messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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, -6, -2, 14, -10, 2, -4],\n [-6, 15, -4, 4, -2, 2, -4],\n [-2, -4, 13, 14, -9, -8, 4],\n [14, 4, 14, 4, 12, 0, -2],\n [-10, -2, -9, 12, 7, -4, 0],\n [2, 2, -8, 0, -4,... | -16 | 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[[7, -17, -8, -2, 15, 0, -1],\n [-6, -14, 4, 5, 10, -11, 7],\n [-4, -18, 9, -5, 15, 12, -13],\n [-14, 12, 18, -4, -4, -14, 9],\n [14, -8, -13, 4, -17, -4... | -28 | 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, 4, 12, 3, 14, -10, 0],\n [4, 6, 10, 6, -1, -6, -8],\n [12, 10, -17, 2, 2, 4, 15],\n [3, 6, 2, 13, 2, 4, -4],\n [14, -1, 2, 2, 15, -7, 12],\n [-10, -6, 4, 4, -7, 15, ... | 706 | 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[[-12, -6, 0, 1, -3, -2, 10],\n [-6, -2, 2, 10, -8, 7, 5],\n [0, 2, 5, -10, 5, 11, 8],\n [1, 10, -10, 2, 0, 9... | -35 | 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[[14, 1, 14, 16, 15, 17, 8],\n [0, -14, 10, -9, -6, 10, -14],\n [0, 0, 3, -4, -6, -18, -18],\n [0, 0, 0, -13, 9, 12, -11],\n [0, 0, 0, 0, 1, -5, -5],\n [0, 0, 0, 0, 0... | 4372 | 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[[-14, 5, 10, 10, 7, -16, -17],\n [6, 0, -17, 0, -18, 8, 16],\n [-14, -15, -2, 2, 12, 3, -8],\n [15, -4, -9, 13, 12, 18, 9],\n ... | 235 | 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, -4, -3, 7, -14, -1, -4],\n [-4, 12, 5, 10, 3, 2, 14],\n [-3, 5, 2, 6, -4, -2, 4],\n [7, 10, 6, -7, 10, 14, 2],\n [-14, 3, -4, 10, -14, -14, -5],\n ... | 123 | 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[[-11, 6, 10, 10, 9, 2, -12],\n [6, -12, -8, -7, -12, -2, -2],\n [10, -8, 17, -14, -6, -16, 6],\n [10, -7, -14, -7, -2, -1, 6],\n [9, -12, -6, -2, -6, -2, 14],\n [2, ... | 525 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-14, 0, 9, 7, 4, 11, -16],\n [9, 14, -16, -14, 0, -18, -10],\n [-14, 15, 18, 14, 6, 10, 6],\n [-10, -16, -4, -15, 1, 4, 18],\n [-11, 18, 14, 14, -12, 3, -14],\n [-4, 2, 6, -2, -12, 0, -12],\n [5, -8, -18... | 5503 | 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[[5, -2, -10, 16, 1, 0, -1],\n [1, 11, -18, 5, 5, 0, 11],\n [7, 10, -6, -15, -2, 14, -14],\n [9, 5, -2, -8, -7, -6, -11],\n [-1... | 48 | 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[[2, 17, 5, -2, 3, 0, -9],\n [0, -17, 14, 12, 16, 18, 17],\n [0, 0, 7, 6, -2, -4, 18],\n [0, 0, 0, 3, -2, -5, -5],\n [0, 0, 0, ... | -2547 | 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[[-13, -10, 16, -11, -12, -15, -6],\n [0, -12, -9, 6, 16, 6, 10],\n [0, 0, -13, -9, -17, 6, -12],\n [0, 0, 0, 4, -12, 8, -6],\n [0, 0, 0, 0, -6, -7, -12],\n [0, 0, 0,... | 3045 | 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[[-10, 16, 4, 4, 7, -18, -5],\n [0, -9, -18, -14, -16, 8, 3],\n [0, 0, -17, -6, -3, -11, -11],\n [0, 0, 0, -7, -10, 18, -10],\n [0, 0, 0, 0,... | 777 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[8, 8, -2, -4, -17, -12, 4],\n [8, -11, 12, -4, 6, 9, 9],\n [-2, 12, 5, -5, 0, 15, 14],\n [-4, -4, -5, -12, -2, 14, 6],\n [-17, 6, 0, -2, -7, 7, -8],\n [-12, 9, 15, 14, 7, 13, 5],\n [4, 9, 14, 6, -8, 5, 1]]\nR... | 7 | 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[[18, -10, 0, -12, -14, 5, -12],\n [0, -10, 11, -16, 3, 1, 13],\n [0, 0, 1, 6, 16, 5, -6],\n [0, 0, 0, -18, -2, -17, -13],\n [0... | 10199 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[4, 2, 5, 9, -6, -7, 0],\n [2, 11, 9, 7, 4, -13, -4],\n [5, 9, -16, -10, -5, 8, -1],\n [9, 7, -10, -13, -3, -3, -1],\n [-6, 4, -5, -3, -10, -6, 4],\n [-7, -13, 8, -3, -6, 11, 8],... | 3 | 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, -18, 15, -10, -7, -9, -9],\n [0, -13, 5, 5, 2, 12, 11],\n [0, 0, -7, 16, -12, 6, -13],\n [0, 0, 0, 10, 9, 3, -11],\n [0, 0, 0, 0, -1, -1, -6],\n [0, 0, 0... | 2052 | 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, 16, -4, -11, 1, 2, -18],\n [10, 5, 11, 16, 14, 1, -3],\n [-10, 12, -2, 12, 4, -13, 11],\n [-12, -8, 15,... | 542 | 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[[9, -5, -2, 5, 15, 3, -9],\n [0, 2, 18, -12, 7, -6, -3],\n [0, 0, -14, 13, -3, -10, 3],\n [0, 0, 0, 1, -4, 7, -10],\n [0, 0, 0, 0, -9, 14, -3],\n [0, 0, 0, 0, 0, -1, 9],\n [0, 0, 0, 0,... | 2702 | 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[[7, -8, -18, -8, 5, -9, -5],\n [-5, -12, 4, 3, 17, 8, -17],\n [0, -12, -7, -16, -14, -11, -5],\n [17, -12, -12, 13, -11, -7, -9],\n [-5, -10, 11, -14, -18, -18, 1],\n [-8, 7, -16, -13,... | -159 | 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[[5, -14, 10, 15, -3, 6, 18],\n [-11, 10, 6, 4, 15, -16, 11],\n [15, 13, 10, -10, -17, -12, -14],\n [-11, 13, -1, -1, -3, 2, -9],\n [-15, -11, 0,... | 11 | 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[[-5, 12, -17, 18, -5, -10, -9],\n [-12, 9, 6, 9, -17, -2, -15],\n [-6, -1, -16, 18, 14, 5, -11],\n [16, -17, 14, -7, 3, -6, -9],\n [-2, -14, -10... | 51 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[14, -2, -2, 18, 6, 7, -4],\n [-2, -5, -6, 0, 10, 13, -4],\n [-2, -6, 9, -4, -4, -8, -8],\n [18, 0, -4, 7, -4, 1, -14],\n [6, 10, -4, -4, 17, -11, 8],\n [7, 13, -8, 1, -11, -17, -1],\n [-4, -4, -8, -14, 8, -1,... | 50 | 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, 1, 6, -6, 8, 0, 2],\n [1, -5, 0, 8, -1, 11, 0],\n [6, 0, -1, 2, 4, -3, 9],\n [-6, 8, 2, -2, 2, -4,... | 936 | 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[[16, 13, -10, -5, -6, 14, 13],\n [0, 11, -3, -7, -9, -17, -1],\n [0, 0, 5, -7, 10, 3, 17],... | -504 | 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[[-9, 3, 11, 11, -3, -8, 3],\n [10, 6, -5, -5, -17, -6, -16],\n [11, -1, 17, 2, 0, -3, 9],\n [-15, -4, -18, -3, 1, 14, -2],\n [-14, -14, -6,... | 602 | 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[[-13, 4, -16, 18, 14, 2, 1],\n [0, -2, 10, -11, 7, 9, 15],\n [0, 0, 18, -6, 6, 4, 3],\n [0... | 286 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[3, 5, 4, 11, 0, -6, 6],\n [5, -16, 4, 4, 9, -2, -3],\n [4, 4, 17, -10, -2, 4, 0],\n [11, 4, -10, 4, 6, -2, 2],\n [0, 9, -2, 6, -13, -14, 12],\n [-6, -2, 4, -2, -14, -14, -10],\n... | -18 | 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[[14, 0, -17, -8, 16, -2, -16],\n [0, 16, 2, 6, -17, -18, -12],\n [0, 0, 17, 2, 16, 17, -11],\n [0, 0, 0, -12, -17, -18, -18],\n [0, 0, 0, 0, 9, -1, 5],\n [0, 0, 0, 0, 0, ... | 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[[17, 2, 11, -7, -5, 12, 8],\n [2, 5, -6, 9, -6, 2, -6],\n [11, -6, -16, 0, -6, -1, 16],\n [-7, 9, 0, 5, 0, 8, 0],\n [-5, -6, -6, 0, 8, -10, 4],\n [12, 2, -1, 8, -10, 10, -1],\n [8, -6,... | 231 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-16, 3, 8, 0, 12, -10, -5],\n [3, -10, 8, -6, -8, -1, -4],\n [8, 8, 16, 14, -8, 10, 13],\n [0, -6, 14, -11, -10, -8, 10],\n [12, -8, -8, -10, -17, 6, -8],\n [-10, -1, 10, -8, 6,... | 6 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[-7, -8, -9, -8, 10, 4, 8],\n [-8, 11, -6, -8, -6, -1, 11],\n [-9, -6, -15, -2, 8, -3, 0],\n [-8, -8, -2, -14, 2, 0, 12],\n [10, -6, 8, 2, -12, 0, -6],\n [4, -1, -3, 0, 0, 11, 4]... | 37 | 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[[-11, -15, 12, 10, 17, -6, -10],\n [0, -16, 6, 6, -7, 10, -8],\n [0, 0, -5, -3, -9, 12, 12],\n [0, 0, 0, 1, -10, -4, -10],\n [0, 0, 0, 0, 1, -5, 3],\n [0, 0, 0, 0, 0, 13,... | 416 | 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, -3, 12, -10, -4, 3, 0],\n [-3, -2, 6, 16, 5, -3, 10],\n [12, 6, 15, -3, 1, -4, -3],\n [-10, 16, -3, 1, 6, 1, -6],\n [-4, 5, 1, 6, -5, 3, 9],\n [3, -3, -4, 1, 3,... | 1034 | 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[[-10, 2, 2, 0, 9, 12, 4],\n [2, -18, -6, 7, -14, -10, 0],\n [2, -6, -18, 0, -9, 0, -2],\n [0, 7, 0, 6, -1, -3, 1],\n [9, -... | 62 | MATH |
[
{
"content": "Find the value at position (3, 5) of the inverse of matrix 1/252 * A where A =\n[[5, 4, 0, -2, -1, 3, 1],\n [4, 12, 8, -9, -3, 4, -12],\n [0, 8, 6, -6, 15, -6, 2],\n [-2, -9, -6, -16, 0, -6, 4],\n [-1, -3, 15, 0, -15, -6, -10],\n [3, 4, -6, -6, -6, 5, 4],\n [1, -12, 2, 4, -10, 4, 4]]\nRound your a... | 3 | 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[[17, -18, -11, -16, -5, -2, 15],\n [0, -14, 10, 16, -1, 11, -4],\n [0, 0, 14, -9, 0, 18, -16],\n [0, 0, 0, 14, 9, 13, -3],\n [0, 0, 0, 0, -7, 3,... | -271 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[14, -17, -8, -9, 14, -12, -4],\n [0, -8, 8, -12, -18, -9, 2],\n [0, 0, 11, -11, 5, 0, -16],\n [0, 0, 0, -1, 0, 11, -6],\n [0, 0, 0, 0, -15, 17, -5],\n [0, 0, 0, 0, 0, 2, -11],\n [0, 0, 0, 0,... | 13734 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 6) of the inverse. Round your answer to the nearest integer:\n[[15, 10, -16, -9, 1, -17, 8],\n [13, -9, -2, 14, -13, -1, -10],\n [-11, 6, 12, -15, 1, 9, -18],\n [4, -6, -3, 7, 12, -18, -2],\n [-3, 18, -9, 12, -9, 15... | 2 | 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, 12, 12, -2, 0, -16, 11],\n [0, 10, -1, -7, 4, -8, -10],\n [0, 0, 6, -10, -7, -8, 9],\n [0, 0, 0, 17, -10, -11, -16],\n [0, 0, 0, 0, 9, -4, 0],\n [0, 0, 0, 0, 0, 18, -8],\n [0, 0, 0, 0, ... | 370 | 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[[-9, 1, 9, 4, 16, -18, 10],\n [-10, -10, 3, -17, -3, -13, -6],\n [14, 0, -4, 14, -9, -18, -7],\n [10, -2, -15, 10, -... | -33 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-11, 0, -10, 9, -5, 8, -1],\n [0, 14, 18, 6, -6, 4, 17],\n [0, 0, 15, 17, -2, -9, 4],\n [0, 0, 0, -17, 0, -3, 6],\n [0, 0, 0, 0, 11, -9, 0],\n [0, 0, 0, 0, 0, 2, 10],\n [0, 0, 0, 0, 0, 0, -9]]\nRound you... | 1488 | 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[[-9, 9, 17, -9, 16, 16, 18],\n [0, -6, -8, 0, 9, -15, 18],\n [0, 0, -5, 12, 9, 17, 0],\n [0, 0, 0, -15, -1, 6, -1],\n [0, 0, 0, 0, 16, -18,... | 7195 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[6, 1, 12, 11, -3, -17, -2],\n [0, -12, -10, -2, -10, -10, 18],\n [0, 0, -11, 6, -17, -9, 5],\n [0, 0, 0, -8, -13, -13, 13],\n [0, 0, 0, 0, -16, 15, -7],\n [0, 0, 0, 0, 0, -1, 8],\n [0, 0, 0, 0, 0, 0, -18]]\nRound your answ... | -4911 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-13, 4, 0, -12, 0, -4, 10],\n [4, -15, -2, -5, -4, 14, -2],\n [0, -2, 15, -6, 0, -3, 0],\n [-12, -5, -6, -16, 12, 10, 2],\n [0, -4, 0, 12, -9, -4, 14],\n [-4, 14, -3, 10, -4, -9, 10],\n [10, -2, 0, 2, 14, 10, 2]]\nRound yo... | 143 | 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[[-10, 1, 16, -4, 5, -3, 17],\n [0, -11, -16, 0, -16, 17, 6],\n [0, 0, -3, -2, 5, -2, 1],\n [0, 0, 0, -5, -8, -7, -14],\n [0, 0, 0, 0, 14, 1... | 2464 | 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, 14, 10, 0, -10, -5, 3],\n [14, -2, -6, -6, -12, 6, 14],\n [10, -6, -11, -13, 4, 8, 4],\n [0, -6, -13, 3, -4, 0, 6],\n [-10, -12, 4, -4, 3, 0, 0],\n [-5, 6, 8, 0, 0, ... | 6 | 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, 4, -14, 17, 5, 17, -14],\n [-13, 17, -15, -9, -18, 2, 18],\n [-16, 12, 8, -2, 4, -6, 8],\n [1, -6, ... | 287 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-5, -13, -5, -7, 8, 7, -7],\n [0, -9, -3, 7, -11, 10, 1],\n [0, 0, -2, -18, 10, -5, -2],\n [0, 0, 0, 8, 14, 10, 18],\n [0, 0, 0, 0, -14, 5, 15],\n [0, 0, 0, 0, 0, 7, -1],\n [0, 0, 0, 0, 0, 0, -1]]\nRound your... | -407 | 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, -18, 9, 14, -15, 1, 17],\n [12, 9, -16, -13, 4, -12, 17],\n [-18, -13, 5, 18, 17, 5, 10],\n [18, 13, 6, -9, 16, 6, 8],\n [13, -7, -15, 7, -16, -2, -10],\n [10, -18,... | -14 | 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, -12, 14, 8, -14, -7, 10],\n [-12, -15, 10, 6, 5, 10, -7],\n [14, 10, 2, 16, 11, 6, -14],\n [8, 6, 16, -3, -5, 2, 0],\n [-14, 5, 11, -5, -13... | -106 | 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, -6, 4, 7, 6, 2, 6],\n [-6, -16, -17, -16, 12, -14, -16],\n [4, -17, -15, 12, -18, 4, 2],\n [7, -16, 12, 3, 2, 12, 10]... | 38 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[9, 15, -3, 17, -12, -1, -13],\n [9, 15, 10, -15, -5, -14, 6],\n [-11, -4, 0, -8, 1, 17, -1],\n [-5, 6, -3, -1, -18, -18, -18],\n [2, 6, 8, -9, -7, 9, 13],\n [14, -11, 7, -17, 16, 15, -13],\n... | -35 | 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, 18, 6, 2, 17, -10],\n [-7, -9, -14, 14, -14, -3, 18],\n [18, 10, -1, 10, -13, -1, 13],\n [12, -8, 7, 9, 8, 0, 8],\n ... | 28 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/252 * A where A =\n[[6, 10, -2, 6, -10, -4, -10],\n [10, 15, 2, 10, -3, -2, 2],\n [-2, 2, -9, 14, 2, 10, 0],\n [6, 10, 14, -2, 4, 6, -4],\n [-10, -3, 2, 4, 11, -5, 0],\n [-4, -2, 10, 6, -5, -1, 2],\n [-10, 2, 0, -4, 0, 2, -6]]\nRound you... | 7 | 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, -15, 13, -4, 7, -8],\n [0, -8, -17, 8, 7, -11, 2],\n [0, 0, -18, -6, -10, 9, -13],\n [0, 0, 0, -10, -7, 3, -7],\n [0, 0, 0, 0, 15, -11, -9],\n [0, 0, 0, 0, 0, -15,... | -29 | 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[[-17, -4, -11, 7, 16, 2, -11],\n [0, -11, -9, 4, -15, 11, 4],\n [0, 0, -13, -2, 6, 5, 3],\n [0, 0, 0, 15, 7, 0, 7],\n [0, 0, 0, 0, 3, -12, -15],... | 41 | 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[[18, 3, 3, 3, -4, -2, 9],\n [0, 2, -2, -14, -1, -2, -15],\n [0, 0, 18, -10, 0, -10, 4],\n [0, 0, 0, -2, 3, 16, 11],\n [0, 0, 0, 0, 13, 6, -6],\n [0, 0, 0, 0, 0, -5, ... | 13974 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -8, -10, -13, 15, 18, 13],\n [-7, 13, -2, -15, 14, -10, 15],\n [11, 1, 4, 16, 4, 4, 18],\n [4, 9, 0, 11, 2, 5, ... | -5 | 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[[3, -15, -17, -3, -3, 3, -18],\n [0, 5, -15, -1, -2, -12, -9],\n [0, 0, 3, 13, 10, 16, -2],\n [0, 0, 0, 11, 1, -12, -12],\n [0, 0, 0, 0, -17, 14, -8],\n [0, 0, 0, 0, 0, 1, -11],\n [0, ... | -128712 | 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[[-8, -14, -17, -6, -1, 7, 6],\n [0, -14, -17, -15, -7, -8, -15],\n [0, 0, 8, -13, -4, 12, 3],\n [0, 0, 0, 2, 11, 2, 17],\n [0, 0, 0, 0, 12, -6, -1],\n [0, 0, 0, 0, 0, -6,... | 102 | 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, -4, 12, -13, 6, -1, 3],\n [12, 17, -10, -16, 14, 8, -18],\n [-10, -14, -4, -10, 9, -6, 5],\n [-9, 3, 3, 18, 1, -9, -9],\n [7, 6, 9, -6... | 662 | 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[[11, -16, 18, -16, -14, 9, -5],\n [-8, -11, 18, -11, -7, -4, 0],\n [9, -12, -12, 11, -1, 5, -13],\n [-15, -16, -13, 7, -8, 10, 1],\n [-9, 7, 8, -5, 17, -7, 4],\n [2, -11,... | -54 | 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, -8, 1, -15, 1, 12, 1],\n [-8, -18, -1, 14, 17, -1, 12],\n [16, -4, -13, -11, 3, -18, -6],\n [5, 2, -15, -12, -7, -6, ... | 6720 | 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, 18, -12, -14, -4, -11, -10],\n [0, 3, 15, 16, -6, -8, 13],\n [0, 0, 5, 3, -16, -5, -17],\n [0, 0, 0, 6, 15, -8, 18],\n [0, 0, 0, 0, -13, -18, 15],\n [0, 0, 0, 0,... | 4553 | 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[[16, 2, 6, 16, -2, -8, 2],\n [2, -16, 4, 6, 6, 8, 5],\n [6, 4, -9, -4, 8, 16, 8],\n [16, 6, -4, -3, 6, 6, 10],\n [-2, 6, 8, 6, -16, -12, -6],\n [-8, 8, 16, 6, -12, -2, 5]... | -123 | 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, 6, 9, 3, 6, -2, -7],\n [0, 18, -3, -2, 12, -4, -6],\n [0, 0, -17, -11, -12, -9, -15],\n [0, 0, 0, -1, 5, 13, 15],\n [0, 0, 0, 0, -4, -7, -2],\n [0, 0, 0, 0, 0, -... | 3838 | 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[[-15, -12, -1, -15, -8, 1, -8],\n [0, -2, 15, -7, 9, 16, -11],\n [0, 0, 5, -17, 12, 3, -18],\n [0, 0, 0, 17, -16, -14, -18],\n [0, 0, 0, 0, -9, 15, -3],\n [0, 0, 0, 0, 0, 11, 16],\n [0... | 352 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-3, -8, 3, 17, 4, 7, 12],\n [0, -14, 6, 15, -7, 3, -10],\n [0, 0, 10, 8, -2, -14, -6],\n [0, 0, 0, -17, 4, -6, -15],\n [0, 0, 0, 0, -10, -13, -9],\n [0, 0, 0, 0, 0, -3, 13],\n [0, 0, 0, 0, 0... | 319 | 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[[0, 15, -15, -16, -9, 9, 15],\n [0, 17, -16, 4, -2, -12, 7],\n [-1, -13, 12, 10, -10, 16, -2],\n [-7, 17, 5,... | 16 | 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[[13, 16, -4, -6, -6, -5, -6],\n [16, -11, -6, 2, 0, 4, -2],\n [-4, -6, 7, 2, 13, 1, -4],\n... | -89 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-2, 14, -2, -8, -6, 6, 0],\n [14, -1, 0, 11, 6, 8, 8],\n [-2, 0, -17, 4, 4, 10, 0],\n [-8, 11, 4, 1, 8, -6, -2],\n [-6, 6, 4, 8, -12, -6, -10],\n [6, 8, 10, -6, -6, 1, 6],\n [0, 8, 0, -2, -10, 6, -11]]\nRound your answer t... | 353 | 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[[-8, -1, 6, 3, 16, 10, 2],\n [0, -7, 17, 5, 13, 8, 13],\n [0, 0, 7, -8, -1, -14, -3],\n [0, 0, 0, 4, 15, -2, -9],\n [0, 0, 0, 0, 5, -16, -17],\n... | 117 | 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[[-12, -8, -6, -5, -1, 3, -2],\n [-8, -4, 3, -10, 4, -14, 6],\n [-6, 3, -4, 4, 4, 1, 6],\n [-5, -10, 4, -15, ... | 9 | 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[[1, -3, 15, -3, -5, 9, -1],\n [7, -12, 15, -12, 14, 16, 2],\n [9, 13, -3, -9, 4, -4, -13],\n [14, -7, 17, 12, -9, 15, -9],\n [... | -38 | 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[[17, -14, -14, -9, -12, -7, 11],\n [0, 9, -6, 3, -1, 8, -11],\n [0, 0, 10, -14, -12, 3, -15],\n [0, 0, 0, -18, -11, 13, 11],\n [0, 0, 0, 0,... | 2883 | 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[[16, 1, 18, -18, -3, 11, -10],\n [-9, -6, 1, 10, -15, 9, 18],\n [-6, -16, 18, 0, 9, 0, -2],\n [-1, -1, 4, -1... | -24 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -13, -18, 5, 15, -12, -8],\n [-8, 17, 1, -3, -14, 5, 11],\n [11, 18, 14, 1, 3, 2, 18],\n [8, 16, -13, 13, -3, 9... | 2 | 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[[-1, -2, 9, -7, 16, 3, -18],\n [0, 2, -18, -15, 13, -18, -6],\n [0, 0, -12, -16, 7, 12, 17],\n [0, 0, 0... | 91595 | 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[[11, 6, -14, -14, 10, -16, -1],\n [6, 18, -2, 1, 0, 8, -6],\n [-14, -2, -16, -13, 2, -2, 2],\n [-14, 1, -13, -15, 6, 0, -4],\n [10, 0, 2, 6... | 3951 | 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[[-12, 5, 1, -4, -9, -2, -8],\n [5, -3, -8, 12, 18, 4, 10],\n [1, -8, -6, 5, -7, -2, -2],\n [-4, 12, 5, ... | 371 | 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, 5, -9, 4, -3, 18, -3],\n [0, -13, 11, 18, -18, 6, 2],\n [0, 0, -7, -14, -10, -10, 16],\n [0, 0, 0, 18, ... | -181 | 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, -18, -15, -5, -1, 15, -18],\n [3, -3, 3, -3, 9, 9, 3],\n [-13, 6, -17, -12, -2, 16, 1],\n [-17, -12, 13, 0, -7, -10, 8... | 0 | 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[[-7, 7, -11, -14, -8, 16, 8],\n [0, 13, 9, 17, -1, -9, 13],\n [-1, -7, -11, 14, -5, -17, -10],\n [-14, 15, 0... | 22 | 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[[5, 1, 14, 12, -11, -9, -18],\n [0, 6, 13, -9, -10, 1, 1],\n [0, 0, 2, 0, -4, -13, -9],\n [0, 0, 0, -11, 9, -16, -17],\n [0, 0, 0, 0, -4, 1, 3],... | 131 | 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[[-16, -4, 14, -1, 4, -16, 11],\n [-2, 13, -12, -5, -4, -7, -11],\n [-3, 15, 5, 10, -3, -14, -14],\n [11, -14, -6, 16, 6, -5, 7],\n [-1, 1, 15, -... | -57 | 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[[-14, -3, 13, 3, 13, -6, 7],\n [-2, -14, 14, 8, -14, 18, -12],\n [-1, 12, -13, -17, -6, -8, 7],\n [2, -17, 1, -2, -3, -14, -5]... | 100 | 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[[-1, 5, -18, 11, -4, -11, 16],\n [0, -3, 2, -4, -14, -12, -12],\n [0, 0, 3, -6, -2, -6, 7],\n [0, 0, 0, -15, 9, 7, -15],\n [0, 0, 0, 0, 16, 6, -11],\n [0, 0, 0, 0, 0, -7, -8],\n [0, 0,... | -2361 | 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[[-2, -11, 4, -9, 4, 10, 4],\n [-11, -13, 1, 14, 5, -2, 2],\n [4, 1, 1, 16, -10, 4, -1],\n [-9, 14, 16, -10, 4, 10, 2],\n [4, 5, -10, 4, -7, -9, ... | 364 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[-1, 6, 6, 4, 8, -10, -3],\n [6, -9, 6, 11, 3, 10, -12],\n [6, 6, 6, 7, 6, -5, 0],\n [4, 11, 7, 6, -2, -16, -3],\n [8, 3, 6, -2, 15, 0, 8],\n [-10, 10, ... | 20 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[1, 7, 13, 5, 12, -7, 17],\n [0, -13, -12, 12, 8, -11, -16],\n [0, 0, -4, -12, -4, 6, -16],\n [0, 0, 0, 17, -16, -14, 6],\n [0, 0, 0, 0, -17, 9, -9],\n ... | -44 | 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, -13, 14, 9, 11, -2, -10],\n [9, -12, 9, -2, -14, -14, -5],\n [-13, -12, -2, -10, 12, 3, -10],\n [-3, 17, 15, -6, 0, -7, 17],\n [-9, -3, 9, 0, -13, -... | -310 | 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[[6, 14, 0, 4, -4, -10, -2],\n [14, 10, 0, 2, 1, 0, 10],\n [0, 0, 0, -6, -12, 16, 7],\n [4, 2, -6, -13, -2, -8, 0],\n [-4, 1, -12, -2, 5, 3, 1],\n [-10, 0, 16, -8, 3, -2, -1],\n [-2, 10... | 37 | 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[[-2, 15, -7, -14, 8, -6, 7],\n [0, 13, -8, -3, 3, -3, -6],\n [0, 0, 10, -1, -17, -17, -16],\n [0, 0, 0, -7, 13, -15, -10],\n [... | 1322 | 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[[13, 10, 2, 16, -14, -7, -12],\n [-17, 6, -9, -13, 8, 16, -9],\n [-10, 1, 18, 16, 18, -11, 12],\n [-3, 9, -1... | 20 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-14, 3, -12, -6, 4, 2, -13],\n [1, -7, -10, 9, -8, 13, -8],\n [5, -4, 16, -2, 6, 16, 0],\n [12, -2, 4, -18, -9, -11, 7],\n [15, 0, -5, -11, -18, 6, 5],\n [1, 11, -14, -16, 13, -2, -14],\n [-8, -15, 0, 4,... | 404 | MATH |
[
{
"content": "Find the value at position (5, 6) of the inverse of matrix 1/252 * A where A =\n[[-18, -17, -1, 17, 14, 17, -17],\n [0, -3, -15, -10, 2, 4, -17],\n [0, 0, 7, -12, 17, 14, 17],\n [0, 0, 0, 7, 9, 9, 2],\n [0, 0, 0, 0, 16, -14, -3],\n [0, 0, 0, 0, 0, 5, 5],\n [0, 0, 0, 0, 0, 0, -8]]\nRound your answe... | 44 | 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[[-14, 2, 6, 6, 4, -4, 1],\n [2, 15, 0, -4, -5, 1, 6],\n [6, 0, -7, 0, 6, 8, -2],\n [6, -4, 0, -14, 1, 0, 2],\n [4, -5, 6, 1, 18, -14, 4],\n [-4, 1, 8, 0, -14, 8, 1],\n [1, 6, -2,... | 19 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[3, -13, -8, -5, 17, -17, 1],\n [0, -15, 10, 5, -18, 5, 11],\n [0, 0, 18, -15, -4, 1, 1],\n [0, 0, 0, 5, -16, 10, -11],\n [0, 0, 0, 0, -15, 16, -7],\n [... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 2, -1, 4, 4, 9, 17],\n [0, -12, -1, 1, -14, -1, 14],\n [0, 0, -18, 2, -11, -12, 11],\n [0, 0, 0, -15, 18, 2, -6... | -76 | MATH |
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