messages listlengths 1 1 | ground_truth stringlengths 1 9 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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[[1, -26, -15, -1, 14, -2, 12, 18, 32, -26, -5, -25],\n [0, -31, -14, 3, 5, -25, 22, -25, 12, 17, 21, 4],\n [0, 0, 25, 16, -8, 30, 6, 33, -1, -27... | 701 | 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[[19, -33, 30, 30, -35, 29, -5, -18, 10, -10, -12, 5],\n [0, -28, 32, 10, 24, 10, -35, 26, 10, -17, -33, 22],\n [0, 0, 18, -18, 33, 23, 8, 13, 20, -16, -12, 4]... | 1075 | 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[[-30, 8, -5, -1, -1, -17, -3, 23, 11, 35, 32, -34],\n [0, -2, 17, -11, -14, 1, -35, -4, 12, -29, 31, 30],\n [0, 0, ... | -29 | 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[[14, 9, -1, 26, 21, 10, 33, -6, 14, -21, 0, 3],\n [24, -9, 18, -34, 34, -32, 11, 12, 21, 29, 22, 15],\n [11, 34, -2, 1, 19, 8, 32, 7, -26, 30, -20, -1],\n [4, 26, -2, 6, ... | -115 | 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[[14, 16, 26, 5, -25, -29, -20, -7, -31, 28, -21, -30],\n [13, 15, 6, 29, -31, -12, 1, 17, -30, 3, 26, 24],\n [5, -26, 34, -29, -31, -9, -1, 19, -19, -29, 25, 29],\n ... | 2680 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (8, 1) rounded to the nearest integer?\n[[22, 21, -27, -26, 8, 17, -9, 16, 28, 18, -23, -5],\n [13, -9, -23, 10, 15, 7, -17, -7, 31, -17, -23, 2],\n [-1, -3, 9, 21, 13, 30, 3, 11, -3, 14, 30, -3],\n [13, 35, -26, -8, 8,... | 13 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (7, 8) of the inverse. Round your answer to the nearest integer:\n[[-33, -4, 26, -6, 13, -24, 14, -18, 11, 27, 8, -15],\n [12, 30, -4, 9, 15, 17, -8, 26, -7, 25, -28, 10],\n [-5, 30, 26, -18, 19, 1, -6, -15, -23, -17, -... | -7 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[19, -31, 29, -5, 24, 7, -27, 22, -20, 34, -2, -1],\n [0, 14, -24, -6, 8, -34, -27, 35, -24, -2, 13, 15],\n [0, 0, -10, 33, 13, 15, 5, -25, 11, -22, -20, 8],\n [0, 0, 0, -10, -33, 13, 5, -17,... | -1963328 | 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[[9, 0, -4, -10, -3, 7, -30, 16, 24, 23, 8, -12],\n [0, 31, 4, -16, -11, -4, 35, 16, -15, 13, -13, 28],\n [0, 0, -31, 29, 28, 7, 12, -34, 30, 31, -3, -13],\n [0, 0, 0, 32, 7, 18, 29, 10... | -3637 | 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, -2, -11, -6, -10, -24, 13, -2, 0, 19, -2, -10],\n [-2, 28, -26, -14, 0, -4, -12, 2, 12, 8, 2, 8],\n [-11, -26, 18, 1... | 386 | 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[[-4, 5, -16, 23, -35, 11, 11, -31, -32, 30, 12, 18],\n [0, -14, -34, 19, -20, -24, 20, 14, 30, -25, -18, 15],\n [0, 0, -10, -30, 20, 11, -17, -33, -23, 5, 5, ... | -4207892 | 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[[-4, 3, 16, -29, -14, 26, -9, -4, 1, -14, 15, -12],\n [3, -19, 6, -8, -18, -12, 0, 10, -14, 3, 27, 18],\n [16, 6, -16, 1, -13, -19, 0, -2, -4, 7... | 703 | 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[[-29, -14, -5, 23, 4, -33, 6, -19, -32, -28, -12, 5],\n [0, -8, -2, -32, -18, -2, -8, 2, 33, -7, 0, 7],\n [0, 0, 3, -22, 9, 9, -26, -29, -20, -22, -10, 6],\n ... | -9729 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[17, -14, -1, -8, 28, 8, 0, -16, -1, -6, 16, -20],\n [-14, 30, -13, 4, 2, 12, -12, 1, 1, -30, 9, -14],\n [-1, -13, 30, 8, 3, 16, -20, -12, 9, 35, 14, 4],\n [-8, 4, 8, -12, -34, 14, -22, 8, 20, -30, 2, -10],\n [28, 2, 3, -34... | 93 | 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[[1, -6, 12, 5, 10, -26, 16, 22, 10, -19, 32, 5],\n [-6, -32, 7, 24, -22, -4, 10, 17, -32, 11, 1, 20],\n... | 2156 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[14, -19, 3, 6, -13, 33, 28, -27, -28, 28, 4, -21],\n [0, -20, -8, 24, -8, -12, -33, -13, 14, 25, -33, -2],\n [0, 0, -12, 1, -2, 13, -15, -21, -23, -20, 25, -7],\n [0, 0, 0, -21, -25, -25, -8... | -3822 | 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, 34, -28, 20, 12, 6, -2, -4, -14, 1, -18, 14],\n [34, 23, 12, -14, -14, -11, -14, -8, 12, 4, -16, 20],\n [-28, 12, -34, 11, -4, -22, -22, -15, 14, 2... | -153 | 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[[12, 19, 2, -10, -1, 25, -14, -6, -18, -10, 10, 8],\n [19, 10, -8, 21, -16, -8, -10, 26, 14, 6, 22, -16],\n [2, -8, -13, 1... | 260 | 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[[-13, -2, 1, -31, 6, -11, 10, -9, -29, 24, -24, -29],\n [0, -28, -32, -8, 10, 25, 4, -2, -9, -10, -25, -35],\n [0, 0, 24, 32, -34, 18, -27, 33, ... | -209 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, -23, -17, 3, 17, 23, 1, -25, -20, -35, -14, 22],\n [12, 11, 18, -17, 28, 30, -20, 3, -15, 9, 29, -13],\n [6, -2... | 7 | 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[[8, 29, 9, 0, 3, 21, -5, -11, -15, -28, -28, -18],\n [0, 3, -24, 18, 33, -16, 6, 1, -9, 35, -20, -21],\n [0, 0, -35, -18, 20, 29, 5, -26, 2... | 148971 | 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[[14, -18, 13, 5, -12, -6, -21, -20, -18, -35, -25, 3],\n [-27, 3, -19, -1, -3, 17, 28, -9, -14, 6, 17, 29],\n [10, -22, -5, -23, -31, -8, -32, -7, -4, 7, -22, 27],\n [-33... | 495 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[11, -19, -4, -11, 2, 21, -27, 32, 34, 9, 29, -27],\n [0, 30, 33, -6, -25, -18, -2, 12, -30, -11, -11, -17],\n [0, 0, 2, 18, -9, -3, 14, -20, 15, -10, 14, -5],\n [0, 0, 0, -28, 3... | -54 | 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[[18, 10, -11, -17, -27, -6, 9, 19, -25, -1, -19, 22],\n [-8, -34, -15, 6, 31, -17, -31, -2, 15, 6, 7, -3],\n [31, -15, -17, 27, 31, -25, -11, 27, 3, 24, 9, -35],\n [... | 4491 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[6, 8, 2, -27, 8, -22, -1, -14, 10, -32, 15, 4],\n [8, -21, 6, 25, -10, 19, -1, 27, 5, -12, 0, 14],\n [2, 6, 1, 14, -27, -2, -2, 33, -7, -27, -3, -4],\n [-27, 25, 14, -30, -10, -14, -20, -4, 5, 10, 18, -2... | 7212 | 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[[-30, -34, -13, 19, 9, -14, 0, -34, -19, 11, -25, -14],\n [-27, -34, 34, 9, 24, -25, 6, 17, 1, -31, -11, 34],\n [8, 31, 20, -10, -19, -21, 31, -7, 28, -7, 19,... | -206 | 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[[-16, -13, 23, 14, -4, 16, 23, 21, -5, 18, -32, -16],\n [0, -10, -17, 3, -17, 11, 0, 1, 0, 15, -22, 2],\n [0, 0, -25, -14, -32... | -36310 | 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[[-11, -4, -17, 24, -25, 11, 7, -30, 25, 31, 26, -17],\n [-4, -5, 34, -32, -1, -23, 3, 22, -33, -19, 22, 10],\n [-7, -29, 15, 32, 28, -25, -... | 2675 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 8) of the inverse. Round your answer to the nearest integer:\n[[25, 5, 24, -2, 31, 15, 0, -1, 27, 23, -22, 26],\n [-15, 5, 24, 21, -24, 21, 4, -26, 26, -23, 26, 31],\n [6, 29, 31, 10, 32, 1, 22, 26, 11, -5, -6, -10]... | -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[[-27, -29, -32, -1, -24, -20, 14, 18, 35, 25, -26, 1],\n [3, -6, 10, 11, 29, -13, -11, -20, -1, 28, 21, 13],\n [-1, 21, 19, 32, -31, -8, 10, -20, -29, 1, -19, -19],\n [-9, -15, -2, 22,... | 358 | 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[[22, -20, -12, -15, -21, 4, -23, -25, 12, 21, 0, -14],\n [-20, -32, -23, 5, -12, -13, -20, -22, 9, 7, 1... | 1544 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-26, -33, 8, -20, 2, 27, -27, 31, 14, -30, -9, 35],\n [20, -21, -12, 19, -12, -17, -8, 32, 12, 33, 14, 30],\n [16, -31, -18, 29, -7, 18, 4, -1, -16, 24, 23, -24],\n [34, 31, 2, 18, 0, 22, -16, 3, 30, 10,... | 1028 | MATH |
[
{
"content": "Find the value at position (6, 10) of the inverse of matrix 1/839 * A where A =\n[[-7, -16, 33, 22, -8, -5, 28, -9, -10, 14, -9, 2],\n [-17, -29, 5, -28, -16, -13, -8, -13, 14, -15, -11, -3],\n [32, 22, 12, 29, -4, 26, -22, 22, 10, 31, 29, -19],\n [3, 16, 19, 32, -17, -9, -18, 17, -22, -31, 1, 6],... | -24 | 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[[-3, 33, -19, 24, 27, -2, -20, 15, -27, -9, 12, -6],\n [-14, -14, -12, 2, -30, -19, 19, 24, 16, -12, 15, -21... | 95 | MATH |
[
{
"content": "Find the value at position (4, 7) of the inverse of matrix 1/839 * A where A =\n[[31, -12, -18, -24, -14, 3, 17, 19, -17, 23, 30, -14],\n [0, 19, -32, 28, -31, 3, -11, -3, 4, -3, 7, -21],\n [0, 0, 13, 29, 2, -29, -21, 3, -4, 13, -6, 30],\n [0, 0, 0, 6, 8, -30, -13, 12, 21, 32, 24, 6],\n [0, 0, 0, ... | -280 | 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[[9, 6, 9, 1, -8, 13, -14, 15, 7, -16, 6, 2],\n [6, 5, 4, 5, -2, -16, 2, 11, 5, -27, -9, -21],\n [9, 4, -16, -4, 6, -12, -2... | -64 | 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[[20, 30, -14, 34, -4, 23, -4, -34, -23, 35, 23, -4],\n [0, 3, 17, 6, 16, -9, -6, -35, 24, -28, -32, 25],\n [0, 0, -18, 12, -24, 5, -1, -2, 12, 31, 23, 2... | 28165 | 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[[-15, 35, 31, -10, -8, -23, 23, 17, 29, 2, -27, 29],\n [-14, -10, 27, 25, 21, -15, -3, -24, 23, 10, -30, -16],\n [-3, -7, 17, 23, 18, 17, -1, -10, -13, 1, -9, 12],\n [12,... | 58 | 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[[6, 5, -12, 1, 7, 32, -28, -27, 3, -35, -33, -27],\n [0, 17, 11, 11, 27, -25, 13, 5, 19, -33, -22, 31],\n [0, 0, 16, -4, -2, -18, 17, 1, -35, -7, -22, -12],\n [0, 0, 0, -... | -773 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[2, 6, -2, -22, 6, -2, -30, 10, 12, 2, -8, -3],\n [6, 15, 20, 17, -15, 32, -28, -12, 4, 2, 15, -2],\n [-2, 20, -3, 27, -15, -22, -20, -5, -20, 30, -14, 20],\n [-22, 17, 27, 1, -7, 10, -28, -1, -6, 19, 18,... | 2006 | 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, 20, -20, 0, 22, -30, -3, 4, 11, 26, 26, 32],\n [20, 15, -20, 3, 4, 7, 21, -15, -6, 13, -12, -30],\n [-20, -20, 5, -23, 18, 11, -23, -3, 5, 10, 13, 8],\n [0, 3,... | 1635 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-31, -32, -28, -34, -33, -6, -29, 8, -12, -29, -35, -6],\n [28, 22, 25, 34, 29, -5, 26, 4, 30, -25, 16, 25],\n [26, 2, 17, 21, 0, 18, -3, 3, -32, 10, -19, -5],\n [3, -14, 28, 31, -18, 17, 24, 0, 12, 35, ... | 2256 | 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, 32, -10, 11, -32, 0, -34, 11, -20, 4, -16, -17],\n [0, -16, -31, 18, 14, 10, 1, 21, -21, -17, 19, 20],\n [0, 0, 11, -27, 0, -31, -7, 31, -11, 25, 11, 24],\n [0,... | 102975 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[33, -5, -2, 18, 4, -28, -7, -10, 23, -23, -26, -27],\n [-25, -27, -30, -6, -34, -17, -21, 21, 24, 26, -33, 10],\n [... | -19 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-23, 7, -9, 10, 10, 19, 14, -10, 1, 4, 0, -8],\n [7, 30, -28, 8, 9, 2, 20, 2, -8, -10, 10, -4],\n [-9, -28, -13, -2, 10, -10, 17, -10, 12, -17, -6, -2],\n [10, 8, -2, 34, 30, 15, 24, -3, -12, -5, -15, 6]... | 2135 | 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[[21, -3, 31, -34, -10, -13, -3, -8, -33, 17, 25, 6],\n [31, 30, 11, 10, -5, 22, -21, -26, 6, 21, -22, 29],\n [-20, 6, -11, 12, -15, 17, -34, -31... | -7 | 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[[-18, -16, -16, -3, -26, -4, 4, 2, 16, -14, 2, -5],\n [-16, 11, 8, 10, -30, 6, -4, 12, 6, -27, 7, 5],\n [-16, 8, -13, 11, -19, 22, 12, 1, -5, 4,... | 1904 | 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[[15, -1, -16, -16, -4, 27, -23, 35, -9, 4, 34, 23],\n [0, -6, -1, 19, 33, -33, 6, 3, 8, 30, 19, -5],\n [0, 0, 13, -7, -28, 13, -20, 24, 4, ... | 1401387 | 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[[-26, 2, 13, 10, -29, 12, 6, -24, 4, -8, -7, 16],\n [2, -2, 14, 1, 8, -20, 0, -8, 6, -2, 7, -10],\n [13, 14, 3, -2, 0, 0, -12,... | -46 | 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[[-32, 32, -16, 27, -8, -15, 3, 10, 21, -29, -17, -31],\n [19, 9, 5, 6, -4, 10, -32, -30, 31, -34, -15, ... | 1641 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-34, -2, -13, 14, -3, 6, 4, -18, 16, 4, 20, -10],\n [-2, -17, 0, 4, 5, -10, -20, -2, 12, 28, -8, -6],\n [-13, 0, -18, 12, 10, 5, 18, -11, 18, 26, -14, 35],\n [14, 4, 12, -20, -10, 14, 18, -6, -4, 0, 2, 4... | 3559 | 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, 6, 7, -4, 6, -12, -6, 0, -4, 23, -30, 2],\n [6, 33, 16, 7, 2, 5, 4, 22, 2, 2, 4, -34],\n [7, 16, 5, -9, -27, -18, -8... | 618 | 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[[-5, 4, 29, -20, 11, -29, -19, -19, 25, -33, 9, 23],\n [22, -4, 31, -35, -28, -6, 19, 20, -30, -4, 31, 32],\n [-8, -23, 31, 2, -12, -24, -27, -35, -16, 20, -4, 33],\n [17, -8, -29, -28... | 15 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (12, 4) rounded to the nearest integer?\n[[3, 17, 18, 10, -18, -29, 33, 6, 16, 30, -35, -19],\n [11, -11, 22, -3, 10, 0, 4, -32, 4, -34, -24, 16],\n [9, -17, -17, 10, 1, -24, 0, 29, 22, -29, 27, -24],\n [-4, 25, -11, 5,... | 12 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (6, 5) rounded to the nearest integer?\n[[9, 15, 22, 35, 3, 21, -7, -23, 8, 4, 7, 14],\n [20, 26, 19, -6, -8, 32, 5, -24, 2, 17, -13, 6],\n [31, -25, -26, -5, 8, 1, -11, -15, -21, -25, 9, -28],\n [-10, -15, 16, 14, -12,... | 105 | MATH |
[
{
"content": "Find the value at position (11, 6) of the inverse of matrix 1/839 * A where A =\n[[-26, -8, -4, -12, -13, -9, 14, -6, 0, 6, 4, 4],\n [-8, -28, 16, 22, -20, -3, 2, 16, 6, 14, -12, -11],\n [-4, 16, -4, -16, -13, -26, 2, -20, 2, -26, -3, -18],\n [-12, 22, -16, 33, -16, 18, -7, -20, 8, 3, -18, 2],\n [... | 3 | 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[[-26, 12, 22, 9, -23, 24, 0, -12, -8, 14, 9, 8],\n [12, -21, -8, 18, -13, -16, -24, 22, 12, -15, 16, -6],\n [22, -8, 7, 2, -5, -4, 3, 0, 28, -10, -28, 6],\n [9, 18, 2, 16... | -105 | 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[[-18, 2, 30, -18, 4, 2, -10, -2, -10, 23, 0, 24],\n [2, -8, 5, 15, 12, 20, -3, 18, 28, -16, 9, 4],\n [30, 5, 23, 30, 17, -2, 13, -8, 2, 5, -15, 8],\n [-18, 15, 30, -26, -10, -2, 27, -1... | 227 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[8, -2, 2, -24, 13, 2, -30, 24, 27, 12, 18, -2],\n [-2, 23, -6, -24, -31, -15, 8, -18, -24, -20, 14, 4],\n [2, -6, 12, 16, -12, 24, -20, 1, -18, 0, 15, -23],\n [-24, -24, 16, 5, -2, 5, -8, 17, -5, 15, 16,... | 3725 | 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[[-23, 0, 2, 24, 0, -22, 0, -3, 12, 0, 14, 21],\n [0, 33, 9, 1, 3, 14, 6, 16, -8, -6, 2, -26],\n [2, 9, 9, -18, 12, 10, -12, 2,... | -94 | 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[[-9, 11, 32, -19, -9, 15, 23, 23, -12, 18, -23, -22],\n [0, 34, 16, -15, -6, 18, -17, 23, 11, 30, -35, ... | 24015 | 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[[-28, -25, -16, 8, 23, -19, -24, -15, 31, -32, 18, -9],\n [32, -2, -35, 23, 16, 9, -18, 14, -2, 18, 18, 16],\n [-6, -32, 17, -12, 14, 9, 25, -29, 9, -2, -26, -25],\n [9, ... | -23 | 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[[4, -4, -17, -13, -9, -32, -1, -2, -24, 6, -23, -30],\n [-4, -11, -4, -4, -5, 16, -1, 24, -25, 13, -16,... | 6241 | 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, 6, 6, 4, -2, 2, 12, 15, -5, -10, -4, 4],\n [6, -14, 2, 1, -22, -24, -3, -14, -8, 31, 2, -2],\n [6, 2, 35, 17, 8, -14, 4, -21, 5, -24, -9, -11],\n [4, 1, 17, -1... | 1382 | 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[[27, -10, -9, 3, -31, 0, -35, 16, -28, -35, -29, 2],\n [0, 24, 31, -29, -28, -2, 4, 6, -4, 33, -23, 19],\n [0, 0, -29, -26, 1, 12, 29, 6, -23, -13, 21, -17],\n [0, 0... | 84967 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-1, -9, -30, 28, 1, 11, 8, 35, 30, 7, 21, 11],\n [0, -16, 31, 21, -35, 20, -28, 12, 22, 28, 35, 21],\n [0, 0, -33, 27, -25, 22, 10, -24, -28, 9, -21, 13],\n [0, 0, 0, -5, -16, -34, -30, -10, 1, 35, 23, 30],\n... | -846 | 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[[8, -18, 8, 10, -16, 14, 8, -10, 6, -22, 4, 2],\n [-18, 2, -6, 0, 22, 12, -2, -20, -3, 17, -3, -19],\n [8, -6, 11, -24, 19, 16, -25, 13, -25, 10, 22, 7]... | -45 | 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[[-20, -8, -19, 12, -12, -16, 19, -10, -7, -14, -16, -7],\n [21, -19, -26, 33, -35, 3, 10, -24, -16, -30, -18... | 11 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 3) of the inverse. Round your answer to the nearest integer:\n[[21, -5, -19, -19, -25, 24, -32, 22, -33, 0, 7, -16],\n [-31, 19, -10, 14, 16, 25, -21, 17, -2, -20, 11, 28],\n [34, 25, 5, 9, -34, 13, -17, 2, -19, -30... | -53 | 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[[-30, -12, -9, 27, -12, 19, -26, -16, -14, 9, 16, -17],\n [0, 12, 34, 11, -23, -28, -31, 32, -1, -21, -1, -3],\n [0, 0, 24, -15, 31, -1, -35, -18, -30, -17, -... | 2767 | 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, -26, -30, 2, -18, -16, -30, -6, -20, -11, 15, -20],\n [0, 1, 28, 35, 24, 19, 16, 20, -19, -9, -33, -7],\n [0, 0, -22, 20, -14, -12, -25, -7, 2, 34, -27, ... | 508577 | 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[[19, 2, 15, -29, 3, -26, -22, -18, -24, -8, 6, 14],\n [2, 35, 8, -6, -14, 12, 7, -18, -12, 18, 11, 6],\... | 1184 | 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[[-9, 8, 24, 17, -19, 0, 30, -34, -16, -26, 33, 22],\n [11, 27, 3, 26, 24, -4, 27, 3, -18, -12, -34, -20],\n [15, 18, 20, 26, 35, 24, -16, 2... | 1218 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 6) of the inverse. Round your answer to the nearest integer:\n[[34, 3, 1, 2, 35, -2, -8, 27, -6, 5, -28, -28],\n [-27, -11, -27, 28, -33, -9, 30, 23, 4, -12, -13, 5],\n [17, 13, 30, 25, 28, -2, -9, 28, 24, -1, 17, 3... | -31 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (8, 11) rounded to the nearest integer?\n[[27, -32, -35, -15, -28, 10, -24, -35, -14, -8, 28, 4],\n [0, 24, 5, 23, 32, 0, -3, 9, 14, 11, 8, 32],\n [0, 0, 10, -5, 26, -20, -24, 18, -27, -1, 17, 7],\n [0, 0, 0, -8, -7, 22... | 10 | 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[[12, 26, 20, -8, -15, 8, 34, 5, -1, 20, -19, -10],\n [27, -2, 35, -4, -32, -26, 20, -1, -3, -11, 11, -25],\n [-2, 0, -19, -24, -10, -23, 0, 33, 9, -24, 2, 31],\n [30, -16, 4, -2, -14, ... | -75 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-5, 12, -14, 35, 19, 4, -32, 7, 29, -34, -33, 20],\n [13, -9, 24, 31, 33, 1, 12, 30, 34, -9, -31, 16],\n [22, -11, 26, -20, 12, 35, 16, 31, -21, 31, 25, 30],\n [33, -12, 8, 35, -11, -16, 30, 30, -26, 14, 34, -25],\n [-6, -... | 138 | 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[[29, -33, 12, -21, 31, 26, -6, 7, -4, -1, 19, -21],\n [0, -13, -4, 14, 14, 4, 8, -24, 32, -14, 7, 6],\n [0, 0, -11, 15, 24, 1, -10, 8, 19, 14, -... | -383 | 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[[-27, -19, -28, 19, 5, -28, -23, 19, -16, 33, -11, -20],\n [0, 23, -1, -26, -17, -23, 33, ... | 1347 | 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[[-30, -21, 2, 5, 20, -18, -1, 9, -7, 33, -4, -31],\n [8, 14, -15, -14, 25, 3, -31, -3, 35, -12, 3, -21],\n [34, -31, 12, -... | 376 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[14, -14, -12, -14, -2, 12, -32, 21, 27, -6, 29, -32],\n [-1, -3, 15, -24, 32, -34, -3, 9, 20, -8, -6, -2],\n [-35, 16, -23, 4, 29, -27, 34, 13, -11, -10, -10, 4],\n [-2, -28, -34, -20, 27, -18, 3, 6, -4,... | 17479 | 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[[28, 0, 6, -8, -23, 2, 17, 21, -4, 4, -22, -2],\n [0, 27, 24, -18, -23, 30, -8, 27, 8, 4, 11, 4],\n [6, 24, 21, -14, -25, -20, -7, -6, -4, 14, 10, 11],\n [-8, -18, -14, 5... | 1868 | 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[[-27, -6, -18, -6, 24, 19, -26, -23, 5, -34, -31, -3],\n [29, 1, 25, 22, -24, 5, -8, 0, 6, 18, 18, 2],\n [35, 33, 22, -27, 12, -18, -24, -9, 0, 13, -27, -2],\n [14, 14, -... | 78 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 12) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, -14, 2, 8, -12, -11, 8, -2, -8, -6, 16, 5],\n [-14, -23, -2, 20, -16, -14, 20, 3, -16, -29, -8, 6],\n [2, -2,... | 15 | 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[[-23, 13, 20, 20, 16, 14, -23, 24, 12, -26, -8, -22],\n [13, 9, 6, -24, -3, 6, -24, -3, 16, 24, 6, -8],\n [20, 6, 32, 0, -19, 24, -12, 20, 6, 18, 4, -10],\n [... | -45 | 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[[30, 27, -24, 8, 18, -10, 18, -5, -14, 12, -28, -8],\n [32, -12, -11, 11, -19, 30, -28, 26, 1, -31, 10, -32],\n [23, 34, -7, -28, 12, 25, 17, 28, -20, -... | -110 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 1) of the inverse. Round your answer to the nearest integer:\n[[-21, 0, -14, -13, 10, 7, 33, 21, -3, -18, 0, -30],\n [0, -18, 16, 10, 3, -8, 5, 10, -12, -10, 6, -10],\n [-14, 16, 7, 20, -6, -8, -22, 20, 13, 0, -18, ... | 29 | 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[[-5, 14, -7, 3, -35, 29, 14, -18, 13, 1, 34, -1],\n [0, 29, 7, 30, -1, -2, 6, -28, -30, 4, 32, -13],\n [0, 0, 22, 0, -2, -15, 9, 22, -21, 9... | 314137 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[12, 20, 26, -12, -8, -8, 16, 8, 19, 14, -1, -18],\n [20, 24, -22, -26, -15, 21, -14, 0, 12, -17, -16, 20],\n [26, -22, -29, 23, 0, 8, 16, 19, 4, -8, 9, -6],\n [-12, -26, 23, 17, 9, 6, -6, -1... | -45 | 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, -13, -26, -31, -34, -11, 24, 31, 17, -19, 5, -3],\n [0, 34, -30, -23, -33, -22, 31, 0, 10, -35, -16, -17],\n [0, 0, 24, -8, -10, -9, -25, -8, 34, 9, 7, -... | 128883 | 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[[-4, -30, -8, -17, 8, -24, 3, 21, 0, -15, -18, -19],\n [-12, 12, -21, 4, 22, 4, 33, 3, -31, -22, 29, -1],\n [9, -9, -13, -31, 6, 17, 20, -33, -9, 10, -14, 27],\n [25... | 2059 | 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[[-17, -30, -28, -15, 19, -14, -4, 22, 4, 8, -4, -24],\n [-30, 22, -12, 0, 7, 8, -30, 25, -10, -3, -3, 9],\n [-28, -12, -17, 12, 14, 8, 6, 0, -2, 17, 13, 34],\... | 168 | 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[[24, 18, 9, -32, 0, -25, -35, 34, -20, 19, 17, 28],\n [0, 27, 30, 16, -32, 30, 4, 4, 3, -27, 8, -7],\n [0, 0, 3, 8, -21, 26, 4, -9, -18, -23, 5,... | 328 | 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[[23, -12, -20, 16, 25, 15, -31, 34, 5, 23, 24, -31],\n [29, 4, 6, 5, 27, -8, 7, -11, 20, -29, 13, 25],\n [-17, 7, 18, -11, -12, 9, 28, 32, 26, -... | -103 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 12) rounded to the nearest integer?\n[[23, 3, -15, 7, 31, 14, 21, -31, 17, -35, -30, 31],\n [-19, 4, -35, 35, -23, 9, 21, -21, -7, 12, 25, -13],\n [32, 14, 16, 21, 4, -14, -4, 1, 30, 25, 5, -9],\n [7, -18, -7, -7, -... | -1 | 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[[-17, 23, -17, 2, -15, 1, 21, 11, -5, 2, -33, -27],\n [11, 25, -27, 11, -5, 4, 13, 16, 6, -30, -21, -8],\n [... | 375 | 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, 17, 24, 14, -22, -22, 18, 29, 19, 2, -19, 17],\n [0, 4, 7, 11, 17, -27, 27, -9, -11, 23, -25, 32],\n [0, 0, -16, -19, -13, -32, -25, 30, -20, 1, 9, -4],\n [0, 0... | 24010 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 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[[11, -9, 19, -8, -9, -18, -35, 30, -18, 13, 8, 19],\n [0, -2, -11, 22, 24, 9, -32, 20, -11, 20, 0, -2],\n [0, 0, 2, ... | 30 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[34, -22, 24, 30, -18, -28, 34, -8, -11, 35, -1, -20],\n [0, -18, -17, -34, 19, 32, -28, -6, -10, 26, 35, -3],\n [0, 0, -2, 0, -7, 32, -1, -8, -14, 22, 15, -10],\n [0, 0, 0, 10, 35, -29, 1, 32, -13, -4, 18, 19],\n [0, 0, 0,... | 638118 | 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[[15, 11, -32, -35, 18, -13, 0, -1, 35, 19, 4, 13],\n [25, -17, 10, 32, 25, 34, 21, -22, -5, 16, -21, 25],\n [-18, -14, 32, -15, -25, 21, -22, -24, -24, -28, -34, -8],\n [12, -14, -23, ... | 15 | MATH |
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