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[[33, 18, -22, -21, -26, -14, -23, 29, -22, 8, 3, -1],\n [0, -9, 9, 21, -14, -2, -27, 14, 18, 22, 26, 2],\n [0, 0, -33, -25, -12, -7, 33, -28, -17, 32, 33, 12],\n [0,... | 15465 | 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[[-32, -34, 31, -6, -32, 12, 7, 9, -23, 11, -8, 1],\n [-8, -9, -6, -30, -27, -30, -7, 34, 30, 17, 34, -31],\n [-16, -24, -28, 2... | 37 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, -4, 11, 20, -12, 16, -30, -10, -8, 25, -10, -1],\n [-4, 27, 11, 22, -22, 8, -20, 8, 3, -4, -18, 10],\n [11, 11, -24, 7, 26, 14, -12, -7, 7, 26, 7,... | 42 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[34, -2, -6, -4, -22, 0, -4, -10, 16, -6, -25, 8],\n [-2, -30, -16, -8, 2, -6, 4, -4, 2, -4, -28, 6],\n [-6, -16, -1, 8, 0, -8, 0, 19, 5, -18, -13, -15],\n [-4, -8, ... | 2496 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-14, -29, -34, 26, -31, -16, 18, 27, 0, -20, 21, 28],\n [-26, 15, -9, -29, 5, -23, 30, -33, -25, -31, 24, -34],\n [28, -23, 18, -24, -18, -18, -19, 3, -23, 9, -17, -17],\n [-15, -12, -6, 12, -1, 23, -19,... | 2180 | 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, -27, 2, -10, 7, 17, -9, -25, -10, 21, -35, -25],\n [-6, -32, -3, -3, 30, -32, 15, -9, -3, -4, 31, -8],\n [21, -17, -5, 17... | -43 | 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, -12, 21, -18, 21, 10, 7, -20, -22, -27, 33, 25],\n [0, -17, 28, 2, -26, -20, 33, 6, 8, 17, -1, 0],\n [0, 0, -24, -1, 14, ... | -32477 | 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, 3, -6, -13, -13, 11, 12, 27, -27, -13, 27, 11],\n [0, 1, 2, -35, 12, -1, 35, 17, -11, 6, -13, -27],\n [0, 0, 21, 0, -2, -23, 19, 10, 16, -8, -6, 9],\n [0, 0, 0,... | 640531 | 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[[-1, 4, -13, -2, 22, 25, -8, 24, -4, 22, 8, -2],\n [0, -35, 19, 13, -15, 19, -9, -16, -20, 12, -4, -4],\n [0, 0, -34, 21, -14, 16, 22, -2, ... | 7778556 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-16, 0, 0, 0, 2, 14, -1, 22, 24, -14, -30, -4],\n [0, -30, -20, 4, -20, 9, 9, 10, 26, 19, -15, -10],\n [0, -20, -29, 3, -11, 17, 1, -13, 8, -2, -14, 19],\n [0, 4, 3, -10, 29, 28, 8, -7, -14, 10, -2, -16],\n [... | 111 | 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, -31, 34, -18, -15, -21, 23, -30, -12, 24, -8],\n [0, 10, 1, -22, 12, 35, 0, 24, 18, 27, 12, -14],\n [0, 0, -19, 27,... | 3648 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (7, 6) rounded to the nearest integer?\n[[-13, 13, -6, -2, -3, 20, -7, -8, 7, 10, -32, -30],\n [13, 12, -26, 6, -5, -24, -32, 5, 18, -7, 13, 18],\n [-6, -26, -10, 24, 11, -9, -3, -2, -4, 17, 0, 2],\n [-2, 6, 24, 33, 4, ... | 46 | 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[[8, -5, 29, -18, 0, 26, -7, -13, -33, -6, 9, 13],\n [0, 28, -31, 20, -2, 12, -10, -31, -5, -12, -14, -14],\n [0, 0, 11, 31, 3, 30, -7, -22, -32, -31, 8, -12],... | 2514 | 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, 2, 2, 6, 6, 13, 21, 18, -26, 24, 4],\n [-35, 28, -24, 21, -10, 4, 7, -23, 20, -19, -12, 22],\n [25,... | 13 | 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[[-25, -9, 2, -8, -10, -3, -4, 18, -11, -12, 4, -9],\n [0, 33, 33, 3, -7, -5, 29, -21, -27, -23, 9, -30],\n [0, 0, -7, 12, -24, 31, 14, -25, -31, 9, 11, -30],\n [0, 0, 0, 11, -2, -24, -... | -1632 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[18, 29, -14, 25, 22, 18, -17, 34, -2, 8, 31, 16],\n [-14, -7, -22, 26, -21, -22, 31, -14, -29, -29, -19, -4],\n [20, 26, 22, 22, -33, -35, 31, -16, 26, 20, 17, 29],\n [20, 9, -18, 12,... | 49 | 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[[-8, 11, 11, -19, -7, 12, -34, -3, 27, 32, 3, -31],\n [32, 16, 16, -7, 1, -28, -16, 5, 34, 0, -4, -31],\n [-16, 32, -14, -5, 5, -31, -26, 1, 20,... | -27 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-27, 10, 10, 0, 10, 6, -6, -25, -3, 4, 34, 7],\n [3, 3, 17, -5, 27, -11, 5, 14, 23, 13, -6, 9],\n [32, 17, -10, 35, 4, -24, -35, 34, -35, -28, ... | 59 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-27, -6, -1, -12, 10, 8, -9, -1, -12, 14, 8, -2],\n [-6, -19, -3, 24, -30, -11, 12, -10, -19, 22, 4, 21],\n [-1, -3, 18, -4, 18, 0, -3, 0, -8, 6, -32, 0],\n [-12, 24, -4, 17, -3, 16, 13, 1, -12, -8, 12, 5],\n... | 27 | 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[[34, -10, 7, 18, 4, -18, -10, -18, -25, -3, 15, -18],\n [-10, -20, 16, 13, 20, 2, -30, -8, -5, 15, -10,... | 1546 | 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[[-24, -15, -21, -24, 20, -20, -3, 7, 13, -18, -20, 4],\n [0, 26, -9, -22, 30, -9, 18, 24, ... | -3260 | 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[[-35, 12, -14, 5, -11, 10, -27, 25, 11, -33, -28, -11],\n [0, 7, 14, 27, -2, -26, -9, -23, 15, 32, -20, -24],\n [-11, 13, -20, -34, -1, -14... | 1670 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, 29, -16, -30, 3, -15, 1, -24, 34, -21, -15, 10],\n [0, -26, 30, 3, -14, 6, -30, 16, ... | -427339 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[-31, -2, 26, -27, 18, 13, -26, -32, 11, -11, -30, -8],\n [-2, -31, 22, 1, -22, 6, -16, -4, 10, -28, 0, -12],\n [26, 22, 9, 18, -7, 22, -2, 10, -3, -4, -6, 2],\n [-27, 1, 18, -31... | -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[[19, 0, -26, 34, 27, -2, -19, 25, -18, 25, 0, 17],\n [0, -13, 28, 2, 33, -6, -20, 18, 23, -30, -31, -35],\n [0, 0, 15, -17, -4, 21, -5, 22, -10, 12, 5, -11],\n [0, 0, 0, ... | 165 | 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, -12, -10, 2, -10, 22, -20, 9, 2, -2, 26, -11],\n [-12, 0, 6, 0, -3, -16, 11, 8, 12, -6, -2, -27],\n [-10, 6, -30, -12, 26, -1, 16, -7, 21, 14, -11, 8],\n [2, 0, -12, -18, -8, -8, 1... | 279 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-23, 2, -4, -6, 11, 2, -6, -20, 26, 2, 10, -18],\n [2, 34, -19, -2, -7, -14, 16, 12, -11, 28, 8, -6],\n [-4, -19, -10, 2, 4, -1, 6, 16, 14, -2, 9, -8],\n [-6, -2, 2, 10, 8, 0, 5... | 654 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 11) rounded to the nearest integer?\n[[7, 10, 3, 15, -10, 24, -4, 12, 9, 0, -22, -10],\n [10, 28, -4, 10, 13, -8, 6, 10, -7, -16, 14, 16],\n [3, -4, 1, 22, -8, -20, -5, -2, 5, 4, 4, 1],\n [15, 10, 22, -22, -18, -3, ... | -104 | 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[[-22, 10, 14, -31, 7, -18, 12, 28, -10, 34, -22, 30],\n [0, -15, 19, -34, -33, -23, -15, -3, -16, -18, 2, -11],\n [0, 0, -7, 28, -4, 7, -23, -11, 13, -28, -8, -25],\n [0,... | 271 | 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[[-8, 0, 2, 24, 18, -24, 2, 24, 1, 4, 10, 7],\n [0, 5, -20, -4, -3, 2, -22, 20, -6, 3, -2, -11],\n [2, -20, -3, 10, 24, -14, 14, -3, -26, 0, 12, -31],\n [24, -4, 10, ... | 5378 | 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[[10, 0, 8, 12, -18, -1, 4, -20, 18, 6, 4, 14],\n [0, -35, 0, -6, 10, -16, 6, -4, 0, -16, 14, -12],\n [8, 0, 18, 22, -30, 1... | -5346 | MATH |
[
{
"content": "Find the value at position (6, 10) of the inverse of matrix 1/839 * A where A =\n[[-5, -13, 2, 6, -9, 0, 12, 4, -10, -13, 8, -16],\n [-13, 5, -3, -19, -25, 25, 16, 30, 12, 6, -4, 1],\n [2, -3, 35, 26, 4, 9, 12, -14, -17, -28, 5, 5],\n [6, -19, 26, -5, -22, -12, 9, 18, 7, 5, 4, 4],\n [-9, -25, 4, -... | -53 | 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[[-31, -23, -12, -1, 32, -10, 2, -2, -2, -17, -33, 0],\n [0, -10, -33, 13, -27, 10, 30, -22, -33, -34, -3, -26],\n [0, 0, 2, -15, -1, 31, -14, -1... | 284 | 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, -29, 31, 10, 22, -8, -5, 16, -27, -28, -18, 13],\n [0, -34, -7, 19, 17, -10, 15, -30, -24, -2, 34, 28],\n [0, 0, -28, 1, 10, -5, -25, 0, 32, -19, -20, -6],\n [0, 0, 0, 1, -10, -15, -17, ... | 10297 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 12) of the inverse. Round your answer to the nearest integer:\n[[-14, -33, -17, 7, 31, -31, -7, -31, 9, 18, -12, -15],\n [-4, -31, 26, -18, -1, -31, -27, -32, -3, -14, 23, -25],\n [33, -26, -33, -21, 1, 4, -19, -16... | -13 | 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, -26, 14, -26, -20, 2, 31, -16, 33, 34, -11, 18],\n [0, 29, 18, 31, -15, -31, 22, -32, -17, 19, 25, -12],\n [0, 0, -12, 18, -15, -17, 17, 14, -13, 1, -8, 35],\n [0, 0, 0, -1, -35, 31, 34,... | 5435253 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (6, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 28, -19, 15, 20, 12, 26, 20, -25, -16, 32, -2],\n [6, 5, 26, -19, -24, 32, 5, -22, -32, -22, -27, 7],\n [-16, -... | -5 | 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, 20, 7, -35, 0, -30, 10, -13, -16, 17, 2, -1],\n [0, 14, 11, 0, -20, 13, 29, 27, 16, 24, -19, 31],\n [0... | -1365 | 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[[-8, -17, -6, -15, -15, 12, 19, -6, 6, 1, 5, 10],\n [0, -35, 18, -1, -20, -31, -5, 1, -11, 26, -11, 31],\n [0, 0, 28, -34, 28, 33, -16, -25, -5, -1, 8, 19],\n... | -17155 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[33, -12, -12, 20, -14, 0, -11, 8, 14, 28, 18, -16],\n [-12, -29, 4, 22, -34, 24, -8, -1, -18, 2, -8, 22],\n [-12, 4, 6, -2, 1... | 939 | 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, 13, -33, 6, 27, -7, -34, -22, -24, -12, -8, -18],\n [0, -6, -2, 22, -8, 17, -20, -10, 29, 21, -5, -9],\... | -157 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-6, 33, -29, -12, 12, 7, 0, -35, -29, 8, 25, -10],\n [-6, -35, 27, -21, 27, 19, 21, -16, -14, 14, 0, 1],\n [10, -9, -17, -20, 18, -2, 15, 0, 17, 26, -5, -32],\n [-24, 17, 25, -17, 20, -27, -11, 18, 11, 5, 15,... | -33 | 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[[3, 34, -16, -32, -23, 13, -27, 23, -33, -25, -31, -1],\n [0, 34, -30, 6, 7, -22, -11, -18... | 987939 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[20, 8, 28, -12, 5, -8, 26, -21, 26, -26, -7, -5],\n [27, -18, -29, -9, -27, -16, 14, 25, 31, -19, -15, -4],\n [12, 2, -8, 24, 34, 22, 34, 17, -26, -34, -11, 2],\n [-35, -23, 35, -35, -5, 31, 20, -17, -32... | 945 | MATH |
[
{
"content": "Find the value at position (5, 3) of the inverse of matrix 1/839 * A where A =\n[[-6, -22, 9, 10, 31, -20, -26, 32, 16, 14, 32, -34],\n [0, 14, -35, 1, -13, 13, 28, -19, 35, -21, 15, -9],\n [0, 0, 27, 17, 6, 34, -1, -19, 8, 7, 8, 2],\n [0, 0, 0, 24, -34, 29, -33, -22, 9, -2, 0, -21],\n [0, 0, 0, 0... | 0 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[3, -2, 2, 15, -19, -13, 14, 12, -4, 16, -9, -14],\n [-2, -33, -13, -14, 6, 2, -21, 23, -10, -17, 14, -16],\n [2, -13, -4, -1, 20, -20, 7, 11, 4, -8, 0, -10],\n [15, -14, -1, 35, 6, 28, 11, -13, 18, 6, 8, 8],\... | 172 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[23, 31, -33, -6, 28, 34, -34, -16, -7, -27, -32, 4],\n [19, -23, -30, -10, 5, 6, 25, 26, 32, -15, -5, 7],\n [-15, -7, 19, 22,... | -313 | 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[[15, 31, 21, -16, 9, -30, -3, 7, 14, -9, -6, -18],\n [-6, -21, 26, -15, -24, 13, -35, 19, -11, 11, 3, -9],\n [14, 19, -8, 21, -20, 20, -1, -8, 10, 31, -20, 13],\n [3... | 120701 | 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[[19, 20, -32, -11, -34, -17, -28, 28, -30, -22, 34, 35],\n [0, -6, -28, -22, 12, -8, -30, -6, -32, 31, -26, -9],\n [0, 0, -23, 19, 7, 32, 7, 4, ... | -297 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-8, -14, 30, 6, 24, -9, -2, -16, 5, 2, 4, -19],\n [-14, -11, -1, -16, 4, -8, -20, 4, -12, 14, 2, 10],\n [30, -1, -11, -6, -12, 4, -1, -6, 8, -10, 16, -6],\n [6, -16, -6, -18, 12, 0, -12, 18, -14, 14, 24, 18],\n [24, 4, -12... | -119 | 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[[-1, 27, -5, 6, 30, 5, -35, -3, 1, 21, -25, 11],\n [0, -32, 19, -24, 30, 1, -13, 19, -17, 31, -13, -32],\n [0, 0, -1, -9, 7, 31, 33, 28, 16, -19, -3, 16],\n [0, 0, 0, 32, 14, 22, -6, 3... | 328352 | 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, 1, -22, 26, 1, -2, -6, 12, -11, -22, 14, -4],\n [1, -18, 10, 8, 4, -8, -1, -4, -12, 26, 18, 7],\n [-22, 10, -9, 5, 10, -19, 6, -16, -2, -1, 30, -16],\n [26, 8, 5, -20... | -4 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, 34, 27, -2, 7, -31, -17, 18, -22, -26, 13, -25],\n [0, 30, -26, -15, -35, 10, -16, -15, 1, -22, 22, 21],\n [0, 0, 34, -12, 24, -13, 11, 2, ... | 825 | 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, -19, -11, 25, 1, 30, -23, 4, 6, 34, -11, 6],\n [0, 7, 32, -8, -12, 5, 25, -31, -25, -28, -15, 28],\n [0, 0, -27, 2, 7, -26, -24, -18, -24, -5, -25, -9],\n [0, ... | 182396 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 25, 22, -1, -5, 21, -26, -18, 20, 0, 15, 25],\n [-17, -25, -31, 9, 9, 12, -22, -8, -27, 23, 2, -11],\n [12, -17... | 39 | 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, -20, -4, -7, 16, -21, 8, -13, 12, -13, 35, -22],\n [0, 34, 7, 9, -14, 25, -18, 8, -18, 21, -21, 22],\n [0, 0, -15, 7, 9, -2, 35, -24, -29, 33, -8, -11],\n [0, 0, 0, 10, 11, -4, -2... | 2629 | 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, 28, -24, 17, 8, 10, -25, 34, 10, 23, 23, -2],\n [0, 16, 12, -17, -32, -4, -8, 22, 5, -3, -22, 17],\n [0, 0, -11, 16, 4, 34, 26, -27, 33, -15, 17, 34],\n [0, 0, 0, -8... | -1587 | 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[[-13, -28, 14, -20, 7, 10, 13, -21, 13, -15, -30, 19],\n [-21, -25, 3, 15, 1, 13, 21, 29, -19, 27, -22, 2],\n [-11, 1, 20, -29, -25, -1, 0,... | 4930 | 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[[35, 10, 2, -3, -14, -9, 27, -9, -15, 17, -1, 11],\n [14, -26, -8, 1, 5, 25, 15, -28, 22, 25, -3, -17],\n [-6, -22, 0, -29, -2, 14, -4, 6, -3, -22, -8, 3],\n [-5, -12, -3... | -210 | 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[[8, 21, 5, 3, -16, -14, -7, 10, 32, -33, -31, 20],\n [31, -4, 5, -7, 30, -25, 23, -32, 18, 31, -34, 12],\n [32, 8, 26, -17... | 28 | 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[[-10, 14, -34, -29, -9, 13, 10, -10, 29, -34, 28, 28],\n [0, -27, -21, 1, -30, 7, 9, 35, -8, 16, -1, 30],\n [0, 0, 26, -35, 17, -6, 24, -26, -14, -7, 33, -28],\n [0,... | 432094 | 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[[12, -12, -19, -20, -16, 8, -5, 2, 9, 12, 11, -10],\n [-12, 16, 15, -10, -9, 1, -5, -4, -2, 32, 0, -26],\n [-19, 15, -32, 9, 6, 12, 21, 25, -16, -13, -18, 15],\n [-20, -1... | 38 | 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, 14, -17, -18, -26, 14, 13, 5, -21, -13, -9, -30],\n [0, -27, 26, 31, 34, 6, 24, 12, 20, -31, 18, 2],\n [0, 0, 35, -12, -26, -15, -21, 28, -23, 35, 4, -28],\n [0,... | 6182 | 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[[-16, -32, 17, 35, 26, 2, 0, -2, -30, 30, -18, -9],\n [0, 15, -17, -2, -12, -11, 34, -6, 18, -11, -31, -34],\n [0, 0, 2, -19, -5, -35, -30, 34, 0, -28, -26, -12],\n [0, 0, 0, -16, -3, ... | 64763 | 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, 27, -14, -2, 1, 5, 7, -14, -21, -15, 16, -32],\n [0, -18, 35, -1, -29, 5, -26, 26, 29, -24, -8, 22],\n [0, 0, 29, 21, 14, 9, 26, 29, 19, 2, -32, -21],\n [0, 0, 0, -1, -32, -4, -24, 18, ... | 34146252 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -11, -32, -5, -17, -34, -32, 2, -3, -18, -4, -3],\n [-2, 15, 27, 11, 30, -23, 16, 16, 7, 25, -33, 32],\... | 104 | 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[[35, -8, 14, 2, 30, -4, 10, -3, 0, -16, 1, 4],\n [-8, 9, -18, -16, -3, -12, 4, -20, 20, -2... | -67 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-16, -15, 10, -18, -18, 12, -7, -7, -28, -3, -2, 2],\n [-15, 25, -34, 30, 5, -2, -16, -1, 21, -3, -12, -20],\n [10, -34, 0, 6, 12, 28, 12, 2, 4, -16, -8, 10],\n [-18, 30, 6, -2, -22, 12, 18, -30, -4, -20, 23, 20],\n [-18, ... | 791 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, -22, -29, 18, 22, 25, -8, 19, 17, 8, -8, 10],\n [0, 31, -9, 3, -9, -1, 11, 16, 33, 30, 5, 14],\n [0, 0, 35, 0, 34, -12, 0, -31, -16, 17, 4,... | 947 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -2, 12, -4, -11, -16, 10, 11, -14, -10, 13, -10],\n [-2, 25, 18, -16, -2, 5, 13, 10, -18, -17, 0, -13]... | 45 | 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[[18, 0, 17, 24, 8, -3, 8, 19, 8, 15, 15, -29],\n [-35, -23, 12, 11, 11, -26, -10, 14, 11, 8, -35, 27],\n [-19, -19, 3, 7, 5, -... | -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[[35, 13, -28, -30, 4, 18, -19, 15, -34, -6, -4, 14],\n [0, -20, 19, 21, 9, 16, 35, 11, -3, -12, -1, 28],\n [0, 0, -18, 22, 12, -25, -33, 6,... | 22634 | 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[[-11, -1, 29, 3, -18, -11, -35, 26, -27, 5, -14, 30],\n [9, 16, -16, -24, 28, -4, 26, -31, 8, -7, -3, -23],\... | 67 | 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[[-2, -8, -17, 12, -2, -20, 35, -9, 15, 18, -19, 32],\n [-35, -22, -29, 28, -28, 18, -12, 19, -35, 33, -4, -35],\n [3... | 3 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -10, -34, 19, -18, 14, 9, -21, -29, -9, 4, -19],\n [0, -20, 27, 24, 16, 13, 13, -10, 15, 7, 34, 35]... | 184896 | 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[[-12, 0, 0, -15, 4, 12, -4, 0, -22, -12, -25, -20],\n [0, 23, -16, 12, 15, 16, 15, -22, -1, -12, 1, -14],\n [0, -16, -18, -12, 20, -17, 5, ... | 5835 | 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[[11, -27, 12, 0, -27, -12, -34, -12, 6, 26, 2, 6],\n [-27, 15, 18, 12, -21, -2, -2, 18, 30, -6, -8, -16... | 1442 | 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[[-16, -21, -25, -20, -14, 26, -12, 0, -18, -16, -28, -21],\n [0, -12, 11, -18, -4, 6, 1, -3, -35, -9, -19, 1... | -806 | 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[[10, 35, 10, -20, 22, -22, 7, -11, -21, -6, 8, -27],\n [-25, 30, -14, -16, -7, 27, 5, 12, -9, -5, -11, 13],\n [34, 28, 20,... | -1365 | 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, 23, 0, -30, 30, -4, 17, 33, -34, 7, 4, 32],\n [-32, 10, -16, -22, -22, 13, -33, -15, 25, -34, -15, -26]... | 93 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, 17, 8, 0, -2, 16, -30, 2, -3, 19, -13, 8],\n [0, 28, 12, 23, 23, 7, 7, -23, 7, -23, -1, -25],\n [0, 0, 14, 13, -23, 3, 19, -29, 7, 6, 22, -... | 62 | 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[[9, -23, -34, -5, -8, 23, -25, -1, 13, 8, 22, 15],\n [-19, -32, -3, 26, 7, 6, 15, 2, 7, 12, 6, 21],\n [18, -19, 15, -27, -28, 27, 20, 34, -27, -... | 55 | 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[[-3, 10, 23, 21, 26, 27, -5, 3, -14, -19, -33, -4],\n [-3, 28, -26, -31, 32, 2, 5, 25, -21, 16, -28, 20],\n [-6, -2, 23, 20, -... | 633 | 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[[-14, 29, -16, 11, 12, -12, 3, 19, 19, 34, 27, -17],\n [0, -10, 11, -22, -33, 33, -22, -28, -21, 9, 9, -33],\n [0, 0, -32, 14, -30, 8, -31, 21, 13, 33, -8, 3],\n [0, 0, 0, 33, 18, 1, -... | 14763 | 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[[-8, 4, 6, 7, 0, 14, -4, 4, -25, -5, 10, -7],\n [4, 15, 18, -3, 25, -16, -13, -4, -10, 5, -10, 7],\n [6, 18, -21, -28, -6, -18, 6, 6, -10, 2, 6,... | 225 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (4, 10) of the inverse. Round your answer to the nearest integer:\n[[-27, -32, -13, -18, 16, -10, -14, -1, -21, 17, -26, 31],\n [-32, -29, -9, -24, 26, -12, 28, -20, 18, 18, -28, -14],\n [-13, -9, -34, -30, -26, 4, 16, ... | -52 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 8) of the inverse. Round your answer to the nearest integer:\n[[18, -28, -26, -15, -1, -32, 17, -11, -16, 35, 35, -14],\n [0, -30, 15, -9, -18, -24, -8, -17, 7, -21, 33, 0],\n [0, 0, -6, 3, 10, 22, -6, 20, 18, 1, -1... | 112 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 20, 34, -6, 19, -8, 15, -9, 16, -2, -4, 8],\n [-32, 12, -20, 24, 11, -21, 20, -20, -35, -11, 28, 7],\n [-22, 12, 32, -22, -21, -19, 16, -26, -19, -... | 38 | 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[[-30, 16, -10, -14, -16, -20, 21, -4, -16, -12, 17, 4],\n [16, -27, 3, -17, -16, -2, 14, 6, 22, 28, 22, -4],\n [-10, 3, -14, -12, 26, 4, 0, 16, 30, -12, 0, -6],\n [-14, -17, -12, -27, ... | -35 | 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, 2, -18, -34, 18, -6, -32, -29, 21, -6, 8, -7],\n [0, 12, -17, 27, -34, -22, -1, -15, -19, -4, -13, -30],\n [0, 0, 34, -32... | -92651 | 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, -17, 34, -8, -14, -8, -3, 9, 12, 27, -10, -35],\n [26, -33, -31, 9, -24, 12, -22, 17, 9, -4, -6, -24],\... | 84 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-15, 22, -20, 17, -18, 21, 2, -4, -17, 12, -10, 9],\n [9, -21, -18, -5, -21, -21, 29, 10, -20, 19, -6, 5],\n [31, -19, -10, 28, 22, -33, -8, -32, 4, 21, 29, 11],\n [-2, 9, -4, 8, -25, 0, -23, 21, -11, 34... | 2609 | MATH |
[
{
"content": "Find the value at position (9, 12) of the inverse of matrix 1/839 * A where A =\n[[18, 32, 13, -30, -3, -31, -18, -33, -34, 29, -1, 15],\n [0, -1, 8, -7, 0, 6, -29, -23, -14, 21, 9, 18],\n [0, 0, -2, 8, 33, 17, 26, -3, 33, -35, -1, -11],\n [0, 0, 0, -16, 4, 31, -21, -8, -1, -29, 18, 6],\n [0, 0, 0... | -1521 | 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[[-6, -25, -10, 2, -6, -24, -6, 2, 8, 13, -10, 4],\n [-25, 21, -18, -10, -30, 1, -20, -20, 18, -2, -6, -6],\n [-10, -18, -20, -5, 20, -12, 20, -10, 2, 2, 22, 2],\n [2, -10, -5, 26... | -37 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (7, 2) of the inverse. Round your answer to the nearest integer:\n[[-16, -31, 5, -23, -33, -21, 20, 7, 31, 10, 12, 0],\n [0, 19, 19, 18, 29, 15, -4, -16, 0, -4, 21, -7],\n [0, 0, 16, -21, 15, -5, -20, 0, 3, -25, -16, 20... | 0 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (12, 4) rounded to the nearest integer?\n[[-22, 32, 30, 23, -21, -5, -7, 11, 21, 22, -5, 17],\n [0, -34, 24, 12, 12, 25, -32, -10, -14, 7, -16, 12],\n [0, 0, 25, 27, -17, -23, -34, 15, -35, 5, -26, -33],\n [0, 0, 0, 3, ... | 0 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-33, -2, 18, 4, -2, 2, -13, 16, 12, 13, -11, -6],\n [-2, -4, -26, -24, 14, -13, -3, -3, 14, -22, -8, 2],\n [18, -26, -34, 0, 16, 18, -26, -24, -12, 23, 2, -11],\n [... | 1738 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 6, -17, 4, 18, -4, 0, 0, 12, -20, -14, 10],\n [6, 17, -2, -17, 16, 5, -15, -18, 19, -8, -11, 10],\n [-17, -2, -13, 0, -4, 15, 22, 12, -22, 8, -14, -... | 58 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-20, 34, -23, 12, 4, 22, -28, -11, 16, -13, 3, -2],\n [34, -25, 20, 2, 0, 22, -8, -12, -12, -18, -8, -2],\n [-23, 20, 12, 10, -8, -5, 11, -26, -24, -14, -4, 3],\n [12, 2, 10, -21, -22, 20, -18, -30, 10, 11, 0, 16],\n [4, 0... | -79 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[27, -22, -3, -14, 8, 6, 22, -9, -4, 19, 4, -6],\n [-22, -3, -4, -16, 12, -13, -3, 11, -8, 9, -24, -19],\n [-3, -4, 18, -2, -12, 3, 23, 17, -2, -10, 18, 20],\n [-14, -16, -2, -24, 2, -8, 18, -3, -4, -1, 0, -13... | 520 | MATH |
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