messages listlengths 1 1 | ground_truth stringlengths 1 9 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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[[14, -14, -14, 4, -4, -30, 26, -32, -6, -14, 11, -4],\n [-14, -7, 24, 3, -27, 8, 7, 16, -10, 6, -11, 6],\n [-14, 24, 10, 2... | 319 | 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[[-32, -24, -24, -19, 0, -2, -14, 24, 12, 1, -4, -10],\n [-24, -24, -8, 10, -25, 2, -3, 0, -2, 20, 13, 4],\n [-24, -8, 18, -5, -14, 6, 12, 10, 14... | -274 | 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[[-4, 18, -22, 6, 2, -18, -8, -14, -2, -4, -2, -24],\n [18, 20, 6, -23, -5, -21, -24, 0, -29, -24, 15, -4],\n [-22, 6, 24, -3, -9, 8, 16, 22, 24, 4, -2, 4],\n [6, -23, -3, -22, 8, 14, -... | 476 | 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, 23, -34, -34, -31, -14, -3, 33, -8, 22, -22, 14],\n [0, -21, 32, 7, 19, 13, -18, -11, -24, 19, 11, 31],... | -537 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-3, 22, -14, 14, -2, 2, -16, 19, -12, 22, -2, -20],\n [22, 19, 19, -18, -1, 7, 20, -12, -9, 10, -8, -8],\n [-14, 19, 20, -10, 10, 24, 28, -9, -9, -6, 9, -13],\n [14, -18, -10, -13, -12, -8, -10, -8, -4, 2, 10, -14],\n [-2,... | -149 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[17, -2, -6, -4, -25, -6, -35, -30, 20, 31, 22, -17],\n [25, 26, 35, -1, 7, -31, 10, -1, 0, -32, 25, -34],\n [-1, 10, -32, 24, 12, -32, 34, 15, -19, -32, 21, -29],\n [12, -3, 32, 20, -11, -1, 3, -13, -25, -14, 11, -24],\n [... | -47 | 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[[-19, -33, 6, 12, -5, -35, 33, -35, 0, 23, 25, -32],\n [13, 5, 24, -15, 4, 4, -9, 6, 0, -25, -1, 1],\n [-24,... | -18 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[8, -3, 24, 34, 10, -9, -8, 10, -2, -7, 19, 21],\n [-14, -21, -9, 24, -15, 1, -12, 12, -13, -23, 23, -31],\n [-21, -12, 20, -28, 6, -29, -12, -9, -33, 12, -14, 4],\n [12, 13, -7, -19, -29, 7, -1, 4, 31, -30, -34, 3],\n [-3,... | -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[[-1, -8, 9, -5, 4, 18, -12, 16, 24, 12, 9, -5],\n [-8, 8, 24, 7, -16, 11, 14, -29, -4, 0, 16, -10],\n [9, 24, -20, -9, 4, 15, -6, 7, -26, 4, 16, 21],\n [-5, 7, -9, 7... | 2426 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[-12, -12, -1, 11, 9, 8, 0, -10, -6, 12, -16, -12],\n [-12, 11, -4, 12, -24, -8, -16, 19, -1, 17, 20, -19],\n [-1, -4, -24, 10, 9, -8, -4, -22, -6, -8, ... | -4 | 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[[-33, -18, -12, 5, -21, 0, -4, -10, 0, 2, -10, 9],\n [-18, 7, -8, 4, 2, -24, -22, 20, -4, 12, 1, -4],\n... | 2143 | 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[[-28, -29, -11, 12, -1, -18, -25, -7, -20, -30, -21, -7],\n [0, 30, -23, 35, 21, 15, -8, -13, -35, 35, -1, 0],\n [0, 0, 26, -24, -22, 26, -14, -7, 23, -... | 0 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-35, 6, 21, 21, -1, -4, -20, -25, -7, 8, -10, -17],\n [6, 8, 10, 24, -24, 28, -14, -4, -2, -3, 22, -28],\n [21, 10, -14, 8, -8, -12, -20, -24, 0, 9, 8, 0],\n [21, 24, 8, -23, -8, -12, 14, 10, 20, -8, 0, ... | 6601 | 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[[19, -22, -35, 21, -22, 15, 22, -27, 12, -9, -8, 20],\n [-2, -34, -12, 13, 4, -28, 33, 31, -6, 16, 3, 35],\n [-23, -34, 30... | -198 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 2) of the inverse. Round your answer to the nearest integer:\n[[19, -2, -23, 15, 4, 14, -8, 29, 32, 12, 1, 10],\n [-2, -3, 10, 0, -2, 24, 0, -22, 23, 2, 6, -17],\n [-23, 10, 8, -2, 14, -8, -9, 8, -24, -18, -2, -7],\... | -10 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -24, -20, 4, -16, 7, 15, -12, 24, -12, 34, 10],\n [-24, -25, -20, -20, 14, 23, -32, -29, 25, -2, 0, 0],\n [-20... | 6 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[32, -29, -12, -27, -2, 19, -24, 22, 23, 32, -19, -6],\n [0, 26, 26, -18, -15, -1, -19, 18, -12, -21, -22, 11],\n [0, 0, 4, 26, 18, 24, -25, -10, -9, -6, 17, 1],\n [0, 0, 0, -10, -1, 33, -25, -6, -15, -32... | 5133671 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[20, -9, 16, -16, -10, -15, -9, -2, -4, 11, -11, 12],\n [-9, 7, 0, -6, -2, -4, -18, 19, -12, 26, 17, -26],\n [16, 0, 18, 6, -18, -10, -22, 4, -22, 0, -14, 2],\n [-16, -6, 6, -13, -19, 0, 13, -22, 27, -2, 10, 3],\n [-10, -2,... | 6196 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (7, 3) of the inverse. Round your answer to the nearest integer:\n[[-13, -29, 20, -14, -16, -30, -5, 26, 6, -23, -9, 11],\n [21, -32, -14, 18, -35, 15, 27, -6, -2, -7, 32, 35],\n [21, -3, 29, -2, 14, 21, 13, 12, 20, -24... | -5 | 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, -17, -23, -10, 3, 15, -30, -23, 16, 0, -19, 29],\n [0, -23, 27, 19, -22, 35, 5, 7, 27, 5, -27, -16],\n [0, 0, 30, -6, -11, -6, -5, 0, 5, 2... | -271 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 9) of the inverse. Round your answer to the nearest integer:\n[[15, 10, 23, 3, 2, 19, -31, -31, 14, 6, -17, -2],\n [0, -15, 9, 24, 17, -17, -1, -22, -24, 13, -33, -9],\n [0, 0, -9, -21, -6, 23, 9, 17, 9, 25, -25, 15... | -24 | 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, -10, -10, -34, -14, -14, -10, 20, 10, -2, 14, 10],\n [-10, 32, -8, -11, 16, 4, -16, 24, 25, -5, 13, 14],\n [-10, -8, 1, ... | -81 | 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, 30, 23, -23, -30, -11, 27, 23, 10, -21, 30, 6],\n [0, -13, -21, 2, 20, -2, 29, -2, -20, 14, 33, 6],\n [0, 0, 33, -8, -6, 14, -19, -26, -25, 11, -28, -5],\n [0, 0, 0, 10, -33, -23, -8, 1... | -13632 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[7, -6, -12, 24, -26, -9, -18, -7, 8, 2, -20, 23],\n [-6, -14, 28, -2, 16, 26, 8, 6, 20, -9, 0, 6],\n [-12, 28, 30, -13, -24, 24, 8, 3, 18, 11, 8, 12],\n [24, -2, -13, 12, -10, 10, 12, 16, 18, 14, -12, -16],\n [-26, 16, -24... | 293 | 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[[14, -16, 27, 19, -2, -4, 7, -23, -34, 25, -22, 6],\n [-21, -26, 20, 17, 22, 26, 21, 27, -32, -2, -4, -2],\n... | 80 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-12, 12, 22, 4, -29, 10, -21, -31, 23, 34, -14, -8],\n [0, -17, -22, 12, -29, -4, -14, 10, -23, -14, -26, 8],\n [0, 0, 26, 19, 13, 14, -17, 22, 12, -24, -16, 9],\n [0, 0, 0, -33, -18, -15, 21, 6, 26, -6, 25, 0],\n [0, 0, 0... | 10518 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[27, -30, -8, 15, 17, 8, 29, -24, -8, 32, -6, -1],\n [-30, -6, 27, -28, -3, 7, 7, 9, 18, 29, -29, 0],\n [-11, 1, -24, -4, 13, 2, 20, 29, -10, 21, -22, 20],\n [34, 5, 15, 31, -24, 13, -35, -17, 30, 22, -32, -28],\n [-9, -10,... | -682 | 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[[1, -19, -5, 23, 11, -30, -4, -5, -18, -27, -33, 35],\n [0, -23, -2, 7, -3, 33, 0, 32, 11, 25, 9, 12],\n [0,... | 691 | 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[[-35, -17, 20, 28, -2, 28, -26, 24, 3, 30, -4, 15],\n [0, 21, 24, 19, -30, -29, 30, -10, -31, -35, -34, 29],\n [0, 0, 15, 33, 5, 22, 32, -12, 20, 0, -34... | 296200 | 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, -23, -11, 31, 32, 11, 19, 7, -34, 9, 12, 26],\n [0, 11, -32, 24, 13, -2, 8, 20, 6, 14, 33, -3],\n ... | 2423306 | 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[[-19, 33, -6, 3, 25, -12, -1, 25, -21, 0, 19, 1],\n [26, 28, 3, -24, -28, 5, 33, -33, 7, 1, 21, -11],\n [-32, 22, 1, -28, -27,... | 44 | 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[[34, 12, -2, -9, -1, -3, -16, 1, 4, 8, 2, 16],\n [12, 12, 10, -7, -6, -2, 22, 18, -2, -2, -10, 3],\n [-2, 10, -25, 2, -4, -16, 0, -8, 4, 7,... | 38287 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-12, -12, -8, -33, -33, -7, -4, 18, 2, 20, 29, -15],\n [5, -16, 24, 23, 19, -33, -22, 9, 24, 13, -27, 18],\n [34, 16, 27, 16, -14, 19, -33, -34, 23, -8, 1, 33],\n [-27, 26, -4, -1, 11, -18, 0, -17, -11, 10, 24, -13],\n [-9... | 424 | 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[[-27, -12, 20, -5, 1, -14, -8, -8, 0, 4, -16, 18],\n [-12, 28, 24, 2, -16, 29, -11, 14, 0, 24, 14, 26],\n [20, 24, -18, 11, 24, -6, -14, -1, -14, 0, 4, -8],\n [-5, 2, 11, -7, 4, ... | -9 | 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, 2, -4, -7, -14, 14, 17, 30, -10, 9, -23, -6],\n [2, -5, -4, 18, -12, 4, -14, 11, -6, -5, -20, 10],\n [-4, -4, 8, -12,... | 105 | 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[[-10, 16, 7, 14, -15, 2, 2, -3, -22, -10, -9, -16],\n [16, -34, 4, -15, 12, -15, 4, 2, -24, -14, -6, -1],\n [7, 4, 30, 12, 4, 26, -14, -10, 20, ... | 245 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[13, -28, -33, 29, -34, 5, 17, -20, -27, 3, 28, 0],\n [0, 11, 13, 19, -26, 27, -10, 12, -6, -34, -7, 18],\n [0, 0, -15, -9, -2, -13, 3, 33, 9, 27, -28, -29],\n [0, 0, 0, 28, -7, 19, -24, -14, -13, 12, 9, -10],... | -169 | 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, -26, -32, 3, -2, -11, 16, -21, -24, -35, -27, 23],\n [-22, -5, 17, 27, -26, 7, -18, 31, 23, -13, 10, 13],\n [-13, -24, -7, 23, 17, 32, 27, -7, -33, 1, 27, -13],\n [1... | 36 | 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[[25, 0, 18, 1, 7, 10, -14, -23, -3, 5, -6, 1],\n [0, -23, 12, -24, 8, 7, 3, -22, -6, -22, -14, -26],\n [18, 12, 16, 6, -2, -10, 19, 11, 0, -2, -31, -3],... | 113 | 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[[20, -8, -18, -2, 0, 8, 28, -10, 10, 2, 9, -2],\n [-8, 14, -2, 6, 24, 14, -16, 12, -19, 26, -8, 28],\n [-18, -2, -21, 12, -10, 4, -6, 6, -26, -16, 2, -15],\n [-2, 6,... | 1620 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-29, -17, 4, -15, 22, -10, 0, 8, 28, -9, -28, -35],\n [0, -5, -29, -27, 35, 17, -20, -12, 10, -7, -6, 15],\n [0, 0, -2, -17, -8, -30, -19, 0, -35, -20, 32, 11],\n [0, 0, 0, -21, 31, 7, -28, ... | -485329 | 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, 32, 27, -10, 24, 25, -21, -31, -4, -14, -14, -24],\n [0, -20, 29, 15, -4, 17, -33, -23, 22, 9, -12, 15],\n [0, 0, -31, 14, 13, -18, -3, 22... | -183 | 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[[-25, 17, -18, -29, -1, 8, 35, 3, -25, -26, -27, -28],\n [0, -15, -30, 23, 32, -13, -1, -24, 35, 21, -7, 31],\n [0, 0, -6, -9,... | -393499 | MATH |
[
{
"content": "Find the value at position (3, 9) of the inverse of matrix 1/839 * A where A =\n[[23, 14, -10, 2, -12, 0, -8, 2, -5, 3, 2, 14],\n [14, -2, -23, 12, 4, 4, -6, 4, -2, 4, 2, -18],\n [-10, -23, -11, 22, -6, 24, -25, 0, -8, -4, 12, -18],\n [2, 12, 22, 13, -14, 23, 28, -6, -13, 10, -5, 0],\n [-12, 4, -6... | -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[[-29, 6, -5, 0, 25, 4, -12, -9, -6, 4, 14, -18],\n [6, -3, 7, 2, -2, 14, 8, 31, -6, 35, -23, 10],\n [-5, 7, -32, 4, 14, -8, -5, -26, 8, -26, -20, 16],\n [0, 2... | 916 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[33, 8, -34, 9, -6, -12, -28, -2, 7, -32, 13, 0],\n [8, 13, -12, -28, 26, -25, -12, 7, -18, 8, 34, -30],\n [-34, -12, 11, 14, -13, 0, -12, 8, 6, -12, -12, 8],\n [9, -28, 14, 25, -12, 6, -4, 19, 2, 4, 21, 18],\... | 870 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -14, 16, -17, -3, 28, -12, -6, -5, 25, 24, 9],\n [-14, -23, -7, -14, -10, -16, -16, 0, -18, -14, -2, 0],\n [1... | 4 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-17, -19, 8, 25, -35, 22, 5, -12, 7, -27, 30, -4],\n [0, -25, 29, -18, -28, -9, -27, -34, 10, 34, -31, -24],\n [0, 0, -6, 16, 11, 0, 34, -4, 8, -20, 35, -19],\n [0, 0, 0, -23, -24, 9, -20, 1... | -5844 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[32, -4, -2, -4, 15, -3, 20, 4, 0, 1, 0, 14],\n [-4, 7, -4, 15, 22, 29, 4, -6, 21, 11, -14, 12],\n [-2, -4, -13, 30, 23, 2, 24, 3, -6, -26, 4, 6],\n [-4, 15, 30, 22, -14, 14, 20, 13, 4, 10, 10, 26],\n [15, 22, 23, -14, -31,... | -49 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[3, 23, 29, -35, 9, -17, 12, 13, -22, 31, -6, 29],\n [0, -30, 10, 6, 25, -5, -10, 22, -3, 16, -4, 18],\n [0, 0, -14, -31, -28, 34, 27, -26, 26, 4, 11, 20],\n [0, 0, 0, 16, 26, 6, 11, 1, -25, ... | -380132 | 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[[-26, 25, 3, -22, 11, -26, 19, -12, 4, 27, -2, 13],\n [0, -27, 11, 9, 0, -27, -25, -12, -35, 25, 33, -15],\n [0, 0, -29, -35, 33, 28, -28, 24, -2, -27, 9, -19... | 18731 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[2, 31, 33, 23, -5, -33, 33, 31, -21, -9, -18, -26],\n [0, 32, 30, -6, 16, 21, 10, -33, 27, 8, 33, 19],\n [0, 0, -29, -17, -17, 12, 21, -15, -35, -12, -6, 26],\n [0, 0, 0, -9, 31, -32, 9, 21,... | 89086 | 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[[-17, -2, -13, 31, -32, 17, -21, -19, -14, -2, -3, -11],\n [0, 14, -6, -14, -32, 9, -8, 18, 22, 29, 1, 18],\n [0, 0, 29, 8, 7, -9, -35, -6,... | 7184 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 8) of the inverse. Round your answer to the nearest integer:\n[[-25, 15, -9, 13, -20, 14, -21, 18, -22, -10, 4, -18],\n [-10, -18, -35, -20, -15, 30, -33, -28, -18, -11, -18, -12],\n [33, -10, -25, -32, -26, -24, -... | -36 | 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, 0, 13, 0, -30, -34, -8, -29, -15, 26, 5, 7],\n [-28, -22, -25, -26, -7, 19, -34, -35, 11, -18, -1, 26],\n [-11, -7, ... | 1148 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-14, 26, -10, -22, -27, -29, 11, 22, -16, 20, 7, 24],\n [0, 30, -16, -23, -11, 0, -33, 11, -24, 24, -8, -22],\n [0, 0, 30, 24, -16, -25, -32, 16, 11, 31, -25, 14],\n [0, 0, 0, -22, 11, -18, 31, -13, 24, 23, 1... | -99 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (1, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 4, 18, 2, 30, 30, -28, -12, -11, -12, 18, -20],\n [4, 9, 16, 7, 8, -20, -18, -15, -10, 16, 32, -12],\n [18, 1... | 1 | 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, -11, 8, 24, -22, 31, 32, 0, -11, -28, -11, 0],\n [0, 24, 9, 11, 14, 33, 6, 14, -29, -32, 18, 9],\n [0, 0, 9, -33, 11, 13, -33, -33, -32, 23, -1, 17],\n [0, 0, 0, 2, 32, -2, -15, 5, 23, -3... | -8336218 | 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, 12, -12, 14, 13, -2, -22, 9, -8, 2, 22, -22],\n [12, -1, 14, -4, 20, 2, -22, 0, -2, -12, 18, -22],\n [-12, 14, 31, 10, -... | -50 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[5, 27, 26, -34, -29, -28, -33, -22, -3, -9, -25, -25],\n [0, 6, -33, -4, 0, -26, 19, 35, -11, 26, -2, -11],\n [0, 0, -26, -35, 22, -17, -16, 12, 22, 2, 6, -29],\n [0, 0, 0, -10, 20, 34, 35, 26, 26, 0, -1... | 6877103 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[12, -22, -9, -29, 8, 20, 23, -12, 4, -10, 2, 16],\n [-22, -3, 20, -9, -9, 18, 12, -20, -2, 26, 0, 28],\n [-9, 20, 23, -12, 3, -13, -10, 2, 10, 16, -2, 16],\n [-29, -9, -12, -34, 6, -6, 24, -6, 29, 19, -12, -2... | 214 | 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[[-21, -31, 28, -19, -28, 21, 21, 12, -18, 6, 33, 18],\n [-20, -19, 8, -3, -25, 4, 1, -8, -6, 10, 7, -28],\n [7, -3, 19, 22, -15, 11, 15, -7, -20, 32, 33, -17]... | -39 | 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[[-21, -25, -30, -34, -13, -29, 26, -6, -35, 0, -35, -14],\n [0, 8, -27, 2, -14, 5, -34, -35, -26, 14, -12, 11],\n [0, 0, 24, -13, -13, 26, -32, -9, 21, 32, 30, 35],\... | 922196 | 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[[2, 5, -5, -20, -33, -20, 32, 33, 18, 6, 28, -17],\n [0, -33, -28, -5, -17, 29, 17, -23, 23, 21, 7, -24],\n [0, 0, -27, 12, 32... | 9487 | 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[[31, 5, -8, 1, 1, 30, 19, -8, 29, 17, 13, -10],\n [5, -20, -2, 27, 4, 27, -6, 0, -8, -9, 9, 10],\n [-8, -2, 24, -14, 28, -15, 22, -16, 2, -16, -16, 34],\n [1, 27, -14, 10... | 128 | 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[[2, -8, 33, 9, 26, -19, 4, -1, 21, -11, -21, -17],\n [15, -23, -11, -13, 23, -20, 15, -26, 19, 26, 9, 30],\n [-11, 22, 28, 8, -12, 15, 27, -12, 12, -16, -4, -2],\n [16, 2, -22, ... | -2 | 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, 6, 9, 6, -2, -2, -9, 6, -10, 16, -9, 15],\n [32, 25, -2, -33, -11, -11, 29, 1, -23, -21, -30, 3],\n [-23, -10, -9, -14... | 691 | 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[[16, -10, 35, -25, -15, 33, -5, 9, 28, -9, -2, 14],\n [33, -10, 12, 16, -31, -24, -23, -20... | -44 | 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, 22, 35, -26, 19, 6, 34, 32, -23, 1, -28, 4],\n [0, 24, -26, 35, -14, 20, 10, -18, 23, 25, 16, -27],\n [0, 0, -22, -19, -... | -112179 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[20, -2, 31, -15, 3, 1, 6, 0, 30, -19, 18, -7],\n [0, -15, -17, -7, -33, 19, 15, 3, -5, -1, 33, -9],\n [0, 0, -23, -13, 29, 33, 35, -14, -35, -21, 17, 31],\n [0, 0, 0, 20, -11, 26, 7, -22, 16, -9, 16, -35],\n ... | 59 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[18, 18, 29, 26, 34, 16, -17, 7, -30, 32, -26, 7],\n [0, -27, 29, 15, 27, 20, -24, 10, -20, 34, 11, 24],\n [0, 0, -6, -31, -21, -5, -18, 7, -25, 15, -24, 20],\n [0, 0, 0, 30, 2, -16, 16, -13, 29, -30, -19, 0],\n [0, 0, 0, 0... | -1042 | 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[[-25, 0, -20, -14, 2, -20, 4, 8, -24, 30, 22, -16],\n [0, -23, -4, -15, 24, 11, 12, -12, 23, 24, 0, 8],... | 1885 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 0, -16, 20, 12, 4, -4, -16, 8, -8, 10, 10],\n [0, -20, -9, 1, 29, -14, -12, 0, 15, -4, -5, -1],\n [-16, -9, 30,... | 7 | 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, 25, -20, 29, 25, 28, -6, -26, 34, -7, -14, -22],\n [-30, 8, 27, 14, 25, -16, 30, -21, 2, -31, -21, -25],\n [15, -3, 0, 5, -1, 21, 28, -3, -3, -18, -25, 26],\n ... | 1829 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-22, 23, 17, -7, -32, -4, 13, 2, -7, -35, -33, 6],\n [-4, -13, -10, 2, -14, -24, 27, -20, 22, -21, -31, 15],\n [5, -32, 11, -14, -5, -7, 5, 25, 17, -20, 19, -19],\n [-18, 1, 24, -7, -14, 18, 9, 16, 22, -33, -... | 202 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (3, 10) of the inverse. Round your answer to the nearest integer:\n[[-4, -16, 8, 20, -3, 2, -1, 20, 12, 2, 6, -10],\n [-16, -17, -27, 29, -8, 10, -9, -14, -23, 0, -23, -4],\n [8, -27, 21, -12, -3, -14, 13, -8, -19, 12, ... | -10 | 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[[2, 8, -27, 32, -6, 26, -3, -24, 28, -1, 26, -19],\n [-2, 25, 26, -26, 14, 16, -29, 6, 21, -3, 18, 19],\n [-27, 9, 2, -17, 8, 26, -23, -1, 13, 5, 19, -21],\n [-22, 23, 10... | 93 | 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[[11, 18, 24, 15, -23, -1, -20, 32, -33, 26, -5, -35],\n [0, -35, -3, 6, 29, -20, 1, 16, -1, 11, -34, 8],\n [0, 0, 9, 22, -12, -14, 5, -31, -32, 23, -14,... | 115391 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/839 * A where A =\n[[7, -12, 10, 16, 22, 20, -4, -3, 7, -20, 30, -10],\n [-12, 25, 6, -9, 8, -4, 6, -20, -4, -2, 20, 10],\n [10, 6, -16, -6, 8, -15, -29, -12, 20, -24, -17, 30],\n [16, -9, -6, 16, 1, 6, -25, 15, -26, 16, 14, -10],\n [22,... | -16 | 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[[35, 12, -33, -33, 11, 2, -7, 9, -15, 13, 13, -10],\n [0, -8, -14, -8, 28, -17, 11, 11, 12, -34, -13, -31],\n [0, 0, -8, -30, -16, 32, 31, -5, 14, 7, -24, 12],\n [0, 0, 0, -3, 7, -35, ... | 4777 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (6, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -26, -12, 19, 2, -26, 10, -14, -28, -6, -18, -4],\n [-26, -20, -4, -2, 12, 2, 22, 24, 8, -26, 10, -32],\n [-12, ... | 13 | 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[[-35, 30, -2, 23, 29, -14, 17, -5, 30, -33, 10, 8],\n [5, -23, -26, 26, -30, 33, 14, 3, 7, 6, 4, -31],\n [31, 25, -21, -26, -3... | 91 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (3, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -33, -17, -7, 29, -15, 19, -25, 0, 3, 14, -8],\n [-16, 3, -11, 10, -4, 27, 8, 5, -27, 2, 1, 6],\n [-13, -20, 3... | -60 | 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[[14, -7, -14, 22, 6, -13, 32, -34, 4, -10, -14, 10],\n [24, -21, 11, 24, -19, -18, 30, 1, -12, -21, 15, -12]... | 570 | MATH |
[
{
"content": "Find the value at position (5, 2) of the inverse of matrix 1/839 * A where A =\n[[5, -12, 18, -3, -6, 24, 24, -8, 23, 16, -15, 33],\n [-12, 16, 12, 4, 1, 24, -30, -16, 6, 12, -2, 8],\n [18, 12, 34, -4, 4, 17, 12, 2, 10, -3, 16, -12],\n [-3, 4, -4, -14, -2, -26, 1, -2, 10, 0, -1, -14],\n [-6, 1, 4,... | 10 | MATH |
[
{
"content": "Find the value at position (5, 3) of the inverse of matrix 1/839 * A where A =\n[[-22, 21, 34, 11, -17, 26, -26, 20, -25, -29, 17, 32],\n [-20, 24, 15, -27, 13, 0, -27, -4, 21, 21, 8, -17],\n [7, 32, 28, -23, -26, 12, -16, -30, 8, 12, 28, -7],\n [-27, -13, 19, -8, 11, -21, 22, -18, 4, -18, -29, -3... | -20 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (2, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[28, 21, -15, 30, -25, -19, 25, -7, -15, 33, 15, -8],\n [0, -32, 2, 31, -7, -25, 15, 0, 21, -31, -20, -11],\n [0, 0,... | -2330 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/839 * A where A =\n[[-6, 11, 25, -29, 18, -16, -20, -34, -26, 7, -8, -26],\n [0, -2, -20, 19, 28, 17, 6, -6, 24, -34, -2, 6],\n [0, 0, -4, -6, 28, -17, -6, 22, 5, -9, -20, -11],\n [0, 0, 0, -4, 1, 16, -2, 14, -2, -27, 6, 3],\n [0, 0, 0, ... | -210 | 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, -27, 28, 13, 32, -3, -30, -7, -17, -9, -27, -18],\n [0, 35, -4, -10, 16, -14, -8, 19, -8, -7, 29, -5],\n [0, 0, 17, -18, 1, 25, 15, -31, 19, 8, -26, -11],... | 6306 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[0, 16, -27, 28, -24, -20, 34, -27, -2, -29, -4, 13],\n [18, 6, -35, -16, 2, -24, 23, 14, -29, -9, -23, -16],\n [-18, 22, 32, -13, 32, -34, 8, 14, 23, 8, 29, -2],\n [-5, -22, 16, -17, -7, 19, -6, 23, 17, 30, 3, -11],\n [9, ... | 388 | 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, 24, -13, -1, 16, 13, -4, 2, 10, 33, 26, -4],\n [0, -21, 33, -15, 31, -6, -31, 16, -20, -30, 4, -10],\n [0, 0, 22, 18, -16, 3, -32, 2, 10, 6, -6, 0],\n [0, 0, 0,... | 13620 | 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[[-7, -1, 1, -26, 33, -32, 35, 25, -29, 13, 25, -22],\n [0, 15, -5, -34, 7, 15, 34, -25, 13, -20, 5, -6],\n [0, 0, -20, -5, -25, -28, -24, 25, 2, 19, -23, -1],\n [0, 0, 0, 31, 27, 35, -... | 18102 | MATH |
[
{
"content": "Find the value at position (5, 11) of the inverse of matrix 1/839 * A where A =\n[[-18, 0, -12, -35, 10, -12, -15, -7, 28, -26, -23, -25],\n [0, -30, 15, -26, 28, -1, -19, -33, -6, -9, 9, -32],\n [0, 0, -5, -17, -25, 1, 25, -34, 14, -9, 14, -12],\n [0, 0, 0, -3, -13, -28, -3, 28, -17, -24, -32, 27... | -29636 | 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[[-16, -2, 18, -4, 4, 2, 2, -9, -13, -13, 30, -21],\n [-2, 18, 5, 8, -10, 24, -4, -20, 11, 22, 2, 2],\n [18, 5, 28, 6, -2, -13, 10, -2, 18, -8, -10, -28],\n [-4, 8, 6... | 28243 | 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[[20, -11, -20, -14, 0, 6, -7, 18, -7, 20, 16, 4],\n [-11, 1, 22, 14, 5, -4, 18, -20, -22, -10, 10, 1],\n [-20, 22, -2, 6, -5, ... | 123 | 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, -3, 34, 12, 1, -14, 14, -17, -8, 28, 22, -11],\n [0, -4, 11, 2, -18, -9, 1, 6, 0, -2, -21, 25],\n [0, 0, -29, 25, -3... | -38605 | 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[[-7, -24, -8, 0, 0, -29, -3, 2, 20, 30, -6, -25],\n [-24, -16, 9, 6, 0, 27, 8, -9, 7, 19, 6, -18],\n [-8, 9, 25, -1, 1, -4, 22, 17, 3, 19, 10, 12],\n [0... | -72 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-22, 4, -6, -32, 1, 23, -20, 6, -3, -8, 11, -9],\n [4, -25, -2, -26, -20, -6, 17, -8, 7, 0, 4, -5],\n [-6, -2, 8, -6, 12, -6, 6, -30, 10, -20, -24, 16],\n [-32, -26, -6, 25, -26, -8, -6, -4, -16, -6, -16... | 1668 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-33, 4, 28, 14, -16, 3, -14, 10, -4, -10, 8, 35],\n [0, 25, -25, 23, -20, 32, -26, 23, 17, 5, -31, -33],\n [0, 0, 2, 30, 26, -30, -17, -18, 26, 2, 3, -16],\n [0, 0, 0, -20, -29, 24, -6, -1, 3, 7, -20, -2... | 341860 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-23, 28, 13, 35, -12, -9, 7, -26, -23, 25, -14, 18],\n [0, 14, -15, 8, 34, -29, -1, 28, -6, 22, 22, -15],\n [0, 0, 34, 11, -11, -4, -9, 10, -24, -23, 33, -24],\n [0, 0, 0, 31, 7, 12, -10, 29, 15, -27, -4, 33]... | 182 | MATH |
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