messages listlengths 1 1 | ground_truth stringlengths 1 9 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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[[-22, -13, 28, -19, -12, 18, -20, 32, -4, -2, 18, -32],\n [-13, -23, 18, -11, 28, 4, 11, -20, 4, 24, -25, -7],\n [28, 18, 22, 0, 0, 6, 22, 8, 9, -30, -26, 3],\n [-19... | 2979 | 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[[35, 34, 17, -22, -15, -22, 17, 31, 12, 20, 3, 5],\n [12, -8, -34, -14, 35, 25, 0, 30, 13, -33, -13, 23],\n [-8, -3, 32, 35, -25, -28, -16, 26, 7, 34, -29, -2... | -497 | 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[[-17, 22, 21, 6, -30, -14, 17, 21, 15, -31, -14, -29],\n [28, 21, -10, -11, 33, -4, -28, -27, 18, -16, 32, 31],\n [8, 5, 6, -2... | -159 | 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[[-7, 20, -21, -21, 1, -17, 23, 15, -1, 0, 17, -24],\n [0, 35, -3, 19, 14, -7, 22, -10, -13, -19, -31, 23],\n... | -517 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-31, 10, -32, -5, -32, -18, -2, 12, 27, -22, -3, 6],\n [0, 7, 21, -21, 14, 35, 27, 34, -27, -23, -18, -1],\n [0, 0, 31, 10, 1, -7, 8, 32, -22, 15, -27, 33],\n [0, 0, 0, 4, -28, -30, 17, -31, 18, -18, 35, 0],\n [0, 0, 0, 0,... | 11701 | 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, -10, -35, 25, 3, -27, -9, 34, -16, 29, -20, 32],\n [0, -14, 20, 21, 18, -28, -29, -35, 18, -24, -22, -17],\n [0, 0, -21, 27, -13, 7, -26, 0, 27, 13, -22, -2],\n [0, 0, 0, -1, -13... | 118952 | 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[[-31, -16, 2, 3, 4, 5, -4, 0, -10, 8, 5, -9],\n [-16, 6, 6, -11, 8, 2, 1, -2, -8, 6, -10, 16],\n [2, 6, 6, 0, 26, 14, 18, -8, ... | 212 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[21, 1, 11, -13, -17, -8, 3, 0, -6, -30, -13, 26],\n [1, 28, -8, 27, 16, 12, 4, -10, 10, 0, -6, 4],\n [11, -8, 22, -16, -4, -23, -16, 6, 2, -18, 4, 2],\... | -10 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-13, -8, 7, 27, -19, 0, -17, -31, -13, -17, -35, -9],\n [0, -11, 18, -30, -11, 10, 23, 19, -12, -12, -33, 4],\n [0, 0, 34, 30, 33, -28, 19, 1, -22, 12, 31, -4],\n [0, 0, 0, -25,... | 0 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[7, -17, -25, 16, -4, -7, 0, 11, 7, 16, 17, 32],\n [-31, 12, -12, -35, -34, -26, 27, 23, -30, 12, 0, 12],\n [-7, 5, -4, -31, -19, -12, -30, -8, -16, -17, -28, -18],\n [1, 25, 9, 2, -34, 19, -21, 23, -31, -16, -24, 21],\n [3... | 75 | 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[[17, 6, -7, 11, -6, -22, 23, 28, 8, -22, -11, 8],\n [0, -34, 7, -27, 25, 31, -12, 29, 2, 34, -31, 32],\n [0, 0, 26, -29, 15, -4, -10, 7, 26, -5,... | -127 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (4, 7) of the inverse. Round your answer to the nearest integer:\n[[0, -18, -7, 10, 24, -7, -12, 0, -14, -17, 1, -1],\n [-18, 23, 22, 10, 22, -18, -4, -5, -4, -20, -23, -6],\n [-7, 22, -11, 10, -12, 2, -8, 2, 0, -2, 22,... | 1 | 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[[25, 19, 35, -7, 12, 27, -15, 21, -23, -9, 32, 28],\n [0, -29, -25, -8, -9, -14, 6, -4, -22, -10, 19, 35],\n [0, 0, -6, 30, -10, -35, -12, 19, 2... | 22 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[0, 33, -2, 1, 15, 1, -11, -31, -28, 17, -9, 25],\n [29, 35, 9, -33, 25, 14, 12, 11, -22, -17, 26, -30],\n [-29, -23, 10, -3, 5, 33, -7, -29, 18, -25, 6, -31],\n [11, -34, 7, -32, 27, 23, -6, -34, 7, -18, -12,... | 689 | 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[[0, -2, -24, 14, 20, 12, 3, 4, -28, -12, 1, -16],\n [-2, 24, 6, -18, -22, -19, 14, 2, 2, 12, 4, 6],\n [-24, 6, 16, 16, 6, 17, 2, -10, 19, 6, -4,... | 918 | 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, 34, -13, -19, -11, 2, -33, 31, -22, -26, 30, 35],\n [-22, -26, 13, 26, 12, -33, 11, 24, -11, -29, 3, 7],\n [10, 7, -7, 30, 33, -9, -33, 20, 28, -15, -12, -16],\... | 1585 | 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[[-27, -33, 2, 34, 33, -6, -22, -34, -28, -18, 35, -23],\n [10, 18, -24, 4, 2, -24, 31, -11, -1, -20, 9, -23],\n [-12, -34, -26, -17, -12, 2... | 24800 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 7) rounded to the nearest integer?\n[[14, -1, -1, 23, -23, -14, 20, -31, 7, 19, -21, 6],\n [-27, 35, 21, -26, 28, 5, -23, -20, 24, -5, 19, 35],\n [-2, -32, 19, 30, 23, 5, 30, 11, -9, -15, -25, -14],\n [-13, 29, 23, ... | -284 | 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[[15, 8, 14, -10, -7, -12, 24, 18, -6, -4, -30, 30],\n [8, -21, 6, -10, -5, 8, 12, -26, 4, 6, 6, 16],\n [14, ... | -710 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-33, -8, 9, -8, -26, 4, 12, -2, -14, 24, 6, -14],\n [-8, 29, 6, 14, 26, -10, -2, 21, 12, -7, -8, 10],\n [9, 6, 2, -6, 14, -2, -17, 1, 12, 10, 6, -2],\n [-8, 14, -6, 26, 20, 7, -3, 3, 2, -26, 7, -10],\n [-26, ... | -942 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -24, -27, -16, -21, -28, -15, 9, 4, -30, -25, 28],\n [0, 23, -28, 19, 3, 15, 19, -33, 7, 9, -20, -31],\n [0, 0,... | 0 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 11) of the inverse. Round your answer to the nearest integer:\n[[5, 17, 28, 4, 26, 19, -25, 16, -10, 12, 9, -3],\n [28, -27, -34, -22, 0, -1, 28, -11, -27, 7, -26, 21],\n [-3, -27, 18, -23, -12, 26, 4, 23, 20, 28, 2... | -25 | 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[[-34, -10, -16, -22, -16, 0, 22, -10, 23, -18, 8, -2],\n [-10, 30, 24, 30, 15, 17, 12, 17, -14, 5, 12, 12],\n [-16, 24, -6, 8, -10, 12, 12, -15, -8, 7, ... | -64 | MATH |
[
{
"content": "Find the value at position (8, 7) of the inverse of matrix 1/839 * A where A =\n[[0, 22, 19, 10, -9, -12, -18, 4, 0, 27, 2, -12],\n [22, -3, -15, -5, 8, -8, 10, 10, 21, 2, 17, -15],\n [19, -15, 28, -4, -7, 27, 6, 22, 4, -18, -15, -6],\n [10, -5, -4, 24, -6, 18, 18, -2, 0, 14, -14, -4],\n [-9, 8, -... | 13 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[16, 28, 2, 8, 26, 32, 2, 14, 25, -8, 34, -5],\n [21, -26, -24, -29, -8, -16, 29, -9, -20, 0, 34, -26],\n [8, -17, 29, 26, -3, 1, -23, 1, -17, 30, -6, -4],\n [-3, 4, -21, 34, 2, ... | 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[[-3, 1, -8, 10, -34, 10, 2, 2, -15, -13, -3, 7],\n [32, 34, 28, 28, 1, -13, -2, -2, -9, -32, 33, 27],\n [-22, 30, -8, -15, -26, -10, -1, -2, -34, 7, 8, 8],\n [7, 16, -31,... | -378 | 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[[-15, 4, -3, -3, -8, 29, 10, -3, 33, 30, 0, 18],\n [0, 15, 16, -15, -6, -21, -27, -4, -13, -9, 6, -28],\n [0, 0, 8, 3, -3, 31, 19, -23, 0, -10, ... | 818 | 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[[9, 23, 7, 17, -9, 33, 33, 12, -11, -28, -4, 25],\n [-35, -5, 35, -21, 34, -20, 21, -25, -18, 9, -16, -22],\n [-9, -27, -23, 9... | 123 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[26, -23, 28, 11, 24, -21, -31, 33, -34, 2, 18, 3],\n [-16, -16, -7, -1, -4, -19, 15, -28, -15, -13, 15, -30],\n [16, -28, 33, -3, 26, 29, 27, -4, 19, -3, 2, -34],\n [-26, 30, -21, 25, -5, 2, -7, 7, -13, ... | 2049 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[5, 14, 29, -24, 3, -7, 22, 31, 35, -11, 13, 27],\n [-9, 34, 34, 22, -27, -35, 29, -12, -17, -22, -22, -4],\n [-30, -13, -17, -34, 5, 17, -9, -28, 7, -3, 7, -6],\n [-2, -16, 26, -34, 32, -17, -1, -16, 5, ... | 1851 | 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[[2, 6, 2, -2, -10, -6, 26, 6, -10, -2, 22, 32],\n [6, 12, -2, 6, -30, 17, 10, 6, 8, -1, -4, -12],\n [2, -2, -22, -1, 8, -18, -6, 9, 18, -3, -2, ... | 314 | 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[[3, 12, -31, -15, 14, -16, 35, -9, -34, 11, 4, 0],\n [35, -23, -14, -18, -30, 32, 31, 16, 34, -33, -19, 30],\n [21, -14, -25, 0, 17, 4, -1, 7, 9, 5, 28,... | -32 | 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, -10, -4, 11, 20, 14, 22, -8, 19, 22, 4, 22],\n [10, 9, -26, 12, 26, -8, -16, 34, 5, -30, -25, -6],\n [-33, -3, 18, 11, -26, -17, -27, -29, 25, -22, -34, -14],\... | 1494 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-29, 0, 4, -10, 33, -20, -27, -14, -31, 7, -6, -4],\n [0, 31, -10, -24, 1, 6, 21, -24, 10, -9, -29, 2],\n [0, 0, -9, -26, 6, 22, 5, -27, 10, 18, 23, -23],\n [0, 0, 0, 4, 8, 11, 34, 24, -1, 24, 1, -14],\n... | 724515 | 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, -19, -16, -10, 23, -11, -18, -7, 31, -1, -21, 15],\n [-33, -15, 25, -33, 17, -1, 14, -28, 12, -33, 18, -34],\n [-3, -24, ... | 807 | 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, -5, -5, 16, -2, -4, -21, 8, -3, -3, 12, 2],\n [-5, -9, -20, 4, -12, -8, 2, -10, 8, 4, 15, 8],\n [-5, -20, 13, -12, -18, 9, -26, 2, -24, -2, -4, -12],\n [16, 4, -12, -15, 10, 4, -8,... | -515 | 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[[13, 6, 13, -23, 32, -22, 0, 20, 33, 10, -21, -28],\n [20, -25, 35, -13, 9, -9, -5, 11, 30, 25, -28, 29],\n [-11, -19, -6, -12, 16, 27, 25, 22, -4, -1, -20, -27],\n [-17,... | 71 | 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[[9, 32, 8, -11, 16, -18, -29, -14, -32, -7, 4, 16],\n [0, 5, -21, 21, -1, -17, -15, -23, -15, -10, 20, -5],\n [0, 0, -6, -10, 18, -15, -13, -8, -13, 23,... | 40615 | 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[[0, -4, 5, -6, 16, -33, 4, 8, 8, -16, -24, 2],\n [-4, -1, -12, -10, 14, 12, -2, 6, 1, -12, -14, 2],\n [5, -12, -27, 27, -3, 1, -14, 20, -6, 6, -4, -14],\n [-6, -10, 27, -33, 0, -26, 0,... | -185 | 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, 17, -19, -24, -35, 20, -13, -29, 5, 17, -29, 30],\n [17, -31, 0, 8, -25, 28, -15, -32, -1, -1, -1, 3],\... | 707 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-33, 3, 7, -8, 6, -27, -18, -15, -10, -13, -26, 8],\n [0, 17, 1, 20, 23, -24, -33, -22, -1, -6, 35, 30],\n [0, 0, 10, -24, 22, 21, -4, 28, 30, 1, -22, -26],\n [0, 0, 0, -15, 33, -27, -27, -1... | -1992 | 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[[11, 18, 11, 16, -18, 10, -10, -18, 13, 29, -29, -6],\n [-11, -11, -9, -1, -6, -22, -1, -2, -21, -29, -23, 4],\n [24, -2, -23,... | -46 | 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[[-19, -29, 24, 12, -26, 5, -17, 26, 30, -28, -6, 0],\n [14, -34, -31, 10, 4, 21, -25, 2, -19, -10, 3, 31],\n [-11, -6, 10, 5, 14, 8, -26, -34, -15, -11,... | -110 | 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[[-24, 33, 1, -11, 32, -12, 0, -34, -1, -28, -8, 24],\n [0, 8, -26, -31, 11, -5, -7, -33, -10, -34, 20, -22],\n [0, 0, 11, -16, -18, 25, -31, 22, 24, -23, 4, 31],\n [0, 0, 0, 31, -25, -... | -3574 | 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[[-32, -9, 0, -8, 29, -8, -12, -2, 8, 5, 19, -6],\n [-9, -21, -2, -2, 8, 1, -19, 11, -4, 23, 10, 10],\n [0, -... | 121 | 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, -16, 12, -3, 0, -29, 26, 7, -8, 20, -10, 8],\n [-16, 9, 13, -30, -7, 6, 20, -12, -3, 12, 16, -3],\n [12, 13, -1, -4, 17, -6, -9, 12, -1... | 1455 | 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, -31, 35, -10, 13, 34, 25, -33, 3, 13, -22, -16],\n [0, 8, -27, 27, 26, -30, 30, 7, 28, 8, -31, -23],\n [0, 0, 20, -6,... | -157917 | 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[[-33, 27, 6, -20, -12, -12, 4, -12, 1, 9, -32, -19],\n [27, 19, 19, 2, 6, -4, 19, 1, -14, -6, -24, -12],\n [... | 45 | 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[[-27, 23, -3, -29, -3, 30, 23, -1, -4, -35, 16, -1],\n [4, 8, 3, -16, -33, 17, -24, -28, 28, 5, -25, -10],\n [2, -31, -4, ... | -124 | 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, -12, 12, 2, 22, 23, -14, 4, -32, 2, 10, -20],\n [-12, -8, -11, -2, 4, 16, 0, -17, 2, -20, -3, 27]... | 2754 | 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[[2, -24, 27, 29, 24, -16, 30, -18, 6, -30, 30, 33],\n [0, -14, 29, 13, -24, 27, -23, 26, 23, -25, -35, 32],\n [0, 0, -27, 33, -14, 33, -13,... | 203522 | 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[[-23, -5, -13, 1, 23, 22, -20, 3, -27, 28, -14, 18],\n [-14, -22, 30, 14, -31, -19, -35, -22, 19, -19, -27, -24],\n [30, -21, -2, 1, 17, 5, -32, -28, 35... | 149 | MATH |
[
{
"content": "Find the value at position (8, 11) of the inverse of matrix 1/839 * A where A =\n[[-29, 4, 22, 26, 18, -27, 15, -26, 13, -6, -27, 10],\n [0, 28, -2, -9, -9, 5, -18, 14, 7, 5, -18, 25],\n [0, 0, -23, -10, 20, 25, 14, -15, -28, 34, 28, 14],\n [0, 0, 0, -14, 10, 25, -1, 26, 33, 21, -11, -11],\n [0, 0... | 0 | 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[[35, 8, 35, 21, 12, 26, 25, 31, 9, 25, 35, -34],\n [0, 31, -7, 27, -11, -32, 11, 33, 27, -30, -18, 0],\n [0,... | 397 | 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, -18, -19, 0, -23, -8, -22, 12, 16, -19, 14, 34],\n [-18, -27, -26, -4, -18, -4, 26, 1, 20, -2, -4, 4],\n [-19, -26, 22, 27, -4, 4, -1, 4, 3, 0, -3, -22],\n [0, -4, 27, -32, -2, -2... | -335 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-5, 18, 11, -10, -10, 12, 3, -20, -14, 3, 16, -4],\n [18, 2, 0, -6, -8, -12, 16, 1, -29, 11, 21, 18],\n [11, 0, 0, -20, -6, 8, -8, 16, 25, 22, 14, -2],\n [-10, -6, -20, -25, 19, -30, 21, -16, 32, 13, 0, 11],\... | 558 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-32, -33, 19, 33, -4, 22, 31, -2, 27, -26, -4, -31],\n [0, -29, -21, -34, -26, -25, 17, 20, 4, 22, 32, -9],\n [0, 0, -14, 25, 2, -20, 33, -19, 25, 8, 8, 5],\n [0, 0, 0, 15, 18, -18, 4, -26, 5, 8, -28, 0],\n [0, 0, 0, 0, 6,... | -8666 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-9, 11, 4, 33, -4, 9, 1, -21, -27, 19, -27, 28],\n [0, -21, 0, 0, 29, -8, -3, 29, 18, -30, 12, 33],\n [0, 0, -10, 14, 18, -23, 29, -1, -7, -5, -24, 33],\n [0, 0, 0, -9, 3, -15, -20, -7, 35, -22, 5, 5],\n [0, 0, 0, 0, 23, 3... | -1459630 | 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, 21, -2, -25, -1, 6, -12, 30, 0, -2, -5, 12],\n [21, 11, -4, -6, -12, -6, 13, -14, 16, 7, 8, -28],\n [-2, -4, 14, -22, 10... | -470 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-25, 32, 31, -16, 29, -3, -26, 31, 19, -4, 9, 23],\n [-5, 16, -26, -30, -35, 10, -6, 27, 27, -35, -16, -7],\n [-2, 30, 30, -34, 18, -18, -6, -28, 6, -7, 15, -12],\n [-26, -20, 14, 5, 18, 8, 24, 33, -13, 35, -... | 7 | 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[[17, 8, -13, -8, -4, -16, -30, -33, -33, -13, -3, 0],\n [28, -24, 26, -10, 1, 12, 8, -25, 33, -12, -17, 34],\n [20, 13, 21, -25, 27, -19, -21, 34, 26, -4, 4, -25],\n [-23, -8, -8, 12, ... | 69 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 12) of the inverse. Round your answer to the nearest integer:\n[[-18, -28, 8, 0, -8, -2, -6, 6, 4, -10, 6, 0],\n [-28, -25, 6, 16, -22, -10, 6, 28, 8, -12, 28, -20],\n [8, 6, -23, -5, 32, -14, 29, -8, 6, -11, 1, 22]... | 6 | MATH |
[
{
"content": "Find the value at position (11, 4) of the inverse of matrix 1/839 * A where A =\n[[5, 21, -4, -18, 10, -15, -8, 4, 5, 10, -19, 2],\n [21, -13, 15, 0, 2, 16, 19, 23, -13, -8, 4, 17],\n [-4, 15, 6, -14, 12, 20, -18, 18, -20, 4, 0, -4],\n [-18, 0, -14, 6, 8, 4, -2, -16, 2, -2, 1, -16],\n [10, 2, 12, ... | 19 | 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[[23, -4, 5, -12, 29, -26, 14, 27, 29, 22, 10, -8],\n [0, -32, 5, 24, 26, -25, -16, -29, 26... | -10880 | 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, -9, -29, -28, 6, -10, 25, -16, 15, -34, -6, -19],\n [31, 7, 13, -32, -7, -2, -27, 22, -12, 20, 25, 27],\n [6, -19, 35, 3... | 72 | 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[[-3, -10, 12, -4, 14, 6, 18, -1, -14, -12, -3, 0],\n [-10, 24, 16, -28, -22, -2, 6, 16, -26, -10, 16, 20],\n [12, 16, 21, ... | -487 | 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, 32, -15, -16, -19, 10, -2, -26, -16, 28, 26, 3],\n [26, -24, -12, 17, -3, 33, 10, -29, 7, -29, 25, -4],\n [23, -6, -32, -2, -27, 24, -12, 19, -7, 18, 15, -14],\... | 5138 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, -11, -26, -3, 6, 14, 12, -13, 10, 18, -23, 6],\n [-11, -1, 0, -6, -2, 26, 28, 22, 13, 26, 0, 0],\n [-26, 0, 2... | 2 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-28, -5, 2, 26, -3, 12, -3, 0, 7, 20, 1, 0],\n [-5, 7, -28, -32, -11, -12, -12, 16, 7, -2, -24, 8],\n [2, -28, 15, 0, -7, -24, 16, 22, -4, -12, 10, 17],\n [26, -32, 0, -21, -14, 3, 8, -4, -18, 12, -2, -2],\n ... | -92 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-31, 16, -4, 18, -6, -14, -16, 1, -6, -24, -8, 13],\n [16, -26, 9, 4, 4, -18, -4, 8, -12, -13, -4, -20],\n [-4, 9, 11, 0, -10, 12, -24, 2, 2, 8, 0, -20],\n [18, 4, 0, -29, 20, 11, -3, -19, 1... | -43 | MATH |
[
{
"content": "Find the value at position (1, 11) of the inverse of matrix 1/839 * A where A =\n[[19, -24, 27, -1, -14, -26, 14, -1, -20, 0, 25, -19],\n [0, -24, -33, -17, -14, -35, 17, 8, -26, -28, -19, 34],\n [0, 0, 1, 32, 28, -29, -20, -22, 0, -25, -35, -27],\n [0, 0, 0, -12, 35, 10, -18, 31, 27, -12, -5, 2],... | -299500 | 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, 15, 21, -31, 16, 29, -24, -13, 16, 27, -33, -12],\n [6, -15, -11, -24, 12, 34, 21, -7, -7, 10, -27, -4],\n [-23, 17, 18, -7, 15, 13, 5, -24... | -120 | 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, -9, 34, -29, -10, 6, -6, -30, 31, 18, -1, -1],\n [0, -30, -13, 23, 15, 26, -4, -35, 13, -8, 35, 1],\n [0, 0, -17, 15, -21, -12, 25, 17, 23, -29, 32, -2],\n [0, 0, 0, -24, 22, 16, 20, -33... | -15425 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (3, 6) of the inverse. Round your answer to the nearest integer:\n[[-17, 20, 21, 2, 23, 2, -26, 12, 12, -30, 4, -6],\n [20, -21, -4, -26, -2, -8, 6, -2, 0, 14, 18, -8],\n [21, -4, -25, 10, -20, 17, 4, -16, -28, -27, 4, ... | 12 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[12, -17, -5, 24, 8, -13, -9, -35, -14, -28, 33, -12],\n [0, -24, -32, 28, 24, -27, 6, 17, 24, -22, 15, 29],\n [0, 0, -14, 28, -12, -6, 4, -13, -26, -3, -31, -9],\n [0, 0, 0, -16, 7, 31, 22, 5, 28, 10, 24... | 15120 | 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[[21, 20, -6, 4, -8, 9, -31, 12, -13, 31, -18, -1],\n [20, -15, 23, -5, 16, 5, 4, 5, -14, 0... | 49 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-21, 27, 7, -9, 25, 18, 23, 3, -1, -27, 24, 26],\n [0, -20, -20, -4, 2, 3, 26, 27, -20, 18, -21, -18],\n [0, 0, 4, 27, 32, -19, 12, -17, 3, 29, 17, -18],\n [0, 0, 0, -2, -21, -17, 27, -10, 13, -32, 30, -19],\n [0, 0, 0, 0,... | -390383 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[4, -7, 9, -2, -21, 34, 35, -34, -35, 18, -34, 0],\n [0, -8, -16, 1, 23, 8, -24, -4, 2, -5, -18, -7],\n [0, 0, 27, -16, -5, -5, 22, -29, -24, 25, 7, 13],\n [0, 0, 0, 27, -21, -24, -10, -6, -6... | 1401505 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 11) rounded to the nearest integer?\n[[-34, -5, 19, -1, -9, -31, 15, -20, 4, 32, 8, 5],\n [-20, 6, -16, 26, -8, 24, 5, -35, -20, -32, 18, -7],\n [30, -12, 5, 27, 20, -22, 17, 8, 7, -35, -25, -16],\n [-15, -16, -19, ... | 17 | 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[[5, 4, -31, 7, 31, -12, -5, 23, 31, 27, -35, 33],\n [0, -3, 27, 6, -5, 16, 14, -23, 29, 2, 3, 6],\n [0, 0, 34, 6, -7, 32, -11, -20, 21, -2, -27,... | 48 | 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[[-18, -16, 24, -8, 5, -10, 14, -12, -6, -18, 10, 0],\n [-16, -8, -18, -12, 18, 10, 2, 14, 5, 10, -3, -16],\n... | -261 | 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[[1, 11, 35, 35, -1, -10, 20, 7, -17, -14, 21, 29],\n [-2, 14, -4, 17, 15, -16, 22, 9, 14, -28, -15, -18],\n [-21, -26, 27, -16, 26, 16, -6, -33, -35, -26, 13, 29],\n [-3,... | 31 | 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, 1, 31, -11, 13, 7, -17, -10, -21, 17, -16, -31],\n [28, 12, 4, -12, 34, -24, -32, 7, 16, -15, 33, -... | 4054 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[19, -8, 2, 19, -22, -5, 27, 10, -32, -16, -12, 2],\n [-12, 33, 12, 9, -15, 30, 17, 29, -28, -2, -26, -35],\n [-1, 19, -10, 32, -31, 31, -17, 7, 3, -9, -14, 13],\n [22, 23, 4, -21, -4, 22, 20, 16, -8, -12, 1, 26],\n [-31, 8... | -309 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 12) of the inverse. Round your answer to the nearest integer:\n[[33, -34, -17, 31, 34, -28, 23, -31, -5, -23, -35, 10],\n [-32, -16, -4, -33, 16, -25, -27, 21, 26, 20, 15, -34],\n [-21, 33, 3, -2, 7, 30, 9, -9, 31, ... | 11 | 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[[-18, 25, 33, -2, 18, -7, 5, 34, 22, -6, -3, 27],\n [0, 13, -24, -14, -12, 20, -11, 30, -35, -2, -31, -19],\... | -170 | 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[[-10, -31, -14, -22, 34, -19, -35, -18, -25, -24, -2, -28],\n [0, -22, 15, -27, 2, -7, -7,... | 17245 | 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, -12, -10, 18, -3, 21, -27, 28, 23, -20, -31, 8],\n [10, -26, 22, 34, 28, 34, 24, -11, -25, 27, -10... | 7157 | 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[[21, 0, 15, -14, 1, -33, -1, 2, 19, 5, 2, -2],\n [0, -22, -15, -8, 24, -2, 29, -32, 20, 34, -26, -1],\n [0, 0, -11, -4, 20, -1... | 1217 | 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[[8, -4, -1, -12, -1, -6, -26, -4, 28, -8, 20, 18],\n [-4, 32, 28, -4, -6, -8, -16, -2, 0, -2, -24, -22],\n [... | 38 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 12) rounded to the nearest integer?\n[[-32, -6, 4, 6, -3, 23, 2, -4, -30, 8, 4, 12],\n [-6, 13, -12, -32, -14, 4, -10, 0, -22, -6, -2, -2],\n [4, -12, 20, -16, -22, 11, -10, -6, 4, 10, -8, -10],\n [6, -32, -16, -17,... | 15 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[17, 13, -10, 31, 0, -13, 3, 23, -13, -13, 7, -11],\n [24, -3, -3, 29, 11, -3, 2, -12, 13, -6, 22, 23],\n [-20, -20, -3, 3, 10, 2, -13, -10, 13, -12, 6, -9],\n [-34, -28, 5, -23,... | -98 | 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[[13, 20, 29, -5, 24, -2, -19, -7, -30, -30, -33, -5],\n [16, -28, -10, -21, 20, 26, -23, 10, 18, -27, -33, -13],\n [-24, 5, 8, 22, -25, -17, 23, 1, -26, -3, -16, 8],\n [-... | 17 | 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[[-19, 2, -32, -18, 13, 2, 20, -8, -16, 0, -2, 18],\n [2, 11, -2, 4, -10, 20, 17, 14, -3, -15, -8, -10],\n [-32, -2, 16, 20, 2, 7, 20, -18, -20, 6, -28, -26],\n [-18, 4, 2... | -72 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-26, -16, -20, 21, 10, -35, -11, 20, 10, 23, 26, 25],\n [0, 5, -21, 8, -35, 29, -2, -32, -34, 3, 18, -26],\n [0, 0,... | 0 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[27, -14, 17, -24, -14, 3, 11, 28, 8, -20, 23, -2],\n [0, 34, 19, -12, -9, -20, -34, -5, 27, 11, -17, 20],\n [0, 0, -30, -5, 14, -7, -15, 5, 33, 33, 20, -8],\n [0, 0, 0, 8, -4, -7, -33, 33, -25, 12, 17, 2... | 23618 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[23, -17, 26, 17, 30, -28, 10, -24, 29, -13, 3, 24],\n [-9, 21, 8, 34, -8, -13, -2, -11, -25, 12, 29, -26],\n [-10, -26, -18, 24, 9, -10, -27, 0, -21, -12, 4, -34],\n [-32, -16, 3, 9, -10, 24... | -558 | 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[[-9, 1, 34, -20, -16, 10, -11, 23, -4, -19, -26, -19],\n [0, 30, -7, -32, -6, 25, 22, -2, -12, -11, -11, -6],\n [0, 0, 3, -34, -2, -20, 12, -12, 14, -34, 3, 2... | -1281701 | 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[[-20, 12, 20, 0, 2, 3, 14, -2, 20, 20, -10, 6],\n [12, -12, -16, -7, -5, 2, -21, 1, 24, -10, -4, -2],\n [20, -16, -27, 15,... | -2586 | 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[[12, 12, 21, -1, 7, -10, -1, 10, -10, 10, 22, 26],\n [12, -34, 10, -15, -5, -13, 8, -29, -... | -5711 | MATH |
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