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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -21, 25, -15, -12, -33, -14, 17, -34, -6, 2, -34],\n [0, 24, -15, -3, 22, -14, 13, 23, 6, 24, -21, 26],\n [0, 0, 26, 15, 19, 28, -33, 15, -29, -15, 3, -1... | -4811 | 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, -12, 23, -4, 16, 26, 22, 16, -24, 3, -34, -33],\n [0, 23, -34, -34, 18, -35, -17, -34, 17, 8, -4, 34],\n... | 791 | 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, -34, -19, -3, -27, 7, 12, 3, 6, -10, 14, -11],\n [-12, -23, 24, -29, 21, 0, 9, -16, 29, -28, -20, -22],\n [-21, 30, -4, 27, 15, -11, 2... | 1645 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 10) rounded to the nearest integer?\n[[-12, -13, 26, 1, -24, 19, -23, -13, -6, -19, 26, -23],\n [0, -17, 13, -24, 25, -17, -27, 35, -8, 16, -20, 33],\n [0, 0, 16, 17, -13, -20, 21, 3, 17, 6, 22, 3],\n [0, 0, 0, -18,... | 8679 | 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[[-25, -10, 27, 23, -9, 13, -3, -35, -15, 19, -30, 33],\n [-31, -33, 17, -13, 17, 1, -19, -35, 15, 9, -32, 26],\n [29, -4, -2, 3, -10, -2, 18, -33, 14, -24, 29... | 5779 | 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[[-30, 16, -10, 28, 23, 20, 23, 34, -3, 17, -14, -15],\n [34, 34, -32, 26, 26, -12, 19, -27, -33, -5, 4, 0],\n [-12, -30, 30, -32, -30, 15, ... | 1324 | 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[[-7, -28, -31, -7, 11, 32, 9, -34, -9, 0, 0, -10],\n [0, -9, 33, -16, -25, 2, -30, -13, 11, 10, -24, -23],\n [0, 0, 7, 32, -31, 1, -5, -27, 15, -7, 4, 5],\n [0, 0, 0... | 683589 | 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, -29, -3, -13, -17, -17, 0, -7, 24, -34, -35, 11],\n [33, -16, -25, -34, 31, -24, -16, -31, 1, 2, -27, 17],\n [8, -12, -6, 23, -22, -27, 4, 30, -11, -14, -32, -10],\n [22, -7, 1, 34, -18... | -1733 | 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[[24, 9, -33, 1, 7, 4, 19, 3, -21, -32, -11, -23],\n [-3, -20, 6, 30, 19, 6, -2, -6, -23, -23, -18, -4],\n [3, 10, -7, 26, 26, 21, -20, 20, -26, -6, -11, -31],\n [29,... | 2050 | 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[[9, -1, 15, -14, -12, -24, -10, 8, -12, 14, 11, -14],\n [-1, 3, 28, -21, 2, -3, -4, 24, 22, -17, 0, -17],\n ... | -112 | 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, -34, -3, -6, -3, -10, -14, 30, 2, 10, -21, 8],\n [13, 25, 31, -30, -27, -30, -4, 5, -28, 14, 26, 26],\n [-29, -32, -30, 22, -14, -10, -33, ... | -109 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-10, -7, -35, -1, 34, 23, 33, -3, 15, -24, -16, 17],\n [7, 14, -7, 21, 3, 20, 7, 14, -13, 8, 2, -13],\n [9, 16, 14, -28, -35,... | -134 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[32, -28, 21, -12, 4, 8, 18, 0, -7, -20, -16, 8],\n [-28, -21, -12, 4, -20, 4, -22, -16, 32, -7, -8, -15],\n [21, -12, -18, -19, -9, 11, 28, 22, 4, -18, -18, -12],\n [-12, 4, -19, -1, 33, -2, -28, -30, 16, -16... | 580 | 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[[13, 6, 2, 9, -1, -6, -6, -30, 31, -29, 16, -22],\n [-21, -15, -1, 30, -34, -1, -16, -26, -11, 30, -11, 18],\n [-3, 0, -22, 29... | -59 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[29, -16, -10, -30, -6, 2, -1, -16, -18, -21, -18, 5],\n [-16, -25, 9, -18, -25, 1, -7, 15, -14, -23, -15, 9],\n [-10, 9, -28, -6, 6, 0, 9, 0, -6, 21, 11, 14],\n [-30, -18, -6, -24, -15, -14, 2, 2, -24, -6, -10, -4],\n [-6,... | 125 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (6, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 35, -32, -22, -33, 22, 19, -32, -12, -2, -6, -17],\n [0, 24, 24, -17, 13, 27, -14, -12, -6, 22, -5, 28],\n [0... | -24 | 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[[-14, 21, 30, -20, 15, 3, 4, 2, 24, 23, -26, 28],\n [0, 13, 28, -4, -29, -15, -16, -10, 32, -21, -22, -9],\n [0, 0, -8, -10, 27, 30, -11, -33, 8, 6, -30, 3],\... | 104347 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[11, 2, -21, 27, -15, 21, 17, 10, -22, -19, 3, -27],\n [0, -13, 23, 10, 2, -22, 26, -1, -17, -6, -11, 4],\n [0, 0, -14, 12, 15, -33, 6, -17, -8, 9, 35, 27],\n [0, 0, 0, 2, 17, 25, 0, 4, -6, -27, 28, -3],\... | 248736411 | 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[[-19, -15, 15, 23, 3, 19, 5, 3, -23, 28, -25, -17],\n [-25, 10, 9, -35, 4, -17, 25, -24, 25, -3, 9, 33],\n [-28, -11, 10, -6, 11, 13, 11, -... | 6203 | 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, 20, -8, -24, 22, -18, 4, 27, 8, -18, -18, 2],\n [20, 1, 10, -11, -13, 4, 16, -5, 17, -16, 8, 4],\n [-8, 10, -25, 2, -25, 20, 2, 5, -20, 2, -21, -1],\n [-24, -11, 2, -... | 144 | 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, 30, 4, -19, -2, -20, 24, 30, 30, -23, 20, -5],\n [0, 3, 31, -28, 19, -9, 17, 3, 29, -19, -6, 17],\n [0... | 191 | 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[[-26, 8, 0, -9, 6, -10, -17, 12, -10, -34, -5, -16],\n [8, -11, -26, -15, -26, 19, -19, 7, -7, -20, 22, 26],... | -2134 | 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, 8, -27, 1, 0, -8, 6, 7, 6, 30, 19, 12],\n [0, -9, 31, -23, 9, -26, -27, 18, -9, -2, -35, -4],\n [0, 0, -16, -1, -19, -18, 9, 17, 32, 29, -3... | -39 | 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[[27, 15, 0, 30, -21, 3, 34, -35, -13, 3, 21, -2],\n [0, -23, 34, -30, 16, -33, 27, 13, 11, 19, 28, 29],... | 563456 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[32, 29, -10, -26, 17, 23, -14, 15, 12, -15, -14, -6],\n [-11, -8, 29, 9, 32, -29, 13, -27, 0, -35, -26, 0],\n [10, -4, -4, -30, 12, 2, -19, -9, 18, 14,... | -627 | MATH |
[
{
"content": "Find the value at position (4, 11) of the inverse of matrix 1/839 * A where A =\n[[-1, 0, -4, -11, -33, -8, 19, 0, 16, 7, 12, -6],\n [0, 10, -20, 10, -10, 32, -20, -2, -10, 5, 6, -8],\n [-4, -20, 0, -2, 2, -18, -15, 23, 2, -6, 9, -6],\n [-11, 10, -2, 26, -2, 22, -2, 2, 6, 12, -9, -26],\n [-33, -10... | 723 | 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[[23, 35, -27, -30, -7, 22, -19, -20, -33, -15, 28, 0],\n [26, 6, 6, 25, -23, -25, 18, -20, -28, 23, 21, 4],\n [23, -34, -26, 8, -25, -34, 1... | 1399 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-15, -6, -14, 12, 16, 20, 0, 16, 20, 22, -6, 4],\n [-6, -14, -2, 0, 2, -7, 10, 9, -2, 24, 13, 2],\n [-14, -2, 2, -14, -18, 2, 0, 25, -11, 23, 24, 2],\n [12, 0, -14, 7, -2, 0, -15, -10, 2, 11... | -271 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[35, 12, -18, -20, 19, 3, 32, 23, 26, -23, -30, 24],\n [-22, 18, -32, 3, -11, -4, 23, 27, 2, 17, 31, -8],\n [-33, -14, 2, 26, 21, -30, -4, -26, -33, 23, 13, 23],\n [-5, 33, 26, 16, 5, -5, -14, -32, -23, 9... | 3074 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-32, 2, -9, -27, -20, 20, -5, -22, -11, -2, 31, -12],\n [-10, -16, 28, -26, 31, -12, -31, 31, 22, -9, -21, -1],\n [17, 8, -10, 11, -2, 14, -24, -32, 12... | -331 | 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, -1, -4, 12, 8, -12, 25, -19, 35, 14, 29, -4],\n [0, -23, 34, 22, -22, 1, 32, 4, 23, ... | -11138 | 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[[16, -8, -4, 12, -13, 7, -3, -20, -2, -4, 19, -4],\n [-8, -34, 6, -26, -24, 4, -7, -12, -6, -6, -14, -1... | 2431 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (9, 5) rounded to the nearest integer?\n[[9, -13, -8, 21, -10, -11, 18, -7, 0, -22, -1, -6],\n [0, 31, -6, 9, 15, 11, 17, 28, 2, 28, -29, -14],\n [0, 0, 21, -29, 14, 16, -3, -35, 17, 24, -2, -32],\n [0, 0, 0, -32, -35, ... | 0 | 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, -30, -24, 2, -17, 31, -28, -28, 11, -32, 15, 31],\n [0, -28, -20, 31, -27, 24, 35, -21, 35, 5, -14, -12],\n [0, 0, -26, 20, 14, -24, 24, -10, 5, 0, -13, 7],\n [0, 0, 0, -11, -18, 26, -23... | 149744 | 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[[5, -30, 2, -30, 9, -22, 30, 4, -33, -12, -17, -18],\n [28, -1, 26, -35, -11, 9, 13, -20, -17, -13, -11, -20],\n [18, -35, 6, -17, -2, 19, -18, -2, 9, -30, -15, 34],... | 1594 | 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[[15, -16, 23, 35, -27, -35, -7, 27, 20, 32, -1, -33],\n [-29, -9, -35, 35, 8, 5, 6, -3, 14, 27, 1, 23],\n [12, -31, 12, -33, 11, 26, -22, 27, 25, -5, -19, -12... | 343 | 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, -9, 2, 29, 18, -12, 11, 35, 27, 21, 19, 24],\n [26, -6, -14, -7, 5, 6, 29, -5, -6, -18, -19, 2],\n [-22, 20, -14, 31, 20, -17, 21, 8, -1, -35, 16, 34],\n [1, 2... | 7723 | 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[[2, 5, 9, 4, -19, 21, -34, 26, -27, 32, -19, 14],\n [0, 22, -15, -18, 19, -7, -12, -19, -18, 6, 9, -19],\n [0, 0, -7, -32, -16, 11, -27, -9, -21, -17, 16, -10],\n [0, 0, 0, 13, 17, -33... | -338783 | MATH |
[
{
"content": "Find the value at position (8, 9) of the inverse of matrix 1/839 * A where A =\n[[-15, -20, -21, -12, -14, -10, 0, -16, -8, 3, 8, -14],\n [-20, -19, -26, 24, -4, -24, -6, -2, 12, 4, -30, 12],\n [-21, -26, -24, -28, -19, 15, -10, 31, -2, -9, -26, -31],\n [-12, 24, -28, -28, 1, -24, 4, -9, 15, -7, 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[[-31, 16, 5, 17, 14, -21, -29, 4, -8, -4, -21, 34],\n [0, -32, -25, -10, 25, 1, -13, 4, -13, -20, 25, 32],\n [0, 0, -11, 8, -24, -27, -24, 33, 18, 18, -8, 20]... | -119588 | MATH |
[
{
"content": "Find the value at position (5, 11) of the inverse of matrix 1/839 * A where A =\n[[-8, 30, -14, -5, -13, 12, -16, 2, 19, 32, -35, -29],\n [0, -24, -31, 14, 6, -24, -18, 30, -19, 32, 35, 26],\n [0, 0, 34, 9, 22, 15, -2, 8, -21, 34, 14, -4],\n [0, 0, 0, 31, 12, -19, -29, -23, 30, -32, -26, -19],\n [... | 162 | 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[[-23, 5, 23, 33, 17, 9, -16, -12, 25, 22, -9, -10],\n [-29, 6, 11, 17, 23, 2, 33, 17, -21, -10, 12, -17],\n [-27, 28, 18, 15, 3, -32, -33, 28, -7, -25, 22, -9],\n [-15, 3... | 21 | 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[[-14, 1, -16, -12, 29, 29, -35, -33, 10, 19, 28, 9],\n [-10, 29, -12, -1, -12, -8, -20, 23, 18, -20, -21, -25],\n [29, 32, 7, ... | -43 | 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, -33, 21, -6, -27, -10, -34, 26, -33, 10, 32, -11],\n [0, -23, 8, -1, 19, -27, -34, 25, 5, 8, 28, -5],\n... | -386 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-17, 31, -31, 31, -25, 32, 33, -35, 27, -7, -24, 5],\n [0, 1, 9, 12, -12, -14, -25, 22, 10, -7, -1, -21],\n [0, 0, 7, 13, 28, -4, 28, -34, -12, 30, 2, -5],\n [0, 0, 0, -11, 12, 29, 17, 31, -18, -27, 2, -15],\n [0, 0, 0, 0,... | 245479 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (10, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 21, 22, -22, -16, -6, -17, 17, 20, -13, 26, -3],\n [0, -3, -4, 25, 18, -19, -17, 34, -2, -11, 32, -25],\n [0,... | 0 | 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[[-7, -12, -4, -16, 20, -16, -10, 0, -24, 5, -5, 11],\n [-12, 11, -3, 25, 6, 10, 6, -21, 4, -2, -15, -20],\n [-4, -3, -8, -6, -22, 11, -18, ... | 6725 | 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, 31, -25, -24, -26, -11, 13, 13, -25, 26, 0, 3],\n [0, 20, -35, 20, -32, -6, -24, -1, 16, -5, 32, 16],\n [0, 0, 20, 22, 28, -24, -29, 19, 26, 19, 0, -12],\n [0, 0, 0... | 423 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[13, 27, -4, -26, -25, 34, 26, 11, -2, -19, 18, 4],\n [-17, 31, 17, 28, 11, -30, -20, -18, 16, 12, 7, 3],\n [13, -24, -26, 35, 19, -35, 13, 0, -15, 1, -12, 19],\n [-11, -29, 35, 35, -12, -25, -24, -1, 27, 32, 21, -23],\n [-... | -67 | 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[[-19, -13, 6, 9, 4, 21, 4, -14, -12, -2, 14, 7],\n [-13, 29, -4, -4, -24, 2, 22, 3, 32, 10, 10, -12],\n [6, -4, 2, -22, -8, 20, 0, 12, -12,... | 5989 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[12, -29, 33, -20, -35, 1, 1, 28, 26, 25, -3, 30],\n [-6, -16, 24, -12, -32, 1, -32, -18, 30, 12, -3, 22],\n [-8, -1, -26, 29, 6, -27, 24, -21, 21, 33, -14, 28],\n [5, 35, 20, -1... | -89 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[-15, 21, 14, -10, -6, -5, 6, 32, 25, 25, 34, 32],\n [-19, -17, 15, 34, 27, -6, -11, 35, -10, 20, -14, -17],\n [-5, -10, 6, 5, -13, 11, -23, 30, 30, -20, -8, -1],\n [5, -5, -4, 1... | 32 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-21, 10, 28, 10, 20, 8, -7, 26, 16, 18, 21, 30],\n [0, -16, -3, -11, 10, 21, -31, 19, 25, -28, -20, 12],\n [0, 0, 29, -14, -33, 18, -22, 0, 31, -26, 13, 29],\n [0, 0, 0, 35, 21, -21, -6, -16, 1, -33, 5, ... | 3380 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 34, 17, 8, 18, -16, -5, -29, 22, -26, -26, 3],\n [0, -6, 1, 31, 7, 16, 20, 32, -27, -13, 27, 25],\n [0, 0, -12, ... | 0 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 30, -19, 4, 2, 25, -27, 25, -20, -34, 7, 6],\n [0, 31, -6, -23, -17, -29, -27, 18, 25, -34, 14, -5],\n [0, 0, -3, -29, -5, 12, 11, 17, -17, -30, 13, 14],\n [0, 0, 0, ... | 1093 | 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, 24, -18, 20, 17, -29, 33, 16, -32, -2, 33],\n [0, 33, 2, -10, -35, -32, 3, 18, -3, -3, -16, -20],\n [0, 0, 26, -5, 6, -24, 29, -33, -27, 15, -20, -33],\n [0, 0,... | 562 | 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[[7, 24, 21, 35, -19, 14, -4, -14, 19, 21, -23, 11],\n [0, 18, -7, -14, 29, -7, 12, -31, -1, 35, 10, -1],\n [0, 0, -26, 30, 34,... | -9388406 | 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[[-20, -18, 26, -9, -1, 9, -1, -8, -27, -21, -15, 16],\n [-1, 15, 19, 8, 29, -11, 11, 20, 2, -25, 31, -21],\n [-35, -29, -35, 13, -7, -10, 9... | 4644 | 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[[-16, -16, 8, 21, -16, 2, 10, 34, -21, 8, -23, -32],\n [-16, -9, 2, -30, -3, 18, -1, -18, 4, 12, 24, 22],\n [8, 2, -11, 12... | 93 | 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, 16, -2, 0, 34, 7, -20, 23, 17, -17, 5, 11],\n [0, 19, -17, 26, 23, 29, 32, -8, -18, -10, -17, 19],\n [0, 0, -35, -28, 15, -11, 11, 19,... | 3459621 | 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[[-29, -20, -17, -30, -25, 25, 6, -23, -24, -16, 14, 0],\n [33, 1, -24, 4, 18, -34, 14, 5, 9, -27, 26, 11],\n [-31, -35, 8,... | -194 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-28, 5, -33, 33, -22, -10, 34, 22, 4, 15, -31, -4],\n [-35, 18, -25, 17, -28, -11, 4, -4, -8, -33, 26, -9],\n [9, -11, 25, 8, 10, -22, -28, 12, -22, 29, -29, 13],\n [19, -23, 20, 20, -21, 21, 22, -1, -20, -28, 9, 4],\n [18... | 12889 | 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[[-21, 10, -13, -24, 8, -21, 13, -15, -21, -22, 6, -21],\n [27, 32, -9, 17, 16, 27, 17, 21, 16, 7, -29, 6],\n [-32, 33, -31, 5, -32, -34, 31, -15, 34, 7, 33, -27],\n [-8, -10, -33... | -13 | 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[[-26, 11, -32, 19, 30, 31, -29, 19, -5, -17, -8, -8],\n [-17, -16, -23, 7, -25, 12, -21, -19, 18, 14, -8, -32],\n [-14, 3, -2, 8, 6, 4, -24, -34, -8, 31, 35, -26],\n [21, 1, 28,... | 2 | 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[[4, -2, 9, 35, 35, -9, 8, -3, -3, 8, -16, 0],\n [-29, -4, 31, 3, -12, 34, 18, 2, -4, 9, 25, 34],\n [17, 15, 20, -9, 2, 26, -18, 28, -6, 13, 5, -23],\n [... | 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[[-14, 4, 9, 19, 15, -31, -23, -8, 26, -12, -29, 2],\n [1, 32, 6, -31, 28, 14, -21, 17, -11, -27, 2, -14],\n [13, 32, -21, 29, 18, -6, -16, -3, -29, -28, -8, 9... | 215 | 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, 35, -2, 12, -24, -13, -23, 9, 29, 11, 22, -31],\n [0, 24, -15, -12, -18, -15, 18, -26, -12, 24, 21, -13],\n [0, 0, -2, 34, -8, 3, 6, -13, 34, -34, -12, -19],\n [0, 0, 0, 24, 14, -24, 11... | -128542 | 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, -21, 5, 1, 11, -3, 11, 12, -10, 16, -4, -28],\n [-21, 31, -6, -4, 18, -16, -12, -16, 20, -10, 7, -6],\n [5, -6, 18, 21, -2, 28, 10, 26, 6, 20, -14... | 63 | 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[[16, -18, -20, 30, -31, -33, 34, -29, 14, -22, 2, 11],\n [0, 7, -7, 21, -31, 24, 34, -34, 34, 7, -32, 20],\n [0, 0, -33, 12, 7, -35, 21, 17, -20, 15, 19, -35]... | 618422 | 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, -22, 16, 0, -28, 4, -14, -20, 24, 24, -26, -11],\n [-5, -15, -3, -5, -15, 0, 29, -32, 32, -32, -27, -6],\n [9, -32, 33, -13, -20, -14, 12, 26, 24, -31, -29, 15],\n [29, -27, 9, 11, 31, -... | 37 | 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[[-30, 31, 5, 7, -18, 22, 24, -9, 32, -14, -12, 4],\n [30, 4, -30, -18, -6, -15, 26, -26, -23, -27, 32, ... | 5103 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (8, 3) rounded to the nearest integer?\n[[-22, 10, -26, -12, 25, -18, -27, -19, 22, -23, 14, -30],\n [15, 0, 35, -11, -25, 8, -22, -7, 14, -31, 33, 21],\n [-10, -30, -20, 24, -24, -33, 27, 28, 26, -30, -17, -18],\n [7, ... | -13 | 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[[16, 27, 24, 29, 19, 21, 35, -10, -24, 35, 10, 11],\n [2, -15, -22, -34, 34, -3, -30, 1, -22, 1, -28, -23],\n [4, 22, -18, 21, 2, -4, 30, -11, 22, -3, 30, -6],\n [-2, 33,... | -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[[-17, 32, -12, 3, 18, 3, -19, -17, 12, -1, -4, 11],\n [11, 28, 10, -1, -19, 6, -7, 34, -19, -22, -12, 21],\n [14, 21, 25, 3, 19, 0, 1, -22, -9, -5, 8, 32],\n [12, 21, -14, -32, 10, 23,... | 192 | 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[[-2, -3, 10, 9, -17, -21, 30, 3, -18, 34, 23, -4],\n [0, 4, -9, -34, 3, 20, -23, 20, 30, 20, -8, 28],\n [0, 0, 20, 5, 5, -32, 21, -6, 10, 20, -5, -29],\n [0, ... | 32384 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -29, 8, -7, 8, 0, -17, -30, -11, -5, -27, 1],\n [0, -23, 5, 30, -12, 8, 24, -27, -34, 20, -6, -14],\n [0, 0, -2... | 118 | 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[[-15, -30, 5, -21, -33, 7, 11, -22, 30, -7, -32, -10],\n [-24, -34, -19, -1, -26, 7, -15, -21, -1, 24, 8, -31],\n [-18, -15, 15, 5, -12, -12, 2, 8, 21, ... | 257 | 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, -5, -3, 10, 14, 12, 12, 4, -14, 17, 12, 5],\n [-5, 29, 12, 0, -26, 12, -18, 10, 3, -19, 6, -2],\n [-3, 12, 2, 7, -4, 2, -30, 16, -8, -14, 10, 22],\n [10, 0, 7, ... | 3717 | 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[[-29, -19, 28, -24, 20, 10, 11, -20, 33, -34, 18, -9],\n [-5, 5, 0, 11, 7, 29, 14, -35, 21, -20, -8, -14],\n [5, -17, 14, 23, 33, -2, 3, -29, 16, 24, 16, -12],\n [-1... | 1964 | 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, 35, 29, 1, 34, -10, -34, 23, -31, 1, -5, 12],\n [-30, -21, -21, 25, -20, -16, 8, 6, 10, -2, 28, -7],\n [-33, -27, -11, 6, 10, 23, -15, -14, -7, 27, 25, 28],\n [33, 4, -35, 29, 26, 18, 2... | -188 | 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[[8, 6, 4, 6, 30, -3, 8, 26, -7, -8, 9, -2],\n [6, -17, 27, 0, -22, -11, -2, 6, -5, -5, -30, 14],\n [4, 27, -23, -28, 14, 1, -14, -2, 18, 2, 14, -4],\n [6, 0, -28, -6, 8, ... | -135 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 12) rounded to the nearest integer?\n[[31, 17, -34, 32, 29, 21, 34, -29, -17, 8, 27, 29],\n [0, -10, 8, -24, -14, -22, -6, 8, 2, 23, 6, 16],\n [0, 0, -2, 3, 5, 1, 29, -4, -28, -18, 9, -3],\n [0, 0, 0, 4, -31, -2, -... | 62 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-14, -5, -29, -15, -20, -16, 7, 8, 11, -17, 12, 33],\n [-25, -7, 9, 32, 0, 12, -21, 8, 31, 4, -22, 27],\n [15, 22, -21, 29, 19, -26, 6, -25, -20, -17, -5, 17],\n [-28, -12, -28, 12, -6, 22, 19, 26, 12, -... | 1535 | 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, -8, -29, 26, 15, 10, -16, 2, 25, -4, -10],\n [22, 3, -16, 14, 16, -14, 17, 30, 7, -13, 28, -27],\n [-29, 5, 18, 29, -34, -32, -4, -34, 28, -22, -16, 1... | -130 | 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, 9, -34, 32, 14, -7, -26, -9, -21, 24, -5, -15],\n [0, 22, 5, 10, 9, -10, 15, 0, 16, 15, -33, -22],\n [0, 0, 21, -19, 14, -22, 23, -33, 4, 3... | -562 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (8, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -10, -13, 26, -23, -27, -16, 21, -12, -3, -16, 24],\n [12, 28, -6, -19, -22, -17, 35, 23, 31, 8, -4, -25],\n [-... | -5 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-12, -26, -23, 8, 3, -17, 15, -17, 16, 11, -6, 10],\n [-15, 12, 26, 22, -18, 23, 12, 27, -24, -2, 25, 17],\n [-11, 26, -32, -23, 6, 13, 20, 11, -28, 19... | 14 | 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[[-15, -29, -29, -9, -28, -8, 30, 35, 11, -26, -3, -29],\n [0, -22, 8, 10, 25, 0, -23, -20, -31, 2, 14, 2],\n [0, 0, 12, 23... | -5329 | 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, 28, 0, 12, -34, 3, 2, -2, 8, -34, 28, -24],\n [28, -6, 20, -14, -16, -8, -20, 4, 7, 20, 10, -8],\n [0, 20, -9, 4, 18,... | -145 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 10) of the inverse. Round your answer to the nearest integer:\n[[-28, -7, -14, 34, 25, 7, 13, -7, -5, 17, -2, 2],\n [0, -32, -34, -24, -1, 34, -15, 25, -1, 12, -21, 35],\n [0, 0, 32, -14, -4, -14, -9, -21, 8, -27, -... | 2122 | MATH |
[
{
"content": "Find the value at position (10, 9) of the inverse of matrix 1/839 * A where A =\n[[-22, 15, 2, -16, 1, 14, -24, 10, -19, 4, -3, -2],\n [15, -9, 22, -30, 24, 2, -8, 24, 6, -8, -20, 23],\n [2, 22, -5, -6, 24, 7, 22, 12, -5, -4, 16, 14],\n [-16, -30, -6, -19, -2, -8, -14, 12, 10, 18, -5, 4],\n [1, 24... | -18 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[11, 12, -6, 26, 7, 28, -13, 3, 1, 8, 6, 4],\n [12, -12, -6, -2, 19, -12, 15, 6, 12, 2, 10, -32],\n [-6, -6, 6, -4, -12, -22, 19, -16, 14, 14, 14, -6],\n [26, -2, -4, 20, 20, -14, 4, -8, -6, 4, 10, -22],\... | 1865 | 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, 10, 17, -10, 25, 31, 18, -14, -10, 24, 3, 0],\n [-15, 5, 12, -10, 27, 0, -12, -15, -18, -21, -30, 7],\n [-5, -8, -28, -7, -15, 22, 24, 14, -5, 11, -2, -34],\n [31, 16... | -70 | 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, -1, -17, 19, 33, 8, 2, 26, -14, 4, -10, -31],\n [18, 13, -33, 2, -22, 11, -22, 2, 28, 8, 34, 29],\n [-11, -20, -21, -33, 31, 1, 19, 2, 27, -35, 35, -17],\n [16, -6,... | -26 | 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[[11, -4, 8, 18, -4, 22, 14, 27, -2, 10, -4, -6],\n [-4, 21, 12, -6, 14, -14, -8, 15, 2, -16, 10, 32],\n [8, 12, 9, 4, 0, 6, 5, 0, -10, 3, -30, 28],\n [18, -6,... | 1391 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 2) of the inverse. Round your answer to the nearest integer:\n[[-15, 10, 2, -8, -11, 2, 6, 16, -4, -2, -5, -14],\n [10, 26, -11, -23, -9, -19, -16, 10, 18, 1, -7, -6],\n [2, -11, 34, -24, -17, 6, 18, -10, 16, 18, 4... | 165 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-29, 20, 28, -16, 2, 22, -20, 15, -9, 15, -20, 24],\n [0, 31, -34, 12, 16, -12, -34, 29, -16, -2, 5, 5],\n [0, 0, 8, 31, 26, -24, -6, 29, 5, -16, -30, -32],\n [0, 0, 0, -35, -28, 27, -3, -21, -5, -15, -3... | 91065 | 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[[-35, -8, 26, 11, 23, -5, 34, 13, -31, -5, 1, -21],\n [16, 33, -25, 7, 34, -13, 4, 27, -34, 11, -6, -20],\n [23, 11, -6, -27, 29, 23, 28, -28, 1... | 512 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-32, -26, 15, -18, 11, -4, -6, 0, -27, 0, -7, -20],\n [-15, 28, 30, 23, -8, 19, -5, -3, 24, 5, 10, 13],\n [29, 6, -13, -9, -4, -33, 24, -19, -4, -29, 35, 33],\n [22, 4, 12, 15, 21, 35, 1, 19, 5, -16, -3, 4],\... | 278 | 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, -4, 35, 14, 35, -5, 15, -9, 24, -3, 17, -3],\n [5, -17, 5, 6, -13, -3, -16, -11, 16, -24, -4, -3],\n [32, -21, 15, -30, 33, 33, -1, -2, 27, 32, -18, -10],\n [25, 12, -5, -2, -29, -29, 1... | -107 | MATH |
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