messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, -4, -11, 2, 0, 4, -8],\n [0, 5, 17, 5, -16, 3, -17],\n [0, 0, -17, 2, 14, -7, 3],\n [0, 0, 0, -3, -4, -16, 18],\n [0, 0, 0, 0, -15, 6, -5],\n [0, 0, 0, 0... | 129 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, 10, -1, 7, 15, -9, 17],\n [0, 12, -4, -11, -5, 4, 2],\n [0, 0, 5, 7, 6, 10, -4],\n [0, 0, 0, -10, 5, -... | 41 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -18, 16, 18, -5, -16, -18],\n [-14, 7, -5, 8, -10, -4, -4],\n [7, -6, 13, 13, -15, 11, 18],\n [4, -4, 10, 17, -6, 13, -12],\n [3, 9, -... | 262 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[14, 5, -4, 13, 13, 5, -7],\n [0, -16, 18, -2, -17, -17, 9],\n [0, 0, 13, 14, -18, 0, -17],\n [0, 0, 0, 13, -15, -8, -2],\n [0, 0, 0, 0, 3, -8, -3],\n [0, 0, 0, 0, 0, -16, 1],\n ... | -133 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, 14, -1, -18, -8, 9, 6],\n [4, 12, 11, 16, -12, -3, 7],\n [-17, -18, -7, -14, 18, 13, -10],\n [16, 0, -3, -16, 1, 5, 14],\n [5, -8, -11, 17, 1, 16, 6],\n... | 61 | MATH |
[
{
"content": "Find the inverse of 1/252 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, -11, -12, -16, -2, 14, -7],\n [3, 3, 11, -11, 8, 8, 15],\n [2, 11, 14, 9, 14, -14, 0],\n [-15, 16, -2, 9, 11, 10, -13],\n [16, 18, 5, 1... | 351 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, -17, 7, -2, 14, -10, 10],\n [0, 16, 6, 5, -6, -12, 17],\n [0, 0, -11, -3, -5, -7, 4],\n [0, 0, 0, -17, 13, 4, 3],\n [0, 0, 0, 0, -4, 18, 14],\n [0, 0, 0, 0, 0, 1... | 1474 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[7, 18, 7, 4, -10, -7, -18],\n [-18, 15, 13, 6, -18, -3, -14],\n [3, 10, -16, -7, 7, -3, 18],\n [3, 10, -5, 9, -14, 11, -14],\n [-7, -3, 7, 7, 2, 17, 14],\n [11, 18, 4, -9, -14, 17, 15],\n [1... | 17 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 5, -3, -17, 9, 13, 8],\n [1, 5, -7, 16, 14, 14, 18],\n [-7, -16, -18, 14, -9, 10, -6],\n [-7, 12, -17, 16, 4, -2, 7],\n [-11, 10, 7, -9, 7, 15, -12],\n [-15, -8... | 764 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 4, 6, -2, 5, 11, 2],\n [4, 4, 4, 3, -2, -2, -4],\n [6, 4, -6, -6, 16, -6, 0],\n [-2, 3, -6, 9, -6, 12, ... | 149 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, -6, -10, 8, -17, -14, 10],\n [18, 0, -11, -18, 3, -2, -12],\n [6, -15, 17, -13, 12, 0, 8],\n [-9, 7, 0, -16, -6, 9, 1],\n [9, -11, -18, -1... | 4 | MATH |
[
{
"content": "Find the inverse of 1/252 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[[-4, 12, -18, -16, -3, 4, -8],\n [-7, -9, 13, -3, -11, -7, 5],\n [9, -11, 9, 17, 7, -11, 9],\n [9, 18, 17, 8, -2, -10, 14],\n ... | -32 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[6, -8, -3, -3, 0, 11, 14],\n [-8, 2, -14, 4, -10, 0, 5],\n [-3, -14, 4, 10, 16, -12, -2],\n [-3, 4, 10, -5, 2, -12, -5],\n [0, -10, 16, 2, 9, -3, 4],\n [11, 0, -12, -12, -3, -14, 6],\n [14, 5, -2, -5, 4, 6, -... | 75 | MATH |
[
{
"content": "Find the inverse of 1/252 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, -8, 15, 15, -1, 11, -4],\n [8, 15, 14, 5, -4, 11, -2],\n [-14, 10, -15, -9, -2, -9, -2],\n [1, 5, -14, 15, -13, -17, -6]... | -56 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[3, 8, -1, -11, -4, -4, 2],\n [8, -5, 2, 6, -14, 12, 3],\n [-1, 2, 7, 6, -6, -8, 12],\n [-11, 6, 6, 7, 2, 5, 0],\n [-4, -14, -6, 2, -12, 1, 1],\n [-4, 12, -8, 5, 1, 9, -8],\n [2, 3, 12, 0, 1, -8, 1]]\nRound your answer to t... | -71 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -15, -9, -16, -1, 17, 3],\n [0, -11, 0, 18, -13, 7, 15],\n [0, 0, 14, 3, 2, -13, -13],\n [0, 0, 0, 11, 12, 5, -1... | 0 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-13, 7, -15, 0, 1, 14, 1],\n [0, -18, 7, -5, 18, -8, 17],\n [0, 0, 14, -13, -9, -14, 4],\n [0, 0, 0, -17, 1, -18, 18],\n [0, 0, 0, 0, -4, 5, 16],\n [0, 0, 0,... | -852 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[14, -6, 12, 17, 5, -4, 10],\n [0, -14, 10, -15, -7, -17, 8],\n [0, 0, 17, 7, 8, -14, 1],\n [0, 0, 0, -11, 4, 7, -7],\n [0, 0, 0, 0, 14, -7, 17],\n [0, 0, 0, 0, 0, 12, -10],\n [0, 0, 0, 0, 0, 0, 18]]\nRou... | 469 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, 7, 17, 4, -18, -4, 2],\n [-10, -10, -9, 7, 16, 6, 7],\n [-8, -17, -12, -1, 8, 15, 8],\n [-2, 5, 6, -12, -13, 5, 14],\n [10, 3, 7, 9, 2,... | 804 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, -3, -10, 2, -8, -4, 4],\n [-3, 9, 12, -3, -6, -11, 4],\n [-10, 12, -9, 2, 2, 15, 0],\n [2, -3, 2, -12, 0, 2, 0],\n [-8, -6, 2, 0, 18, -2, 8],\n [-4, -11, 15, 2, -2, ... | -15 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -13, -1, 2, 17, 15, -2],\n [0, 6, -7, 4, 3, 2, 8],\n [0, 0, 8, 15, -7, -12, -9],\n [0, 0, 0, 9, -17, -1... | 38 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[-10, -13, -2, -3, -2, 6, 12],\n [-13, 18, 1, 8, 0, 6, 10],\n [-2, 1, -7, -2, 2, -4, -4],\n [-3, 8, -2, 4, 1... | 97 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, -11, 4, 10, -1, 12, 11],\n [0, -1, -2, -5, 12, 5, 16],\n [0, 0, 18, 7, 4, -4, -15],\n [0, 0, 0, -6, -1, 14, -3],\n [0, 0, 0, 0, -6, -6, -1... | -447 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[-5, 11, -15, -1, 18, 6, -18],\n [0, -10, -4, 5, -15, -7, 18],\n [0, 0, 5, -8, -6, 15, 6],\n [0, 0, 0, ... | 8150 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[18, 15, -8, -16, 9, 10, -10],\n [-16, 6, 15, -7, -10, -4, 6],\n [-14, -8, 15, 5, -4, -11, -14],\n [7, -1, -13, 18, -6, 9, -14],\n [-6, -2, 13, 10, -16,... | -45 | MATH |
[
{
"content": "Find the value at position (2, 6) of the inverse of matrix 1/252 * A where A =\n[[12, 10, 2, 14, 13, -2, -4],\n [10, -17, -6, -10, 10, -3, -7],\n [2, -6, 8, -1, 4, 14, 2],\n [14, -10, -1, 11, 0, 4, 2],\n [13, 10, 4, 0, 18, -2, -8],\n [-2, -3, 14, 4, -2, 8, 0],\n [-4, -7, 2, 2, -8, 0, 7]]\nRound yo... | -5 | MATH |
[
{
"content": "Find the inverse of 1/252 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, -5, 10, -7, 17, 16, -7],\n [-12, 10, -8, 14, -13, -4, 13],\n [-8, 4, 7, 15, 15, 10, -15],\n [-2, 16, -6, -4, 10, 10, -8],\n [13, -17, ... | 403 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[15, 6, 1, 3, -3, -4, -2],\n [6, 8, -2, 1, 8, 2, 0],\n [1, -2, -12, -5, 0, 2, -2],\n [3, 1, -5, 11, -1, -12, -5],\n [-3, 8, 0, -1, -17, 4, -2],\n [-4, 2, 2, -12, 4, -1, 12],\n [-2, 0, -2, -5,... | -29 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, 3, 5, -2, -7, 13, -4],\n [-3, 3, 9, 1, 14, -9, 13],\n [14, -17, 14, 14, -6, 11, 14],\n [-6, 7, 3, -17, 7, -4, 15],\n [-8, -16, -13, -10, -13, -10, 12],\n [13, -7, -11, -11, 9, 1, -12],\n [-8, 1, -3, ... | 1225 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, -5, -8, -1, -7, 4, -7],\n [-6, 6, 0, 17, -11, 10, 13],\n [-1, -13, -1, 0, 3, 18, 13],\n [-16, 9, -9, 16, 10, -4, 14],\n [-12, -7, 11, 2, 12, 5, 1]... | -42 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[-7, -16, -1, 2, -4, 14, 16],\n [0, -11, 17, 11, 4, -5, -5],\n [0, 0, -14, -5, 6, 1, -17],... | -567 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[-18, 5, 14, 18, 16, -5, 2],\n [5, -4, -6, -6, 0, -14, -4],\n [14, -6, 7, 12, -4, 9, 1],\n [18, -6, 12,... | 8693 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-1, -2, 7, -11, -7, 8, -11],\n [0, -15, 14, -18, 0, 12, -3],\n [0, 0, 7, 9, -17, -13, -10],\n [0, 0, 0, -10, -6, 12, -8],\n [0, 0, 0, 0, -13, 15, -1],\n [0, 0, 0, 0, 0, 5, -12],... | 0 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[2, 0, 10, 6, 14, 13, 16],\n [0, -8, 16, -11, -5, -9, -17],\n [0, 0, 2, 7, -11, -17, -13],\n [0, 0, 0, 6, -7, -14, 15],\n [0, 0, 0, 0, 4, -13, 2],\n [0, 0, 0, 0, 0, -8, -4],\n [0, 0, 0, 0, 0,... | 2278 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-15, 8, 10, 9, 16, -11, -3],\n [17, 11, -1, -17, -6, -15, 7],\n [6, 11, -8, -12, 12, -9, -6],\n [12, -12, 17, 1, -15, -12, -18],\n [-6, 3, 2, 3, 9, -10, 7],\n [-10,... | 437 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 6, -1, 0, 17, -9, 14],\n [-14, 16, 15, 14, 2, -2, 3],\n [18, -4, 16, 9, -12, 13, -8],\n [-9, -10, -5, -6, 6, -17, 16],\n [-12, 2, -1, -16, -8, 5, 0],\n [... | 2388 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -14, 8, 13, 2, -11, -11],\n [-16, -16, 3, -13, -17, 4, -17],\n [-2, 16, 15, 4, 11, -11, 3],\n [17, -14, -6, 10, 12, -3, 11],\n [-3, -7, -2, -3, -7, -11, 1],\n ... | 467 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 13, 14, -3, -7, 15, -5],\n [0, 14, 4, -17, 2, -17, 8],\n [0, 0, -8, -16, 4, 7, -15],\n [0, 0, 0, 3, -4, 3, 18],\n [0, 0, 0, 0, 5, 11, -5],\n [0, 0, 0, 0, 0, -10, -4],\n [0, 0, 0,... | 1166 | MATH |
[
{
"content": "Find the value at position (4, 5) of the inverse of matrix 1/252 * A where A =\n[[-5, 8, 8, 3, 10, -4, 9],\n [8, 17, 0, -10, -4, -8, -15],\n [8, 0, 6, 0, 4, 1, 1],\n [3, -10, 0, -4, -2, 2, 14],\n [10, -4, 4, -2, -5, -8, -5],\n [-4, -8, 1, 2, -8, 4, 3],\n [9, -15, 1, 14, -5, 3, -17]]\nRound your an... | -64 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 12, -4, -10, 4, 0, -10],\n [0, 2, -10, 9, -12, -3, -3],\n [0, 0, -15, -2, 18, 10, 17],\n [0, 0, 0, 8, 9, 3, -5],\n [0, 0, 0, 0, -17, 8, 2],\n [0, 0, 0, 0... | -1586 | MATH |
[
{
"content": "Find the value at position (7, 3) of the inverse of matrix 1/252 * A where A =\n[[-2, 16, -8, 2, 7, -15, 15],\n [0, 16, 10, 10, 2, -6, -2],\n [0, 0, -17, 10, 14, -9, 2],\n [0, 0, 0, -11, 3, -11, -4],\n [0, 0, 0, 0, -14, 13, -18],\n [0, 0, 0, 0, 0, 4, -18],\n [0, 0, 0, 0, 0, 0, 2]]\nRound your answ... | 0 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, 17, -8, -4, 0, -12, 9],\n [-14, -14, 11, 13, -11, -9, 13],\n [9, -2, 12, -11, 6, -10, -17],\n [-4, -16, 17, -15, -5, 6, -9],\n [2, 17, -7, 8, -17, -6, 13],\n [12, -3... | 34 | MATH |
[
{
"content": "Find the inverse of 1/252 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, 11, 1, 2, 13, 2, 16],\n [13, 11, -7, -1, 2, -6, 2],\n [-11, -12, 4, 13, -8, 3, 3],\n [6, 3, 9, 10, -6, -1, -17],\n [10, 2,... | -79 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -18, -14, -16, -18, -15, 16],\n [0, 15, 6, -9, 2, 8, 8],\n [0, 0, -10, 17, 3, 7, -7],\n [0, 0, 0, 15, ... | 120 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-5, -16, 5, 18, -3, -15, 5],\n [0, 11, -1, 0, 12, 0, 0],\n [0, 0, -7, 11, 12, 17, 0],\n [0, 0, 0, -1, 9, -8, 14],\n [0, 0, 0, 0, 8, -4, -13],\n [0, 0, 0, 0, 0, -14, -9],\n [0, 0, 0, 0, 0, 0, 16]]\nRound your answer to the ... | 4367 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -14, 10, 18, 1, 2, -9],\n [0, 17, -13, 7, -15, 16, -18],\n [0, 0, -13, 12, 1, 5, 6],\n [0, 0, 0, 5, 11, 3, 9],\n... | 0 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -6, 0, -1, 8, 10, -9],\n [-6, 2, -4, -2, 8, -6, -9],\n [0, -4, 4, 0, 12, -4, 2],\n [-1, -2, 0, 14, 0, 2, -7],\n [8, 8, 12, 0, 9, -8, -... | 374 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -7, 5, -9, 16, 13, -12],\n [0, 1, 7, -15, 3, -4, 2],\n [0, 0, 9, -5, 8, 9, 7],\n [0, 0, 0, -11, 14, 16, -13],\n [0, 0, 0, 0, -8, -7, -9],\n [0, 0, 0, 0, 0, 2, -11],\n... | 421 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, -3, -16, -16, 8, 14, 9],\n [-18, -11, 18, 13, 18, -15, 11],\n [-13, 0, 13, -10, -7, -8, -3],\n [-18, 2, 11, -6, 15, -15, 9],\n [12, 8, -14, 6, -16, 14, -15],\n [6, 1, 15, 7, -14, 16, 9],\n [10, -10, -13, 0, -8, -17, -... | -75 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, 8, 16, -6, -8, -8, 8],\n [8, 7, 8, 0, 2, 8, -1],\n [16, 8, -1, 2, 10, -8, 0],\n [-6, 0, 2, -4, -4, 2, 15],\n [-8, 2, 10, -4, 16, 6, -9]... | 385 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[-2, -10, 16, -6, -4, -1, 14],\n [-13, 8, 4, 8, 15, -5, 17],\n [-11, 16, 0, 11, -5, 1, 6],\n [5, -5, 7, 4, 3, 0, -16],\n [0, -10, 9, 1, -12, -5, -10],\n [0, -5, 17, -2, 11, -10, ... | -10 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 9, -11, -17, 3, -3, 10],\n [11, -7, 16, -8, 2, 2, -14],\n [1, 18, -16, 14, -10, -10, -15],\n [16, -2, 15, 5, 1... | 4 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[-14, -11, 6, 8, 4, 11, 4],\n [0, -1, -1, -17, -15, 11, 14],\n [0, 0, 18, 0, 9, 1, 14],\n ... | -3606 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 5) rounded to the nearest integer?\n[[7, 14, 8, 2, 12, 2, 6],\n [14, 2, 6, 15, 2, 0, 2],\n [8, 6, -16, 0, -3, -6, -5],\n [2, 15, 0, 14, 12, 7, -1],\n [12, 2, -3, 12, -18, -4, 8],\n [2, 0, -6, 7, -4, 16, 2],\n [6, 2,... | -12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -15, -14, 11, 5, -16, -8],\n [-15, 7, 8, 8, -13, -4, 11],\n [18, 18, 18, 16, 4, -13, -15],\n [-1, -10, 10, -6, ... | -11 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[17, -2, 16, -1, 3, 5, 0],\n [0, 2, -11, 9, -14, -2, 18],\n [0, 0, 8, 15, -8, -7, 2],\n [0, 0, 0, -2, 1, -7, -13],\n [0, 0, 0, 0, -13, 17, -8],\n [0, 0, 0, 0, 0, -8, -2],... | 11 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, -11, -2, -2, 14, 13, -11],\n [0, -16, -14, -6, 12, -3, 13],\n [0, 0, 3, -16, -9, 2, -3],\n [0, 0, 0, 16, 11, 11, 16],\n [0, 0, 0, 0, 11, -12, -16],\n [0, 0, 0, 0, 0... | 34 | MATH |
[
{
"content": "Find the inverse of 1/252 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[[-8, 3, 14, 17, 4, 15, -10],\n [0, -11, -12, 17, -1, -16, 9],\n [0, 0, 9, -18, 17, 2, 16],\n [0, 0, 0, -6, 18, 5, -17],\n [0, ... | -2683 | MATH |
[
{
"content": "Find the inverse of 1/252 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, 8, 11, 15, 18, -13, -12],\n [13, 13, 6, 14, -12, -7, -3],\n [-3, 17, -6, -12, 17, -10, 13],\n [-8, -11, 14, 4, 6, -11, 3],\n [-15, -16... | 602 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, -1, 0, -10, -4, 9, 2],\n [-1, -8, -12, 2, -14, 12, 4],\n [0, -12, 5, 10, 5, -15, -4],\n [-10, 2, 10, 15, -2, 12, -2],\... | 79 | MATH |
[
{
"content": "Find the inverse of 1/252 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, -3, -15, 16, 7, -7, -8],\n [0, 6, -1, 0, 4, -1, 7],\n [0, 0, 10, 15, -2, -3, -17],\n [0, 0, 0, -11, 11, 13, 17],\n [0, 0, 0, 0, 5, 3,... | 1667 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, 8, 10, -16, -6, -9, 17],\n [-10, 8, 15, -18, 13, 6, 10],\n [-12, -16, 1, 1, 11, 16, 16],\n [8, 7, -5, -2, -1, 10, 1],... | 106 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-7, 7, 0, -12, -12, 7, -14],\n [2, -5, -15, 4, 1, -4, 10],\n [-11, 0, 9, 8, -15, -4, 16],\n [18, -18, -16, 5, 8, 17, 15],\n [10, 5, 5, -15, -16, 15, 4],\n [4, -14, 12, -13, 18, -9, -12],\n [2, 1, -16, 3, -15, 9, -7]]\nRoun... | -101 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[17, -14, -6, 4, 11, 18, 6],\n [8, -5, 17, -3, 3, 2, 2],\n [-11, -3, 12, -9, 13, 15, -10],\n [-2, -8, 13, -9, 3, -2, -15],\n [6, 2, 18, -18, 6, 17, -2],\n [5, -17, -4, 13, -13, -... | 15 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[1, -16, -2, -7, -18, -2, -16],\n [7, -4, 17, 13, 13, -15, -1],\n [0, 16, -5, 14, -5, 15, -15],\n [5, 10, 0, -13, 14, 0, -18],\n [-14, 8, -3, -13, -6, 16, 0],\n [-7, -3, -9, 6, 1... | -14 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, -3, 0, -1, -3, -11, 14],\n [-7, -8, -14, 8, -7, -2, -13],\n [14, -14, 9, -5, -14, 14, 0],\n [3, -14, -17, 11, -15, 14, -6],\n [1, -12, -4, 4, -5, ... | 38 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -14, -1, 7, 1, 8, -7],\n [-12, -16, -9, 15, 6, 16, -3],\n [-17, 5, -9, 3, 7, 8, 10],\n [1, 8, 1, 0, 1, 16, -17],\n [11, 15, 3, -16, -13, -4, 8],\n [-9, -1... | -15 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-4, 3, 2, 3, 17, 15, 11],\n [0, 9, -18, -15, -12, -10, 17],\n [0, 0, -9, 17, -10, 13, 13],\n [0, 0, 0, 8, 16, 2, 6],\n [0, 0, 0, 0, -10, 8, 7],\n [0, 0, 0, 0, 0, 13, 14],\n [0, 0, 0, 0, 0, 0... | 439 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, -2, -11, 0, 8, 11, -12],\n [-2, -9, -6, -4, -4, -8, -4],\n [-11, -6, 9, 16, 5, 0, 4],\n [0, -4, 16, 18, -5, 2, -8],\n [8, -4, 5, -5, -15, -8, -10],... | 126 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -16, 1, 0, 16, -15, -14],\n [0, -15, -7, 8, 4, 6, 2],\n [0, 0, 13, 13, -14, 17, -3],\n [0, 0, 0, -13, 16, 3, -14],\n [0, 0, 0, 0, -3, -16, 11],\n [0, 0,... | 7643 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[11, 3, 14, 11, -2, 13, -5],\n [-9, 17, 15, -10, 9, -8, -5],\n [0, -4, 9, 5, -11, -10, 14],\n [14, 0, -16, -9, -18, 10, 15],\n [-6, -18, 15, 10, -6, 10, 5],\n [7, -2, -12, -6, -14, 7, -16],\n... | -24 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[13, 7, -3, 6, 9, -10, -18],\n [10, 3, -3, -12, -5, 10, 0],\n [0, -17, -4, -16, -8, 11, -1],\n [-17, 13... | 1159 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[9, 12, 15, -4, 6, 17, -11],\n [-10, 18, 13, -2, 16, 18, 0],\n [10, -12, 9, -10, 9, -13, 10],\n [-2, -3, 4, 12, -16, 2, 7],\n [17, 18, 3, -7, -6, -8, -3],\n [-11, -17, 11, 11, -7... | 2 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -1, 13, -16, -16, 11, -18],\n [11, 13, 9, 2, -6, 8, 17],\n [-12, 3, -9, -4, -4, -15, 13],\n [4, -13, 5, 1, 18, 1, -7],\n [14, 9, -11, -18, 18, 3, -13],\n [2, 13, 16, ... | -23 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, 8, 1, -7, 12, 8, 13],\n [-9, -16, 8, 16, 12, -4, -3],\n [-6, 16, -8, 2, -8, 11, 16],\n [3, 12, -5, 5, 13, 17, 13],\n [-4, 16, -16, -3, -14, 2, -9],\n [0, 6, -15, 10, 0, -17, -9],\... | -5948 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -14, -14, 2, -7, -15, 1],\n [0, -5, -8, 13, -8, -1, 8],\n [0, 0, -8, 2, -14, 4, 6],\n [0, 0, 0, -18, -12, -15, -18],\n [0, 0, 0, 0, -2, 10, -5],\n [0, 0, ... | -629 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 1) of the inverse. Round your answer to the nearest integer:\n[[-17, 17, 7, -8, -11, 3, 1],\n [0, 10, 7, 11, -2, 1, -3],\n [0, 0, 8, 4, 5, -10, 16],\n [0, 0, 0, 12, -11, -4, 12],\n [0, 0, 0, 0, 11, 10, 0],\n [0, 0, ... | 0 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[4, -8, -11, 10, 11, -9, 9],\n [17, -6, 13, 17, 18, 7, 3],\n [-15, 12, -1, 5, 4, 3, -17],\n [12, -8, 9, 13, -14, -9, 5],\n [16, 4, -2, -18, 12, 12, 15],\n [-10, 3, -... | 742 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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[[1, -2, -4, 1, 2, -11, -8],\n [-2, -7, 3, -9, 5, 7, -4],\n [-4, 3, 13, 0, 6, 8, 0],\n [1, ... | 84 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, 6, 0, 7, 10, -2, 6],\n [6, -15, -12, 2, 0, 6, 10],\n [0, -12, -4, -8, -2, 8, -6],\n [7, 2, -8, -11, -5, 2, 9],\n [10,... | 451 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -2, 12, 3, -4, -13, 2],\n [-2, 15, -4, 1, 8, 0, -4],\n [12, -4, -11, -6, -2, -2, -4],\n [3, 1, -6, 14, 8, -4, -8],\n [-4, 8, -2, 8, 18, -6, 17],\n [-13, 0, -2, -4, -6, 9, -8],\n [... | -331 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[7, 16, 0, 12, -6, 2, 4],\n [16, 9, -10, 2, 10, -12, 2],\n [0, -10, -15, 2, -4, 2, -2],\n [12, 2, 2, 6, 3, -10, 8],\n [-6, 10, -4, 3, 0, -10, 3],\n [2, -12, 2, -10, -10, 16, -7],\n [4, 2, -2,... | -173 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 6) rounded to the nearest integer?\n[[-15, 3, -11, -4, -6, 14, -12],\n [3, 6, 4, 6, -7, 12, 2],\n [-11, 4, 2, 2, -12, -14, -2],\n [-4, 6, 2, 2, 8, 3, 5],\n [-6, -7, -12, 8, -11, -12, -10],\n [14, 12, -14, 3, -12, -1... | -2 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[11, -10, 12, 2, 15, 12, 6],\n [-7, -18, 3, 18, -18, -18, 2],\n [-4, -2, 3, 16, -3, -11, -2],\n [-2, 7, -6, -2, -2, -5, -13],\n [16, -5, -11, -4, 8, -6, 12],\n [16, -13, -14, 3, 4, 6, 15],\n [7, -14, 7, 1... | 510 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, -2, -5, -5, -6, -12, -4],\n [0, 16, -2, 16, 0, 1, 17],\n [16, 13, 5, -2, -12, -18, 16],\n [13, 17, -6, -13, -5, 18, -4],\n [-15, -3, 9, -3, -15, 7, 9],\... | -110 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, -9, -1, -14, 10, 15, 4],\n [0, 11, -13, -15, 10, 4, -13],\n [0, 0, -4, 13, -10, 18, -9],\n [0, 0, 0, -8, -2, 13, -15],\n [0, 0, 0, 0, 13, 3... | -313 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 4, -9, 0, -14, 4, 11],\n [6, 9, 15, 6, -9, -5, 11],\n [6, -5, 16, 15, -9, 16, -8],\n [-8, 2, 2, 3, -12, -2, -1... | -37 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -2, 17, 2, -11, -14, 7],\n [-3, 17, 9, 10, -7, 18, 11],\n [4, -3, -5, -9, -12, 18, 10],\n [-16, -4, 17, 0, -6, ... | 2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -10, 0, -13, -4, 1, -10],\n [13, -15, -1, -14, 1, 4, -8],\n [18, 3, -15, 10, 15, -6, -10],\n [12, -12, -15, 0, ... | -2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 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, 3, 6, 3, 10, -2, 8],\n [3, -18, 8, -14, -2, 3, -16],\n [6, 8, -8, -6, -12, 0, -12],\n [3, -14, -6, -17, 12, -1, 0],\n ... | 24 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 5) of the inverse. Round your answer to the nearest integer:\n[[-9, 13, 15, 1, -17, -18, 17],\n [0, 8, -17, 12, -5, -17, 10],\n [0, 0, 18, 9, 1, 5, 2],\n [0, 0, 0, -1, 5, -5, 15],\n [0, 0, 0, 0, 17, 3, -5],\n [0, 0,... | -346 | MATH |
[
{
"content": "Find the value at position (5, 5) of the inverse of matrix 1/252 * A where A =\n[[2, -4, 14, 4, -10, 0, -7],\n [-4, 4, -10, 2, 7, 4, -10],\n [14, -10, 8, 1, 6, 0, 8],\n [4, 2, 1, 9, -7, -6, 8],\n [-10, 7, 6, -7, -10, -2, 0],\n [0, 4, 0, -6, -2, 8, -1],\n [-7, -10, 8, 8, 0, -1, 5]]\nRound your answ... | 34 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, -4, -2, -5, 5, -5, -8],\n [-4, -18, 4, -8, 2, 4, -6],\n [-2, 4, 14, -8, 10, -4, 0],\n [-5, -8, -8, -10, -3, 2, 2],\n [5, 2, 10, -3, 3, -3, 0],\n [-5, 4, -4, 2, -3, 9, -8],\n [-8, -6, 0, 2, 0, -8, -8]... | 607 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, 8, -8, 15, 0, -13, 9],\n [-18, 16, -11, -12, -8, -15, 6],\n [-7, 7, -7, 18, 5, -3, -6],\n [6, -15, -8, 13, -12, -8, 9],\n [4, 4, 9, 7, 6, 10, 0],\n [14, 17, -5, -5, 1... | 14 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, 6, -12, 3, -2, -1, -9],\n [-9, -12, 8, 14, -18, 15, -15],\n [-2, -15, 7, -15, -18, -12, 11],\n [-10, 16, -11, 5, 0, 17, 8],\n [13, -5, -1, 9, 10, -3, 16],\n [12, -15,... | 34 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -3, -6, -12, 10, 11, 11],\n [-3, -13, 0, 8, 0, 7, 14],\n [-6, 0, 18, 10, -2, 2, 12],\n [-12, 8, 10, -10, 0, -8, 6],\n [10, 0, -2, 0, -16, -14, -9],\n [11... | -14 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[2, -6, 2, 2, 10, 8, 0],\n [-6, 3, 4, -2, 2, -15, 4],\n [2, 4, -12, 3, -16, -6, -8],\n [2, -2, 3, 16, -12, -2, -9],\n [10, 2, -16, -12, -11, -1, -10],\n... | 46 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[3, 5, 18, -18, -9, -3, -11],\n [0, -7, 6, -2, 7, -5, 17],\n [0, 0, -14, 6, -1, -6, -5],\n [0, 0, 0, 8, 13, -10, 13],\n [0, 0, 0, 0, 15, -16, 7],\n [0, 0, 0, 0, 0, -6, -14],\n [0, 0, 0, 0, 0, 0, -7]]\nRou... | 1888 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, -8, 0, 16, 7, -5, 5],\n [-18, 3, 4, 0, -1, -7, 9],\n [9, 14, 0, 9, 18, 7, 16],\n [15, 16, -3, -6, 4, 3, -3],\n [9, 16, -11, 3, 2, 7, 2],\n ... | 65 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[4, 8, -1, 5, -12, 1, 8],\n [-13, 8, -10, 12, 2, 7, -6],\n [4, 1, 18, 9, -2, 9, -17],\n [6, -13, -8, -13, -8, -5, -17],\n [-16, 16, 14, 5, 0, -1, 5],\n [16, -18, 17, 6, 15, 6, -3],\n [15, 10, 0, 4, 0, 6, -3]]\... | -4 | MATH |
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