messages listlengths 1 1 | ground_truth stringlengths 1 9 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-7, -18, -9, 6, 30, -10, -13, -31, -25, -17, -24, -34],\n [0, -14, -10, -3, -12, 33, -15, 10, -18, -31, -28, 21],\n [0, 0, 30, 1, -7, 33, -4, 12, -34, 33, 15, -1],\n [0, 0, 0, -19, 9, -35, -33, 34, 16, 17, -33, 11],\n [0, ... | -66363 | 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, 16, -22, -28, -1, -18, 19, 16, 13, -28, 1, 30],\n [0, -9, -16, 2, -24, 6, 14, -5, 29, 17, 4, 3],\n [0, 0, 4, -6, -34, -8, 11, -4, -4, -9, 18, 20],\n... | 88367 | 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[[-29, -21, 31, -18, 2, -10, 2, 23, 16, -3, -15, -19],\n [0, 23, -34, 28, -11, 5, -17, 2, -11, 3, -32, -33],\n [0, 0, -9, -35, 8, 16, -11, 2... | 71609 | 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, 23, 4, -18, 15, 25, -13, 0, 2, 20, 3, 33],\n [0, -15, 26, -13, -15, -20, 26, 29, -31, 10, 28, 5],\n [0, 0, 32, 15, 18, 32, 6, 10, -11,... | 23909 | 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[[6, 6, -7, -20, 31, 24, -32, -20, 5, -30, 6, 21],\n [0, -13, 6, -24, 28, 22, 15, -7, -17, 9, 18, 30],\n [0, 0, -24, 35, -22, 6, 12, -12, 29, -19... | 118 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-6, 4, 23, 27, 12, 32, -29, 11, 7, -20, -14, 27],\n [0, 9, 5, -11, 14, 31, 16, -5, 1, -14, -9, -34],\n [0, 0, -19, 20, -5, 7, 17, -31, -34, 23, -32, -2],\n [0, 0, 0, 11, -31, 25, 20, -1, -23, -10, 28, -25],\n [0, 0, 0, 0, ... | -187275 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-16, -9, 22, 8, 29, 10, 18, 3, -29, 18, 7, -16],\n [0, 7, -9, -11, 0, 30, -27, 17, -15, 14, -20, 30],\n [0, 0, -7, 10, 35, 13, -21, -19, -27, -4, 30, 23],\n [0, 0, 0, -6, -25, -10, -34, -2, ... | 9756 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 6) of the inverse. Round your answer to the nearest integer:\n[[23, -33, 3, 15, -28, 10, 30, -30, 22, 5, 18, 5],\n [12, 34, -9, 11, -13, -22, 25, 31, -11, 29, -12, 17],\n [14, -35, 3, 8, -31, 32, 29, -21, 14, -30, ... | 11 | 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[[-28, 4, -24, 13, 8, 11, -16, -14, 14, -2, -3, 0],\n [4, -23, 4, 0, -16, 14, 0, 6, 4, -2, 30, -17],\n [-24, 4, 33, -9, -30, -2... | 197 | 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[[-25, -16, -26, -16, -8, 4, 14, 32, 6, 0, -2, 4],\n [-16, 0, 16, 9, -5, 16, 7, 20, -10, 4, 6, 1],\n [-26, 16, -2, 15, -10, -16, 6, -24, 11, -9, -16, 13],\n [-16, 9, 15, -... | -362 | 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[[-2, 31, -32, 8, -21, -28, -31, 30, 10, 29, 30, -10],\n [0, 15, 5, 15, -17, -33, 2, 34, 9, 35, 5, -11],\n [0, 0, 18, -23, 4, -15, 5, 25, -3, -7, 19, -4],\n [0, 0, 0,... | 3249090 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 5) rounded to the nearest integer?\n[[14, -28, -24, 15, 30, 5, -14, -27, -25, -23, 20, -8],\n [28, 28, 34, 19, 1, -3, -11, -13, 24, 20, 27, -28],\n [-19, 21, 26, -25, 31, 4, 4, 20, 17, -8, 6, 10],\n [-18, -13, -10,... | -33 | 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, 0, 19, -2, 28, -9, 22, 20, 0, -20, -17, -5],\n [0, 24, -24, 3, -8, -4, 18, -19, 2, 12, 8, 18],\n [19, -24, 15, -12, -12, -12, 24, -1, 15, -2, 28, 8],\n [-2, 3, -12, -34, -23, 17, 4, -10, ... | 51 | 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, 12, -26, -30, 18, 15, -15, -14, -14, -8, 14, 4],\n [12, 6, 6, 10, 6, -4, 20, -1, 14, -11, 7, 7],\n [-26, 6, 0, -18, 28, -16, -8, 0, 4... | 2883 | 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[[-30, -10, 14, -15, 8, 20, 4, -14, -10, 1, 10, 0],\n [-10, -34, 8, -3, 0, -8, -16, 1, 5, -... | -85 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (10, 11) rounded to the nearest integer?\n[[-23, -2, 4, 18, 7, 22, -22, 0, -30, 14, 8, -7],\n [-2, 16, 12, 6, 7, -10, -18, 2, -16, -14, 9, -14],\n [4, 12, -32, -14, -21, 22, -6, -16, 6, -4, 0, -12],\n [18, 6, -14, -26, ... | 33 | 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, 12, -5, 12, -13, -2, 2, -4, 0, -10, -4, -6],\n [12, 15, 19, -1, 10, -28, 3, -9, 14, -4, 16, 24],\n [-5, 19, -26, 0, 19, -8, 3, 4, -6, 28, 3, 21],\n [12, -1, 0, 13, -4, 4, 7, -6, -... | 43 | 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, 8, -8, -12, 14, 27, 23, 24, 6, 26, -26, -14],\n [8, 16, -10, 33, 11, 22, 21, 9, 24, 16, -2, -19],\n [-8, -10, 11, 16, 4, 13, 10, -22, -6, 10, -18, 9],\n [-12, 3... | 4831 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[15, 25, -5, -4, 9, -9, -14, -21, -28, 32, -28, -20],\n [12, -2, 21, -31, 8, 35, 1, -8, 32, 2, 10, -10],\n [17, 27, 27, 2, -21, -27, -14, 34, 20, 1, 21, 24],\n [-24, -29, 30, 5, -12, -11, 26, 8, -34, 6, -3, -1... | -45 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[19, -31, 18, 6, -4, -10, 8, -11, 14, 6, 16, 18],\n [-31, -24, -16, -14, 14, -12, -1, 18, -8, 2, 10, -28],\n [18, -16, 15, 9, -12, -34, -31, -21, -22, -5, 32, 20],\n [6, -14, 9, 21, -1, -26, 22, 12, 14, 14, -2... | 526 | 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[[-7, 7, 17, -30, -12, -22, 16, 34, -32, 22, 1, 12],\n [0, 30, -23, 30, 24, 5, -4, 16, -31, 31, 30, 16],\n [0, 0, 2, 34, -2... | -52187 | 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[[-6, 24, -6, 2, 29, 11, 3, 13, 22, -19, -30, -21],\n [31, -8, 8, -18, -4, 33, 8, 34, 27, 22, 11, -19],\n [3, 23, -29, 27, 21, -2, 17, 30, 12, 24, 7, -32],\n [16, -4,... | 3600 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 12) rounded to the nearest integer?\n[[15, 3, 26, -2, -3, 16, -12, -22, 12, 4, 5, 4],\n [3, -19, 12, 0, 14, -30, 5, -5, 17, 12, 6, -11],\n [26, 12, -4, -17, 7, 10, 5, -1, 8, -4, -2, -6],\n [-2, 0, -17, -32, -5, 3, 3... | -6 | 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[[-12, -4, 11, -20, -15, 31, -5, -22, -30, 33, -7, 19],\n [0, 23, 0, 23, 28, 7, 6, 24, 26, 28, 22, -34],\n [0, 0, 20, 0, 33, -23, 3, -30, -17, -11, -33, ... | -230001 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[23, 32, 7, -24, 17, -22, 16, 25, 5, -15, 12, 20],\n [-1, 8, 3, -21, -24, -28, 31, -35, 6, -5, -6, 7],\n [-10, -24, 23, 33, -25, 11, -13, 7, 3, 19, -18, 6],\n [-10, -18, 5, 6, -3, 7, -22, 19, 22, -26, -8, -22],\n [-10, -19,... | -410 | 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[[28, 19, 27, -18, 25, -16, 29, 28, 28, -23, 32, 34],\n [21, 9, 2, 18, 0, 31, -25, -9, -19,... | 57 | MATH |
[
{
"content": "Find the value at position (6, 8) of the inverse of matrix 1/839 * A where A =\n[[19, 11, -14, 21, 6, -2, 24, -2, 12, 3, -2, 17],\n [11, -35, 20, -1, -8, 24, -30, -16, 7, 16, -12, -2],\n [-14, 20, -30, -3, -4, 5, -4, 2, -22, -4, 11, 8],\n [21, -1, -3, 26, -14, 29, 4, -18, 26, 18, 22, 22],\n [6, -8... | -4 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (6, 6) rounded to the nearest integer?\n[[29, 0, -7, 14, 2, -18, -15, -4, 0, -16, 2, 13],\n [0, -31, -12, 3, 1, 16, 4, 27, 1, 7, -12, 21],\n [-7, -12, 3, 15, -2, -6, 6, 9, 21, 6, 12, -10],\n [14, 3, 15, 17, -12, 6, 12, ... | 10 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-26, 6, -20, -33, -12, 4, 12, 22, 2, 10, 24, 0],\n [6, -25, -14, 22, 28, 4, 7, 0, 4, -6, 14, 10],\n [-20, -14, -13, -22, -11, -7, 2, -12, -22, 10, 6, 6],\n [-33, 22, -22, -19, -25, -2, -5, -19, -4, 0, 4, 14],... | -61 | 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, 31, 7, 5, -23, -32, -13, 34, -2, 5, -18, -3],\n [-11, 16, -19, 15, -33, 19, 20, -1, 32, 23, 23, -23],\n [26, 11, -33,... | -133 | 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[[-21, 0, 0, 15, -19, 5, 14, 10, -4, -28, -3, 4],\n [0, 7, 16, 12, -5, -18, 25, 20, 2, 22, 26, -14],\n [0, 16, 6, -18, 7, 0... | -317 | 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[[-30, -17, -7, 28, -22, -6, 35, -15, 29, -32, 10, -28],\n [-18, 24, 9, -5, -8, 28, 1, 31, 32, -1, 0, 21],\n [34, -32, 13, 3, -18, 24, -26, -13, 32, 23, -29, -23],\n ... | 788 | MATH |
[
{
"content": "Find the value at position (9, 10) of the inverse of matrix 1/839 * A where A =\n[[-9, 0, 5, 6, -24, -14, 9, -16, 14, 3, -14, 2],\n [0, 21, 6, 25, 0, -15, 2, 9, -28, -20, 6, -2],\n [5, 6, 24, 3, -10, -28, 2, -18, -4, -31, 0, 13],\n [6, 25, 3, 11, -4, 16, 1, 2, -16, 18, 12, 12],\n [-24, 0, -10, -4,... | -9 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-11, 14, 9, -6, 12, 15, 19, 19, 10, -5, -2, 32],\n [-3, 20, 22, 21, -19, -25, 35, -19, -26, -10, -30, -20],\n [-32, 26, 28, 20, -13, -3, -5, -29, -31, 1, -35, 34],\n [9, 11, 32, -6, 24, -12, -5, -8, 9, -... | 31884 | 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[[6, 35, 9, -34, 31, 7, -18, 3, -30, 6, 16, -9],\n [-21, -17, 26, 28, 15, 11, 21, -16, -16, 28, 2, 2],\n [29,... | 34 | 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[[-34, -2, 23, 18, 20, -1, 2, 21, -20, 2, 13, 16],\n [-2, -19, 9, 12, 2, -22, -26, -24, 25, 6, -27, 18],\n [23, 9, -10, -18... | -233 | 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, 4, -10, -22, -17, 10, 8, -12, -12, -24, -23, 26],\n [4, -16, -6, 0, 3, -12, -4, -20, 21, 1, 2, -18],\n [-10, -6, -7, 0, 25, 26, 11, 18, 0, -3, 10, 26],\n... | -103 | 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, 9, -16, 7, 14, 7, -12, 24, -4, -31, -34, -10],\n [0, 14, 3, -25, 27, 32, -18, -8, 6, 24, -14, 4],\n [0... | 317 | 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[[5, -20, 23, -27, 33, -26, -29, 30, -16, 27, -32, -8],\n [0, -34, 5, -8, -35, -9, 31, 3, 4, -8, -12, 15],\n [0, 0, 16, -30, 23... | -231394 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 8) rounded to the nearest integer?\n[[23, 18, 30, -6, -13, -27, 19, -35, 20, 3, -18, 6],\n [29, -3, -6, -31, 14, 29, -26, 24, -9, -8, 9, 16],\n [30, 26, 24, 4, -21, -29, 3, 15, -29, -24, -22, -2],\n [3, 28, -24, -2,... | 79 | 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, -29, 34, 4, 12, -6, 32, 0, -3, 8, -7, -3],\n [-29, -18, 12, -2, 12, -10, 16, 14, 25, -10, -2, 24],\n [... | -458 | 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[[-5, 0, -4, 27, -10, 29, -34, 34, 9, -11, 4, -18],\n [-24, -12, 7, -4, 11, 9, -1, -27, -26, 29, 23, 21],\n [-26, -17, 14, 32, -31, -7, -31, 24, 29, -8, -35, -7],\n [15, 0... | 457 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, 34, -5, -34, 7, 5, 24, 10, 4, 23, 9, 6],\n [-15, -33, 30, -25, -12, 14, -15, -11, -32, 7, 11, -13],\n [24, -15, 30, 15, -21, 22, -10, 23, 9, 30, -1, 28],\n [-9, -5, -24, 9, -4, 18... | 93 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-35, 2, 12, 12, -8, 10, 0, -8, 2, 3, -4, 4],\n [2, -32, -2, 17, -11, 21, 5, -20, -15, 8, 14, -26],\n [12, -2, -34, 28, -30, 6, -2, 14, -9, -26, 10, -26],\n [... | -849 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[13, -1, -7, 5, -30, -26, -13, 10, -24, 19, -23, -29],\n [-24, 25, -11, -34, -10, 15, 33, 26, 3, -25, 28, 6],\n [-26, -17, -32, -33, -22, -26, -30, -5, -5, 12, -27, -10],\n [-34, -32, -30, -6, 19, -8, 25,... | 4326 | 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[[14, -2, 29, 9, -2, -28, 12, 0, 30, -25, 16, 0],\n [-5, -12, -15, -6, 28, 3, -35, 6, -31, -24, -7, -33],\n [25, 15, 0, -34, -7, 5, -7, 28, ... | 1756 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -24, 26, 4, -34, -11, -5, 11, 24, 5, 14, -13],\n [0, 35, -14, 20, -20, 22, 15, -30, -... | 11259 | 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, 10, 22, 20, -24, -11, -20, 15, 17, 16, 31, -12],\n [0, -14, -5, 22, 33, -17, 17, -34, 17, 31, 11, 17],\n [0, 0, -1, -7, -19, 13, 20, -33, -14, -22, ... | -42571 | 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[[24, 7, -4, 20, 10, -30, 6, 26, -6, -14, 8, -9],\n [7, 11, -30, -2, 9, 12, -8, 8, -25, -18, 12, -32],\n [-4, -30, 8, 5, 8, -10, 6, -2, -14, -12, -3, -27],\n [20, -2, 5, -... | 38 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 1) of the inverse. Round your answer to the nearest integer:\n[[-25, -5, -2, 2, -6, 2, -16, -10, -12, -4, -4, -10],\n [-5, 30, -14, -30, 5, 16, -16, 27, -2, 8, -26, -16],\n [-2, -14, -2, 4, -16, -12, 28, 4, 5, -18,... | -43 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[0, -1, 10, 9, 20, -31, 8, -8, 6, -5, -29, -29],\n [-32, -4, -8, 20, -32, -28, -22, -6, -33, -34, -26, 34],\n [35, -20, 34, -14, -1, 13, -34, 30, -17, 33, -32, 5],\n [20, 19, -5, -14, 12, -32, -15, 5, 9, ... | 52807 | 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[[35, 9, 11, 1, -28, -31, -13, -26, -9, -35, 35, -28],\n [0, -8, -2, 7, -8, 13, 25, 1, -33, -27, -34, -13],\n [0, 0, -11, -... | 485142 | 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, 17, 17, -19, 29, 22, 1, 6, 34, 4, -13, -13],\n [13, -29, 1, -20, 2, 4, -7, -19, -16, -11, 24, 2],\n [27, 3, 28, -15, -4, -8, -24, -13, ... | 3349 | 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[[-23, -7, 35, 11, -10, 34, -13, 20, -17, 14, -1, 13],\n [10, 34, 17, -5, -14, 31, -28, -17, -5, -4, 19, -5],\n [31, 15, -9, 12, 7, 15, 33, 35, 14, 25, 5, 15],\n [-12, -6, 16, 14, 21, 2... | 145 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 5) of the inverse. Round your answer to the nearest integer:\n[[24, -3, 9, -6, -9, -20, -14, -4, -27, 0, 14, -2],\n [-3, 17, -13, 10, 14, 14, -4, 10, 3, -14, 24, 4],\n [9, -13, 3, -14, -6, -25, -18, 20, -8, 13, 2, 1... | -4 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-12, -7, -30, 22, 21, -33, -12, -17, -27, -6, 8, 17],\n [32, 24, -13, 25, -29, 8, 19, 3, 23, -31, 6, -22],\n [-9, -20, -34, -17, -13, 5, -22, 11, 27, -28, -9, 4],\n [-8, 32, 25, 2, -12, -8, 5, -18, 13, -10, -... | 4 | 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, 24, -11, -14, 7, 35, 34, 0, 10, -14, -1, 11],\n [0, -23, 20, 31, -23, 14, 21, -8, 29, -12, 31, -29],\n [0, 0, -21, 20, -1... | 20025 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-32, 7, -22, 31, -29, -28, 8, 28, -29, 12, 26, -11],\n [0, 28, -18, -32, -19, 11, 9, 22, -33, -24, -19, -14],\n [0, 0, -20, 15, -7, 35, 5, 21, -8, -15, -32, -21],\n [0, 0, 0, -18, -15, -28, 23, -16, 31, ... | 26353 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 4) rounded to the nearest integer?\n[[-2, 22, -29, -11, 21, -24, -5, -9, -2, -2, 1, 22],\n [0, -10, 9, 9, -4, 33, 35, -13, 29, 3, 31, 9],\n [0, 0, 34, 18, -9, 0, -31, 31, 15, -4, -15, -19],\n [0, 0, 0, 23, -26, -31... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 11) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -27, -5, -34, -12, 7, 34, 7, 15, 10, -35, 31],\n [-35, 27, 26, 25, 4, -7, -1, -25, -25, 27, 33, 20],\n [-29, 15... | 8 | 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, 34, -12, 25, 26, 4, 8, -6, 22, -4, 7, -16],\n [34, -15, 29, -5, 24, 14, -27, -25, -2, -10, 10, -18],\n [-12, 29, 22, -10, 12, -15, 14, ... | 1791 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[32, 8, 24, -35, -17, -3, 0, -12, -11, -25, -27, -30],\n [22, -7, -25, -13, -10, -35, 11, 5, -13, -31, 14, -27],\n [-32, 35, 29, 21, -11, 22, -30, -22, 27, 29, 16, 29],\n [-28, -28, -22, -12, 28, -11, -30... | 1286 | 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[[15, 20, 35, 15, -28, -23, -4, -2, -18, 19, 7, -12],\n [0, -18, -22, 17, -17, 21, 28, -34, 21, -2, 13, 18],\n [0, 0, -1, -7, -30, 1, 22, 28, -5, 14, 24,... | -1911 | 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[[32, 10, 0, 22, 1, -2, 14, 27, 4, 6, -24, 8],\n [10, 29, -4, 5, -4, 2, -3, 18, 0, -4, 20, -16],\n [0, -4, -28, -6, 4, -4, -3, 20, -16, -7, 2, -29],\n [22, 5, -6, 12, -11,... | 83 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (9, 8) rounded to the nearest integer?\n[[-20, -18, 30, 11, 4, -14, -2, 11, 7, 5, -13, -20],\n [-18, 11, -21, -5, 10, 19, -26, 14, 10, 6, -16, -18],\n [30, -21, -25, 6, -1, 8, -28, 22, 20, 0, 12, 1],\n [11, -5, 6, -31, ... | -11 | MATH |
[
{
"content": "Find the value at position (1, 7) of the inverse of matrix 1/839 * A where A =\n[[10, 27, 0, 10, 1, -18, 7, -7, -18, -21, 23, -8],\n [17, -21, 7, -3, -34, 23, -28, -3, -1, -18, -15, 28],\n [-8, 9, -16, -32, 0, 16, 3, 35, -24, 19, 12, -27],\n [-24, 33, 21, -8, -19, -14, -1, 23, -17, 14, -10, 24],\n... | 15 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[25, -11, 18, -19, 12, -24, 25, -34, 29, 16, -2, 9],\n [0, 16, 31, 20, 22, 14, -11, -24, 29, 20, 14, -8],\n [0, 0, 28, 18, 0, 8, 8, 33, 17, -23,... | 204 | 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[[32, -22, -27, -20, -23, 0, 8, -22, -19, 29, 18, -34],\n [-19, -13, -35, -24, -23, -24, 21, -18, -21, 3, 33, -3],\n [12, -31, -28, -17, 16,... | 4758 | 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[[33, 16, -2, 12, -12, -23, 14, 29, 35, -32, 28, 3],\n [0, 22, -20, 26, -26, 26, -3, 35, 6, 8, 10, -5],\n [0, 0, -30, 14, -8, -12, 33, -8, 22, 31... | -949 | 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, 9, -27, 15, -22, 33, 20, -25, -6, 3, -12, 22],\n [-6, -12, 31, -7, 6, 26, -9, -7, 30, 21, 25, -7],\n [21, 19, 8, -8, 1, -13, 33, 22, -4, 33, 0, -4]... | -64 | 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, 1, -19, -8, 13, 20, 7, -5, 0, -26, 1, 20],\n [1, 19, -5, 22, 2, -2, 24, 2, -29, -12, 6, 19],\n [-19, -5, -13, -20, -2, 22, 18, 0, -16, 2, -17, 11],\n [-8, 22, -2... | 1143 | 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, 21, -32, 35, 33, 32, 14, 31, 32, 23, 27, 31],\n [0, -35, 32, -18, -24, 2, 6, 0, -20, 29, 31, 3],\n [0, 0, -20, -25, -8, -... | 1021260 | 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, -14, -26, 30, 2, 0, -20, 8, -4, 32, -22, -4],\n [-14, -10, 1, 0, -22, 12, -9, 0, 19, -10, 2, -20],\n [-26, 1, -31, 26, -10, -4, 10, -11, -12, 6, -4, -18],\n [30, 0,... | -64 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-2, 18, -8, 0, 19, -12, -25, -5, -15, -4, 20, -12],\n [18, -19, 21, -4, 2, -6, 9, 16, -1, -6, -9, 24],\n [-8, 21, 2, -8, 15, -7, -26, -23, -5, ... | -489 | 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, 27, -21, 4, 2, 19, 8, 30, 30, 7, 2, -7],\n [20, -30, -27, -14, 10, -5, -15, 2, 16, -17, -26, 10],\n [30, 2, 26, 10, -1, 7, -6, 27, -6, -7, 30, -14],\n [-1, 6, -12, ... | -43 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-35, -17, 3, -9, 20, -20, -29, -16, -5, -11, -35, -19],\n [0, -12, 26, 16, 15, 30, 21, 19, 17, -17, -23, -7],\n [0, 0, -12, -30, 12, -16, 31, 19, -18, -15, 28, 1],\n [0, 0, 0, -18, -6, 20, 6... | 2730 | 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, 5, -19, -4, -31, -27, -2, -35, 4, 18, -4, 14],\n [0, 26, -25, -13, -10, 27, 10, 33, -30, 15, 7, 6],\n [0, 0, -34, -22, -... | -14777 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-4, -4, 2, 26, 7, 16, -8, -24, -16, -6, 32, -14],\n [-4, 34, 28, -8, -10, -1, -18, 10, 20, 0, 17, 12],\n [2, 28, 30, 14, 1, 4, -8, -10, -12, -14, -21, 3],\n [26, -8, 14, -27, 22, -17, -32, -4, -30, -19, -6, -32],\n [7, -10... | -67559 | 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[[-11, 18, -12, 22, -2, 6, 18, -14, 4, -18, 22, 9],\n [18, 21, -6, -4, -24, 2, -21, -11, -2, 4, -16, -14],\n [-12, -6, 19, 12, 18, 6, 4, -8, -18,... | -170 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value at position (1, 11) rounded to the nearest integer?\n[[-14, 10, -24, -4, -10, 10, 16, 6, 18, 20, 0, -8],\n [10, -24, 12, 6, -6, 18, 4, 20, 27, -8, -10, 12],\n [-24, 12, -19, 4, 16, 12, 2, 17, 18, 0, 12, -17],\n [-4, 6, 4, 6, -16, 1... | 19 | 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[[-17, -14, 6, -10, 10, -10, -20, 10, -34, -7, -14, -12],\n [-14, 21, -4, -2, 16, 8, -2, -4, -4, -18, 20, -34],\n [6, -4, -... | 66 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, -15, -8, -17, -22, -12, -16, -4, 16, 29, 16, 22],\n [0, 34, -21, 11, -26, -15, -17, 32, -14, 27, 2, -21],\n [0, 0, -6, -12, 10, -32, -30, 2, -10, -17, -34, 32],\n [... | -1354 | MATH |
[
{
"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[17, -31, 31, -16, 15, 10, 31, -33, -13, -27, -25, 11],\n [0, 8, -23, -28, 27, -14, 2, -9, -10, -13, 29, 11],\n [0, 0, -32, -5... | -1858055 | 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[[29, -10, 24, -18, 23, -15, 10, -24, -4, 3, 19, 19],\n [-26, -1, -30, 32, 26, -27, -7, 35, -30, 8, 28, 31],\... | 70 | 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[[12, 6, 2, -20, -9, 23, -15, 8, -8, -14, -4, 0],\n [6, 11, -22, -14, 4, 2, 9, 0, 2, 19, 2, -1],\n [2, -22, 15, 2, 7, -12, 10, -4, -10, 4, -9, -10],\n [-... | -185 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 7, -15, 12, 30, -20, 4, -15, 16, -28, 19, 22],\n [-31, 6, -6, -27, 5, 15, 21, 25, -30, -10, -30, 17],\n [25, -3, 9, ... | 11 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[35, 35, 10, 11, 33, -22, 9, 16, 14, 29, 28, -13],\n [0, 34, 23, 18, 35, -10, 8, -23, 18, 4, -32, 17],\n [0, 0, 19, 30, -18, -7, 17, -3, -33, -16, -32, -28],\n [0, 0, 0, -2, 35, 13, 13, -9, 29, -3, 13, 27... | 38417 | 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[[3, 14, -3, -8, 20, -11, -22, 19, -29, -32, -6, 26],\n [0, 1, 19, 29, 16, -33, -29, 34, 34, -2, -20, -28],\n [0, 0, 14, -30, -21, -25, -9, 9, 2, -32, 9, -26],\n [0, 0, 0, 20, 4, 1, 30,... | 1562 | 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, 29, -15, -10, -1, 22, 6, -7, -7, -27, -34, -34],\n [-18, 33, 21, 35, -13, -17, -17, 22, 13, 9, -8, 14],\n [-25, 19, -27, -22, -15, 12... | 1550 | 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, 0, -10, -6, -4, 11, 2, 34, -16, 7, 32, -1],\n [0, -19, 22, -20, 15, -8, 4, 11, 10, -19, 6, 16],\n [-10, 22, 15, 26, 22... | 45 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-2, -5, 25, -4, 28, -4, 5, 30, -19, 34, -3, 10],\n [-5, 12, -29, 8, -4, -2, -4, 5, 8, 12, 30, 29],\n [25, -29, -4, 15, -1, -4, -16, -2, 11, -14, 16, 26],\n [-4, 8, 15, 19, -3, -12, -10, 9, 8, -6, 4, 0],\n [28... | 271 | 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, 30, -30, 20, -2, 6, -6, 7, 24, -22, -20, 12],\n [30, 18, 12, 7, -8, -2, -8, 22, -16, 16, -24, 20],\n [-30, 12, -28, 16, 24, -4, 0, 16, -16, 6, -12,... | -47 | 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[[9, -20, -17, 1, 25, -10, 28, -23, -2, -13, -16, 18],\n [22, 23, -16, 3, -4, 5, 33, 32, -1... | -55 | 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[[-15, -22, 27, -8, 22, -12, 32, 21, 1, -30, -14, -10],\n [-22, 30, -7, 16, -4, 2, 21, -5, -15, -24, -7,... | 1816 | 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, 35, 12, 18, 0, -30, 35, -24, 23, 29, 14],\n [7, 7, 13, 19, 14, -15, -23, 6, -21, 14, -35, 15],\n [-2, 6, 26, -4, 25, 18, 22, -12, -9, -15, -18, 19],\n [32, 11, 18... | 44 | MATH |
[
{
"content": "Find the value at position (5, 1) of the inverse of matrix 1/839 * A where A =\n[[28, -17, 2, 2, 22, 13, 9, 14, -18, 4, 7, -8],\n [-17, -20, -20, -14, 17, -6, 2, -2, -16, 4, -30, -26],\n [2, -20, 29, -10, 16, 14, -10, -27, 0, -2, -25, -4],\n [2, -14, -10, -28, 3, -4, 2, -19, 18, 20, 10, 11],\n [22... | -15 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[28, 23, 26, -26, 28, 24, -16, 13, -9, 15, 21, 1],\n [0, -7, 32, 11, 33, -15, 6, -15, -34, 33, -29, -1],\n [0, 0, 10, 19, -35, 18, -35, 27, 19, -9, -21, -27],\n [0, 0, 0,... | -86 | MATH |
[
{
"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-19, 33, 21, -18, -20, 15, 4, 3, 20, 18, 8, 10],\n [-4, 12, 25, 30, 2, 7, -32, -31, 22, 1, -10, -27],\n [-21, -10, 27, 34, -9, 18, -5, -4, -34, -18, -8... | 33 | 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[[24, -8, 7, -20, 16, -12, -8, -12, -6, 4, -8, -8],\n [-8, -34, 19, -22, -1, 18, 0, 9, 5, 0, -30, -4],\n [7, 19, -33, 20, -8, 14, 24, -12, 24, 18, 2, 6],\n [-20, -22, 20, ... | 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[[6, -23, -6, 3, -28, 2, 14, -12, -14, -26, 21, 8],\n [-23, 0, -12, -2, -18, 28, 11, -14, 9, -13, -4, -7],\n ... | -30 | MATH |
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