-2, -9, 2, ... | 4 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[8, 14, -2, 16, -12, 6, 7, -21, -10, -19, -34, 10],\n [14, -33, 22, 0, 23, 10, -6, 15, 10, -24, 14, -14],\n [-2, 22, 30, 10, -9, -32, -28, 4, -14, -4, -2, 5],\n [16, 0, 10, 32, 22, 16,... | -43 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[29, -12, 24, 24, -22, -6, -28, 24, -10, 16, 28, 18],\n [1, 32, -4, -25, -28, 33, -6, 21, -11, -8, 29, 4],\n [-10, -17, -15, 27, 7, 29, 5, -16, -17, -15, -1, -2],\n [6, 1... | 154 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-33, -15, -14, -25, 33, -22, 32, 8, -6, 19, -11, -26],\n [27, -14, 17, -11, 17, -12, 1, 9, -22, 3, 32, -31],\n [-12, 4, 7... | -281 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-34, 5, 14, -12, -6, 1, -5, -8, 4, 3, 0, 14],\n [5, 22, 0, -20, 8, 9, 2, 10, -16, -6, -14, -12],\n [14, 0, -34, 13, 26, -4, 11, -4, -20, -8, 4, 2],\n [-12, -20, 13, 13, 30, -16, -18, 26, 17, 34, -25, 2],\n [-... | -27 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[28, -10, -7, -12, -1, 0, 0, 6, -5, -11, 0, 21],\n [-10, -16, 1, -4, 8, -4, -6, -2, 3, -12, 15, 20],\n [-7, 1, -9, -6, 2, -18, 10, -18, 8, -6, -15, -13],\n [-12, -4,... | 1450 | MATH |
[
{
"content": "Find the inverse of 1/839 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, -7, 14, 22, 14, -3, 3, -15, -2, 0, -3, 16],\n [-7, 1, 28, 3, -28, -23, 20, 19, 0, 14, 0, 8],\n [14, 28, 35, -24, -22, -2... | -111 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[35, -20, 9, -1, 20, 22, -28, 12, -6, 26, 22, 7],\n [-20, 31, 13, -8, 18, 14, 30, 6, -6, 22, 6, -4],\n [9, 13, 0, -16, -33, 22, -2, 0, -1, 0, -10, 28],\n [-1, -8, -16, 3, -7, 2, 2, 13, -16, 8... | -27 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -8, -5, 19, -23, -27, 7, 12, 13, 3, -32, -23],\n [8, -35, 8, 17, -20, -26, 30, -33, 11, -27, 10, -9],\n [15, 27, 23, 2, 14, 24, 34, 8, -2, 3... | -281 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[20, -20, -11, -33, 9, 14, -31, -3, 29, -4, -7, -13],\n [0, 24, 11, -25, 2, 32, -15, -30, 35, 0, -21, -27],\n [0, 0, -19, -2, 10, -6, -24, -29, 30, -15, 14, -... | 3936 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -7, 2, 6, 10, 14, -19, -12, -6, -15, -7, -20],\n [-7, -7, -20, 14, 26, -32, -2, -26, -26, 20, 16, 9],\n [2, -20, -18... | -268 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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[[12, -23, -19, 28, 15, -11, -16, 23, 33, -15, -3, 27],\n [0, -30, -24, 21, 21, 32, 14, -9, 25, -31, 31,... | 1077752 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[5, 5, 23, -23, -24, -10, 18, 10, -2, 20, 21, -1],\n [0, -3, 19, -18, -2, -30, 26, 32, 25, 27, -14, -16],\n [0, 0, 20, 29, -21, -8, -20, 24, 21, -21, 14, -15],\n [0, 0, 0, 23, 2, 1, -22, 26, 34, 11, 34, 3... | 86445 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 32, -23, -25, 15, 18, -12, -14, -17, -4, -1, 13],\n [0, 7, 18, 24, -2, -18, 2, 25, 15, 32, -10, 30],\n [0, 0, -24, 33, 29, -20, -30, 20, 2, 8, 9, ... | -25826 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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, 30, -9, -23, 6, -16, -33, 18, -19, -20, 2, -17],\n [28, 31, 0, -28, 3, 31, -3, 12, 10... | 107 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -22, -11, 24, 24, -18, -17, -11, 18, -13, -3, 15],\n [-5, -30, -9, -23, -30, 15, 11, 4, 30, 27, 30, 1],\n [23, 2, -13, 35, 33, 25, -11, -33, -2, -3,... | -71 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 8) rounded to the nearest integer?\n[[-10, 16, 23, 9, -3, 32, -1, 11, -9, 3, -8, -16],\n [-14, -10, 20, -12, -34, 31, -20, 4, -9, -4, -17, -18],\n [-33, 25, -8, -15, -32, 29, -18, 1, -6, 33, 16, 28],\n [2, -19, -24,... | -13 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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, 11, 10, 0, -17, -6, -14, 8, -17, 8, 4, 21],\n [11, -24, 6, -16, 15, -12, -18, 32, 16, -24, 6, 10],\n [10, 6, 32, 0, -1... | -363 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[28, -23, -18, -31, -10, -1, -9, -29, -29, -27, -16, -25],\n [-25, 24, 16, -19, 31, 9, 16, 31, 17, 11, -24, -16],\n [-10, -6, 24, 8, -22, -26, 1... | 477 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -10, -24, 16, 7, -9, -35, -16, -18, -30, 35, 20],\n [0, -31, 12, 31, 33, 22, -28, 29, -1, -32, 33, -27],\n [0, 0, -25,... | 35246 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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[[25, 28, 3, 22, -13, 0, 6, -8, 24, 2, 10, -2],\n [28, 22, -2, -9, -2, 8, -13, 20, 2, -14, 5, -10],\n [3, -2,... | 10 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[1, -12, -6, 2, 32, 16, -6, 12, 6, -3, -16, 5],\n [-12, 1, 8, -2, 24, 8, -6, -6, 5, -29, 10, 15],\n [-6, 8, -4, 10, -16, 11, 11, 26, 20, 14, -6, 4],\n [2, -2, 10, 14, -8, 6, 11, -6, 12, -23, -20, 18],\n [32, 24, -16, -8, -2... | -47 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[27, -2, 19, 0, -30, -24, -22, 21, -14, 27, 7, -20],\n [0, -24, -22, 1, 16, 14, 21, -10, 1, -18, -1, -26],\n [0, 0, 9, -33, 9, -2, 34, -14, 30, -25, -19, 1],\n [0, 0, 0, -25, -6, -34, -1, -7,... | -26287 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-33, 35, -35, 13, -1, -1, 13, 26, -20, 29, -34, -34],\n [0, 23, 6, -4, -20, 13, 17, 30, 1, 17, 15, 30],\n [0, 0, -7, 30, -21, 9, 35, -7, -3, 15, -31, 1... | 2536 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-10, -26, -16, 19, 11, 13, 26, -28, -21, -23, -11, 9],\n [0, 6, -8, 25, 3, 2, -26, 16, 23, -23, -11, 19],\n [0, 0, -15, -15, -8, 27, -16, -31, -13, -27, -27, 16],\n [0, 0, 0, -19, 14, -32, 31, 10, -17, -35, 30, 16],\n [0, ... | -24284 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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, 10, -3, -10, 0, 2, -6, -10, -22, -18, 20, -4],\n [10, -30, 8, 12, 2, -14, 6, -7, -6,... | -56 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-27, 19, 19, 16, 11, -4, 31, -28, 6, -19, 5, -3],\n [0, 9, -27, -17, 2, 7, 2, 24, -35, -15, 26, -32],\n [0, 0, 12, 0, -34, 12, -18, -6, -28, 35... | 670 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-19, 15, 19, -7, 3, -20, 0, -28, 25, 35, -23, -15],\n [0, -31, 5, -8, 23, 7, -32, 20, 1, 4, -27, 4],\n [0, 0, 14, 24, 2, 6, -19, 18, -25, -18, -17, 16],\n [0, 0, 0, 25, 4, -10, 26, 4, 31, 35, -33, -18],\... | 1294222 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[22, -28, -29, -20, -33, -34, -6, -7, 21, 28, 24, 8],\n [-27, -1, -12, 24, 30, -34, -17, -25, -20, -4, 22, 17],\n [15, 22, 35, -18, -28, 8, -4, -32, 14, -30, -5, 8],\n [22, -2, 29, -17, -34, 19, 33, 0, 25... | 1646 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[27, -20, 8, 12, 11, 3, 34, -5, -4, 15, 9, -33],\n [-25, -32, 17, -32, 31, -13, 20, -19, -24, 3, 6, 13],\n [-31, -21, 27, -10, -12, 7, 0, -10, 28, -25, -16, 16],\n [-3, -30, -34, -17, -6, -11, -22, -20, -... | 1713 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -27, -2, -2, 30, -19, -26, 32, 28, -13, -28, 10],\n [0, -18, 32, -19, 2, 34, -28, 20, 24, 15, -24, -21],\n [0, 0, -19, -9, 11, -1, -7, -23, -12, -18, 26, -22],... | 2516594 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 10) rounded to the nearest integer?\n[[12, 27, -28, -1, -4, -2, 9, -14, -28, 3, -2, 20],\n [27, -32, 28, -4, 0, 1, -4, -25, -29, -2, -2, 0],\n [-28, 28, 4, 0, -12, -16, -2, -3, -2, 11, 16, 23],\n [-1, -4, 0, -28, -1... | -21 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 12, 0, -10, 28, -26, -8, -5, 0, 20, 0, 8],\n [12, 9, -6, -6, 6, -18, 21, 29, -20, 16, 0, 24],\n [0, -6, -31, 8, 11, 4, 0, -24, 10, -29, 10, 0],\n [-10, -6, 8, -1... | 2376 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 11) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -35, -9, 9, 1, -10, 14, 2, -25, 33, -31, -22],\n [0, 16, -12, -31, 6, 10, -5, 15, -1, -19, 25, 0],\n [0, 0, -2... | 0 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-31, 34, 3, 10, -15, -4, -33, -24, 12, 12, -12, 13],\n [0, -6, 13, 13, -35, -29, -19, 6, -5, -23, -25, -8],\n [0, 0, 32, 18, -29, 28, 26, -12, 31, 24, 7, 35],\n [0,... | 712129 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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[[7, 9, 2, 4, 0, -2, -16, 1, 6, 20, -7, 22],\n [9, -11, 0, 12, 6, 16, -10, 0, -21, -13, -2, 28],\n [2, 0... | 2103 | MATH |
[
{
"content": "Find the inverse of 1/839 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[[-29, 14, -20, -8, 24, 14, -5, 2, -32, -8, 16, -20],\n [14, 1, -2, -22, -6, 19, -13, 10, 1, 8, -6, -8],\n [-20, -2, 12, -18, 2... | -175 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, -12, -14, 3, 28, 6, -1, 8, 4, 0, -5, -28],\n [-12, 7, -2, -4, -9, 10, 13, 16, 17, 11, 18, -17],\n [-14, -2, -33, 20, -9, 16, -10, -18, 0, 14, 4, -14],\n [3, -4, 20, 14, 12, 8, -18,... | 193 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, -25, 32, -5, 5, -2, 30, 30, -35, -7, 21, 27],\n [12, 0, -33, 13, 22, 0, 9, -2, -14, 29, 26, 16],\n [-10, 33, -30, 22, 0, 10, -15, 19, 7, -1, -22, -11],\n [3, 3... | 1481 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 8) rounded to the nearest integer?\n[[24, 0, -2, -2, -9, 29, -7, -4, 21, -23, 0, -23],\n [0, -31, 17, -19, -34, -11, -29, -2, -10, 22, 25, -16],\n [0, 0, -19, 27, 30, -20, 19, 20, 7, -26, 17, 24],\n [0, 0, 0, -14, ... | 0 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, -28, 19, -17, -3, -12, 13, 31, -33, 17, -35, -9],\n [0, -5, -8, -20, -27, -4, 29, 29, -12, 30, 21, -18],\n [0, 0, 30, -34, -25, 24, 25, 29, -8, -9,... | 18839 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -9, 28, 11, -28, 28, 20, 29, -34, 4, -24, 8],\n [0, -24, -24, 35, 2, -19, 11, 9, 30, 3, 4, -13],\n [0, 0, 5, 2, 14, 27, 27, -7, -18, 9, 17, 2],\n [... | -8842 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[24, 29, -34, -34, -11, -20, -30, -8, 34, -35, 9, -22],\n [-9, 3, -27, -14, -31, -1, -8, 18, -27, 11, 32, -2],\n [28, -25, 1, 24, 24, 23, 4, 8, 26, 0, 25, -21... | 113 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, -30, -2, 7, 33, -15, -35, 7, 23, -1, 25, -17],\n [18, 22, 27, 6, -30, 18, 8, 23, -22, -20, 24, -7],\n [25, -22, -5, 19, -18, -32, 0, 17, -2... | 23 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[28, -8, -8, -14, -13, -16, -8, -22, -16, 10, 0, 16],\n [-8, 23, 13, -33, 18, 12, -14, 34, 27, -10, 0, -14],\n [-8, 13, 19, 19, -17, -24, 3, -2, 8, 4, -1, -5],\n [-14, -33, 19, 9, -4, 14, 25, -23, -8, -10... | 1149 | MATH |
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