messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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[[10, -5, -6, 5, -4, -4, 10],\n [-5, -15, -3, -8, 1, 0, 0],\n [-6, -3, 10, 8, -1, 4, 0],\n [5, -8, 8, 15... | 467 | 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[[13, 2, -8, -8, -9, 0, -5],\n [2, -11, 3, -4, 0, 0, 3],\n [-8, 3, 6, -7, 12, 16, -4],\n [-8, -4, -7, 15, -6, -9, -13],\n [-9, ... | -24 | 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[[-13, 11, -2, 0, -2, -9, -9],\n [11, -17, 10, -2, 6, -12, 8],\n [-2, 10, 13, 12, -6, 2, -16],\n [0, -2, 12, -3, -6, -1, -4],\n [-2, 6, -6, -6, -12, 8, 2],\n [-9, -12, 2, -1, 8, 6, 4],\... | -394 | 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[[-6, -9, -3, 16, -4, 4, 18],\n [-11, 7, 3, -14, 15, 8, 0],\n [16, 1, -6, -1, -1, -18, 13],\n [6, 2, 8, -8, -18, 0, 13],\n [-11, 0, -3, 16, -17, -7, 10],\n [-9, 3, 15... | 273 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 4) rounded to the nearest integer?\n[[12, -2, 5, -1, 7, -12, -5],\n [0, 11, -2, 1, -9, 5, -7],\n [0, 0, -10, -1, -12, 9, 17],\n [0, 0, 0, -15, 16, -10, -7],\n [0, 0, 0, 0, 14, -18, 9],\n [0, 0, 0, 0, 0, -11, -3],\n ... | 0 | 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, 18, -10, -1, -10, 2, -18],\n [0, -14, 0, 16, 14, -1, -5],\n [0, 0, -3, 12, 16, 1, -18],\n [0, 0, 0, -12, 1, 18, 17],\n [0, 0, 0, 0, -16, 17, -10],\... | 283 | 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[[-10, 2, 1, 18, -2, 9, 12],\n [0, 13, 13, 4, 2, 6, 14],\n [0, 0, 9, -17, 13, 7, -14],\n [0, 0, 0, -1, -5, 9, 11],\n [0, 0, 0, 0, -7, 6, -15],\n [0, 0, 0... | -4366 | 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[[5, 11, 10, -9, 13, -10, 6],\n [-3, -4, -1, 4, -16, -12, -8],\n [5, 16, 6, 9, -7, 4, -2],\n [18, -1, -10, 16, 17, -1, 1],\n [2, 1, -13, -10, 10, 10, -6],\n [1... | -79 | 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[[-4, 13, -13, -5, 5, 2, -5],\n [-7, -15, 2, -2, 10, -3, -1],\n [-8, 13, 9, -3, 15, 11, 3],\n [-14, -10, -6, 4, 8, 13, 12],\n [14, 7, -1, -7, -16... | -75 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-3, -12, -8, 1, 0, 6, -12],\n [-12, -15, 6, 0, -8, 11, -2],\n [-8, 6, -4, 8, 6, 3, 2],\n [1, 0, 8, 13, -12, -10, -2],\n [0, -8, 6, -12, 10, -10, 7],\n [6, 11, 3, -10, -10, -14, 1],\n [-12, -2, 2, -2, 7, ... | 431 | 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[[-12, 9, -9, -3, -9, 7, 15],\n [15, -5, -1, -18, -2, 3, 18],\n [-3, -12, -4, 2, -17, 6, -10],\n [1, -9, 2, -15, 11, 15, 11],\n [-5, 3, -18, -11, -8, -18... | -34 | 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, 1, -4, -4, -7, -2, 4],\n [0, -3, 8, 4, -18, -12, -1],\n [0, 0, -17, 7, 13, 4, -1],\n [0, 0, 0, -17, 11, 12, -3],\n [0, 0, 0, 0, -17, 11, 11],\n [0, ... | -27 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 3) of the inverse. Round your answer to the nearest integer:\n[[18, 9, 0, 9, -5, -2, -9],\n [9, 2, -3, -4, -12, -6, 1],\n [0, -3, -18, -2, -2, 2, -12],\n [9, -4, -2, -10, -1, -4, -12],\n [-5, -12, -2, -1, 3, 1, -12]... | 10 | 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[[5, 18, -1, -4, 1, -17, 6],\n [0, 8, -6, 9, -4, 10, 2],\n [0, 0, 18, -16, 16, -5, -17],\n ... | 1799 | 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, 2, -6, -4, 12, -14, -3],\n [2, -3, 6, 6, 11, -3, 4],\n [-6, 6, 14, -6, 4, 2, -6],\n [-4, 6, -6, 7, -6, 0, 6],\n [12,... | 37 | 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, -4, 13, 3, 4, -3, 4],\n [-4, 5, 8, 5, -4, 8, -5],\n [13, 8, 12, 15, -12, -6, 0],\n [3, 5, 15, 5, -4, 2, -8],\n [4, -4, -12, -4, 15, 1, 2],\n [-3, 8, -6, 2, 1, -17, 1],\n [4, -5, ... | -160 | 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[[9, 0, -2, -6, 8, 1, -8],\n [0, -13, 3, -8, 14, -1, 2],\n [-2, 3, -17, -18, -4, -10, -2],\n [-6, -8, -18, -17, 1, 0, 1],\n [8, 14, -4, 1, 13, -1... | -51 | 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[[16, -7, 0, -6, -2, 2, -5],\n [-7, 1, 4, 5, 0, 3, -12],\n [0, 4, 4, 8, -6, -5, -4],\n [-6, 5, 8, -10, 3, -2, 4],\n [-2, 0,... | -14783 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[1, 0, 14, 4, -10, -1, -17],\n [-2, -3, 5, 12, -18, 9, 14],\n [18, -15, -18, 14, -9, -16, 18],\n [2, -10, 5, -11, 5, 5, -9],\n [16, -15, -10, -8, -6, 8, 11],\n [-7, 0, -15, 15, 4... | 7 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -4, -1, 8, -13, 15, -14],\n [-7, 10, 18, -7, 6, 15, -8],\n [4, 5, -1, -9, -14, 12, 6],\n [-2, 9, -18, -17, -17,... | -4 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-16, 10, -9, 1, 15, -4, -18],\n [7, 13, -17, 13, 10, 1, 4],\n [-7, -9, 0, -9, 0, 7, 5],\n [-10, 10, 10, 18, 9, -16, 4],\n [-15, -5, -6, 9, 1, 9, 13],\n [-5, -6, -8, -4, -10, -16, -14],\n [9, -4, -16, 16, -12, 11, 5]]\nRoun... | -11 | 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, 12, -1, 9, 2, -10, 15],\n [0, 5, -3, 9, 16, -13, -8],\n [0, 0, -6, -4, -11, 5, -8],\n [0, 0, 0, -12, -1... | 192 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[6, 13, -2, -8, 3, -7, -6],\n [13, 18, -11, 14, 0, -1, -4],\n [-2, -11, 17, 4, -2, 12, 2],\n [-8, 14, 4, -1, 0, -2, -4],\n [3, 0, -2, 0, -18, 4, -4],\n [-7, -1, 12, -2, 4, 1, -11],\n [-6, -4, 2, -4, -4, -11, 1... | 1 | 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, -4, -10, -5, -9, 3, 12],\n [0, -2, -18, -5, 16, -18, 8],\n [0, 0, -10, 17, 13, 1, 8],\n [0, 0, 0, 10, -14, 14, -11],\n [0, 0, 0, 0, -14, -1... | -137 | 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[[9, -4, 10, -15, 15, 18, 5],\n [2, -17, -12, -8, -7, -15, 16],\n [7, -1, 18, -3, -7, 18, 0],\n [-4, 3, 1, -6, 4, 12, 7],\n [13... | -29 | 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[[3, 1, 10, 8, 2, 4, 8],\n [1, 4, 2, -12, 9, 7, 3],\n [10, 2, 4, 1, -8, 0, -2],\n [8, -12, 1, 16, -4, 2,... | 427 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[3, -17, 14, 8, 0, -15, 0],\n [6, -13, -6, 3, -15, -17, -16],\n [11, -15, 10, 14, -6, 13, 9],\n [18, 9, 8, 6, 11, -13, 11],\n [-10, -13, 10, 4, -13, 3, -17],\n [12, -13, -14, 1, -7, -11, 14],\n [12, -16, ... | 685 | 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[[-13, -17, 4, 11, -10, -12, -4],\n [-4, 2, -5, -8, -8, 1, -6],\n [11, 1, -11, 18, 14, 7, -11],\n [-1, -5, -1, 2, 4, -15, -9],\n [-8, 1, 0, -18, 12, -17,... | -342 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[-13, 16, -16, 13, -6, -5, -11],\n [0, -5, -8, 16, 17, -16, 6],\n [-6, -3, 9, 8, -9, -1, -11],\n [-12, 3, -10, 10, 18, 10, 9],\n [2, 14, 7, -4, -17, -7, 14],\n [-4, -18, 14, -15,... | 3 | 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, -2, 10, 4, 12, -14, -3],\n [-2, -9, 8, -12, 14, -9, -4],\n [10, 8, 14, -2, -9, 0, 12],\n [4, -12, -2, 12, -7, 2, -8],\n ... | -67 | 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[[-16, -8, -16, 11, -13, -13, 12],\n [0, 2, -13, 10, -8, 3, -13],\n [0, 0, 17, -18, 3, -10, -11],\n [0, 0, 0, -11, -7, 12, 14],\n [0, 0, 0, 0, -15, -7, 4],\n [0, 0, 0, 0, 0, -10, -13],\... | 2 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-12, 16, 11, 10, -18, -18, -12],\n [0, 17, 12, 6, 5, -18, 12],\n [0, 0, -16, -7, 1, 11, -9],\n [0, 0, 0, 13, 0, 11, 14],\n [0, 0, 0, 0, -7, 17, -15],\n [0, 0, 0, 0, 0, -9, 10],\n [0, 0, 0, 0, 0, 0, 5]]\nRound... | -16 | 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, -10, 4, -1, 0, 2, 15],\n [-10, -5, 9, -17, -8, 5, -5],\n [4, 9, 17, -7, -8, 2, -2],\n [-1, -17, -7, 10, 10, -3, 9],\n [0, -8, -8, 10, -16, 11, -8],\n [2, 5, 2, -3, 11, -10, -5],\n [15, -... | -162 | 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, 9, -11, 2, 5, 5, -6],\n [0, 6, 9, -11, 12, -12, -2],\n [0, 0, -12, -9, 9, 10, 16],\n [0, 0, 0, -11, 11, 11, 12],\n [0, 0, 0, 0, -2, -8, 3],\n [0, 0, 0, 0... | 24 | 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, 17, -9, 18, 6, -2, -15],\n [0, 6, 13, -11, -7, 2, 8],\n [0, 0, 2, -18, -10, -16, 0],\n [0, 0, 0, 17, -15, -1, 13],\n [0, 0, 0, 0, -17, 18, 18],\n [0, 0, 0, 0, 0, -12, -17],\n [0, 0, 0, 0,... | -2218 | 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[[12, -2, -3, -9, 16, 14, 16],\n [8, -12, 8, -7, 14, -6, -17],\n [-16, -8, -14, -17, 9, -6, 16],\n [-6, -7, -1, -1, -2, 3, -6],\n [0, 5, 0, 2, 5, 11, 9],\n [16, -2, 15, -10, -6, -... | -5 | 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, -2, 2, -5, -16, 12, 6],\n [-2, 7, -2, 0, 8, -12, 7],\n [-14, -17, -3, -8, 4, 16, -13],\n [18, -18, 14, -1, -16, 0, -9],\n [1, -8, 13, 1, 13, 18, 3],\n [-15, -6, -13, 10, -17, 6, 13],\n ... | -69 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[14, -2, 6, 14, -11, -9, 10],\n [-2, -18, -1, -2, 8, -10, -4],\n [6, -1, -11, 0, 12, -4, 0],\n [14, -2, 0, -5, -8, 10, 2],\n [-11, 8, 12, -8, 9, 12, 8],\n [-9, -10, -4, 10, 12, -4, -12],\n [10, -4, 0, 2, 8, -1... | -108 | MATH |
[
{
"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[-5, -18, -8, 11, 5, -15, 3],\n [0, -3, 14, 14, -9, -17, -15],\n [0, 0, 14, 14, 1, -6, -8],\n [0, 0, 0, -6, 9, 3, 0],\n [0, 0, 0, 0, -10, 0, 4],\n [0, 0, 0, 0, 0, 18, 16],\n [0, ... | 84 | 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, -4, -6, -1, 4, 10, -12],\n [-4, -8, 0, 2, 9, 8, -2],\n [-6, 0, -7, 2, 2, -8, 6],\n [-1, 2, 2, 12, -2, -2, -10],\n [4, 9, 2, -2, -9, 0, -12],\n [10, 8, -8... | 73 | 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[[11, -5, -14, 12, 13, 15, -9],\n [12, 8, -1, -14, -2, -8, -14],\n [18, 2, 5, 11, -3, 3, -17],\n [0, 18, -17, -8, 14, -10, 6],\... | 26 | 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, -18, -7, 16, 5, -9, 5],\n [-1, -11, -6, -3, -5, -10, -10],\n [-14, -8, 0, -9, -3, 10, -14],\n [-1, 16, 17, 3, 5, -7, -7],\n [16, 0, 18, -5, 4, 3, -8],\n [-17, -... | 2011 | 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[[0, 4, -5, -16, -4, 7, 0],\n [4, -4, -4, 2, 6, -5, 2],\n [-5, -4, 0, 2, -12, -2, 6],\n [-16, 2, 2, -5, 12, 0, -2],\n [-4, 6, -12, 12, -9, 16, -3],\n [7, -5, -2, 0, 16, -3, 1],\n [0, 2,... | 68 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, 16, 5, 4, 14, 10, -9],\n [-4, -9, 7, 10, 15, -1, -17],\n [6, 2, 12, 3, -10, 8, 6],\n [6, 8, -9, 11, -15, 2, 11],\n [14, 7, -17, 4, 12, -15, 1],\n [6, -18, -17, -13, -12, -15, -1],\n [-14, 6, -18, 15,... | 1529 | 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, -17, -18, 15, -11, -10, 9],\n [0, 1, -12, 16, 0, -2, -1],\n [-12, 8, 11, 4, 1, 4, 7],\n [-5, 12, 8, -10, 4, -9, 4],\n [-9, -17, 18, -18, -1,... | -10 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[3, 5, 11, 1, -13, 14, -4],\n [0, 13, -5, -11, 17, 3, 1],\n [0, 0, 9, 4, 5, 4, -15],\n [0, 0, 0, 12, 14, 0, -9],\n [0, 0, 0, 0, 11, 4, 17],\n [0, 0, 0, 0, 0, 3, -1],\n [0, 0, 0, 0, 0, 0, 3]]\nRound your answer... | 343 | 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, -10, -4, 0, 18, -13],\n [17, -14, -16, -9, -6, -15, 14],\n [15, 17, 14, 2, -14, -6, -2],\n [-9, -9,... | 42 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-6, -7, -4, 10, 4, -6, 16],\n [-7, 11, -14, -17, 11, 16, -9],\n [-10, -2, 11, 16, -12, -7, 15],\n [-16, 14, -6, -8, 1, 12, 14],\n [15, -10, -12, -10, 7, -17, -14],\n [-17, -9, 12, 14, -13, -... | 69 | 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[[10, -10, 10, 15, -10, 11, -2],\n [0, 13, 13, -12, 13, -14, -16],\n [0, 0, -3, -8, -6, -1, -5],\n [0, 0, 0, 2, 7, -17, -3],\n [0, 0, 0, 0, -12, 8, 3],\n [0, 0, 0, 0,... | 3989 | 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[[-5, -18, 13, -13, 3, -8, 4],\n [0, -5, 1, -12, 0, 7, 3],\n [0, 0, -9, 0, 12, -9, 18],\n [0, 0, 0, 2, 1, -12, -4],\n [0, 0, 0, 0, 13, -4, -12],\n [0, 0, 0, 0,... | 2018 | 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, -10, -13, 12, 15, -6, 17],\n [13, 3, 10, -8, -13, -14, -18],\n [-9, -9, 5, -12, 3, 2, 3],\n [14, 6, 12, -3, -4, 10, 0],\n [-2, 7, 17, 17, 16, 4, -10],\n [15, -1... | 285 | 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[[16, 8, 1, 12, -3, -5, 13],\n [13, -17, 3, 18, -2, 13, -2],\n [15, -12, 10, -2, 5, -11, 4],\n [14, 10, ... | 2249 | 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, -3, 16, -8, 14, 15, 14],\n [0, 1, -9, 0, -7, -9, -12],\n [0, 0, 14, -2, 6, 12, -18],\n [0, 0, 0, -18, -14, -7, -5],\n [0, ... | 438 | 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[[7, -3, 6, -18, 2, 1, -14],\n [-2, -18, -6, -1, -15, -5, -14],\n [14, 7, -15, 11, -2, 9, -13],\n [8, 17, -12, -18, -9, -6, 13],\n [-5, 14, 11, -... | -31 | 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[[-10, 4, 12, -2, 10, -12, -4],\n [4, -3, 11, 0, -8, -6, 1],\n [12, 11, 14, 14, 12, 0, -6],\n [-2, 0, 14, 14, -8, 2, -2],\n [10, -8, 12, -8, -2, 0, 0],\n [-12, -6, 0,... | 7531 | 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, -16, -14, 15, -10, 5, -14],\n [8, 1, -17, 4, 15, 10, 16],\n [11, -16, -9, 15, -18, -13, -13],\n [-3, -18, -14, 6, 8, 7, -3],\n [7, 18, 9, 9, 11, -6, 6],\n [0, -... | 1069 | 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[[11, 9, -5, 2, 15, -14, 12],\n [-16, 4, 11, 11, 17, -12, -14],\n [-13, -5, -8, 18, -17, 12, 8],\n [-3, -17, 7, -3, -10, -10, -14],\n [17, -12, 13, 10, 18, -16... | -49 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[2, 2, 4, -6, 1, -2, 12],\n [2, 9, -10, 6, 5, 17, -10],\n [4, -10, 17, -2, 7, -2, -5],\n [-6, 6, -2, -1, -14, -16, -10],\n [1, 5, 7, -14, 16, -6, -4],\n [-2, 17, -2, -16, -6, 9, -16],\n [12, -10, -5, -10, -4, ... | 97 | 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[[6, 7, 14, 2, 4, 18, 18],\n [-7, 18, 2, -6, 14, -13, -7],\n [11, 18, -1, -3, -12, -18, 9],... | -49 | 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[[-18, 3, 8, 13, -11, 15, -1],\n [0, -18, -3, 11, 4, 12, 9],\n [0, 0, -10, -17, -17, 13, -3],\n [0, 0, 0, 14, 2, 0, -6],\n [0, 0, 0, 0, -16,... | 337 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -12, -3, 3, 9, 13, -12],\n [0, -17, -11, -12, 2, 3, 16],\n [0, 0, -17, -2, 1, -13, -8],\n [0, 0, 0, 14, 17, 15,... | -8 | 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, 10, 0, 4, 0, -8, -8],\n [10, -16, -7, -12, 2, 2, 12],\n [0, -7, 8, -4, 4, -10, 6],\n [4, -12, -4, -13, 1... | 137 | 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, -2, 13, 11, -4, 9, -16],\n [0, -14, -17, -3, -2, -7, 7],\n [0, 0, -3, -1, -11, 8, 7],\n [0, 0, 0, 4, 3, 14, -1],\n [0, 0, 0, 0, -15, 7, 0],\n [0, 0, 0, 0, 0, -12... | 1657 | 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[[8, 17, 3, -8, -15, 13, 5],\n [0, -16, -17, 4, 1, -11, 16],\n [0, 0, 12, 12, -18, -7, -1],... | 187 | 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[[-6, 8, 10, -5, -15, -11, -14],\n [8, 5, 15, 9, 5, -14, -6],\n [-1, -2, 11, 0, 3, -1, 7],\n [-4, 9, 11, 9, 1, -15, -15],\n... | 155 | MATH |
[
{
"content": "Find the value at position (6, 4) of the inverse of matrix 1/252 * A where A =\n[[-7, 2, -7, 12, -10, -4, 13],\n [-10, 5, -11, 9, -1, 18, 17],\n [18, 13, 2, 10, -1, 4, 14],\n [-10, -15, -3, -16, -11, -3, -17],\n [0, 5, -3, -17, 13, -18, -1],\n [13, -10, -16, 5, -8, 9, -3],\n [10, -7, -15, 7, -15, ... | 3 | 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, 0, 7, 13, -2, -3, 14],\n [0, -16, -4, 2, -2, 2, 6],\n [7, -4, -11, 10, -8, 4, -4],\n [13, 2, 10, -13, -... | -7 | 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, 6, 7, 14, -11, -6, 7],\n [-2, 5, 5, -7, 12, -3, -3],\n [11, 9, -16, 14, 5, 11, 9],\n [-17, -6, 18, -9, -6, 0, -13],\n [-1, -10, -2, -15, -1... | -31 | MATH |
[
{
"content": "Find the value at position (5, 5) of the inverse of matrix 1/252 * A where A =\n[[2, -12, -8, 10, 18, 9, -15],\n [-15, 8, -13, 15, -1, 11, 14],\n [1, 17, -14, 16, 0, -7, 7],\n [0, -8, 1, -10, 1, 8, -14],\n [-9, -10, 6, -6, 13, -11, 8],\n [3, 9, -1, 4, 12, 15, -12],\n [-14, 2, -13, 16, 4, -16, 14]]... | 16 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[9, 7, 14, 13, 6, 5, 8],\n [0, 1, 14, -14, 10, -14, -2],\n [0, 0, 3, 12, -18, -4, 0],\n [0, 0, 0, 7, -13, -17, 10],\n [0, 0, 0, 0, -14, -9, -13],\n [0, 0, 0, 0, 0, 6, 16],\n [0, 0, 0, 0, 0, 0, 3]]\nRound your answer to the ... | -8878 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 9, -12, 15, -17, -10, -4],\n [12, 17, -4, 14, 12, 8, -17],\n [-10, -18, 0, -10, -17, 18, -18],\n [-7, 7, -9, -... | -16 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-10, 0, 1, 9, 13, 15, -3],\n [0, -8, -15, -1, -13, 13, -14],\n [0, 0, -2, 18, -4, 16, -11],\n [0, 0, 0, -5, 4, 1, -13],\n [0, 0, 0, 0, -17, 8, 13],\n [0, 0, 0, 0, 0, -2, -9],\n [0, 0, 0, 0, ... | 6039 | 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[[15, -16, 10, 16, -9, -18, -18],\n [0, 3, 0, 16, -13, 15, -4],\n [0, 0, 3, 10, -5, 11, -4],\n [0, 0, 0, 3, 14, 4, -12],\n ... | -165360 | 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, -6, 3, -4, 1, -8, -5],\n [-6, -14, 5, -6, -6, -13, -11],\n [3, 5, 17, 9, -2, -8, -7],\n [-4, -6, 9, -8, 10, 2, -2],\n [1, ... | 61 | 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, -6, -14, -5, -12, -13, -7],\n [-3, 13, -8, -15, 10, 15, -10],\n [-9, -11, 17, 13, -13, -13, 8],\n [-17, -10, -14, 15, -5, ... | -21 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[12, 10, 2, 13, 9, 2, 16],\n [0, -2, 10, -17, 14, -15, 6],\n [0, 0, 10, 18, -11, 1, -13],\n [0, 0, 0, 1, -15, 3, 14],\n [0, 0, 0, 0, -8, 18, 3],\n [0, 0, 0, 0, 0, -4, 7],\n [0, 0, 0, 0, 0, 0, 4]]\nRound your answer to the n... | -2690 | 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[[7, 14, 4, 0, 14, 4, -1],\n [14, -16, -8, 10, 10, -4, -8],\n [4, -8, -3, -7, -14, 4, -14],\n [0, 10, -7, 6, -4, -11, 10],\n [14, 10, -14, -4, -17, -4, 6],\n [4, -4, ... | 2461 | 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, 17, -1, 10, 12, -6, 11],\n [0, -13, -17, -11, -9, 3, -9],\n [0, 0, -15, 0, 1, -15, 7],\n [0, 0, 0, -13, 8, -3, -3],\n [0, 0, 0, 0, 1, -10, 2],\n [0, 0, 0, 0, 0, -12, 3],\n [0, 0, 0, 0, 0,... | -328 | 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, 14, -13, 3, 0, 3, 12],\n [0, 11, -15, 7, -12, -7, -18],\n [0, 0, -11, 14, -15, -13, -16],\n [0, 0, 0, 18, 8, -14, -2],\n [0, 0, 0, 0, -17, -9, 0],\n [0, 0, 0, 0... | 2884 | 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[[16, 15, -16, -17, 8, -17, -14],\n [2, -12, 6, -18, -10, -17, -16],\n [18, -15, 2, 7, 18, -5, -9],\n [7, -9, 18, -1, 8, -2, -9],\n [-8, 5, 0, -3, 4, -7, 0],\n... | -44 | 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, -2, 11, -17, -4, 4, 7],\n [-8, 5, -10, -5, 5, -12, -9],\n [14, 14, 8, -11, -5, -12, -1],\n [7, -4, 14, ... | -2 | 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, -14, 4, -16, 18, -9],\n [8, -12, 10, -13, -10, -11, -5],\n [-10, -8, -8, 16, -8, 17, -16],\n [0, -11, 9, -18, 11, -8, 10],\n [12, -9, 16, 10, 18, -17, -18],\n [13, 5, -17, -16... | 8 | 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, 12, -8, -15, -1, 10, 12],\n [0, 8, 11, -8, -5, -15, 17],\n [0, 0, 14, 2, 5, -6, 15],\n [0, 0, 0, 1, 10, -8, -11],\n [0, 0, 0, 0, -10, -9, 6],\n [0, 0, 0, 0, 0, 8, -1... | 303 | 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[[11, 4, -12, -5, -3, -14, 8],\n [4, -13, -4, -6, -16, 4, 6],\n [-12, -4, 7, 0, -5, 11, -2],\n [-5, -6, 0, -18, -2, 8, 7],\n [-... | -26 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, 5, -9, 6, 9, -1, -5],\n [0, 1, 6, -7, -10, -10, 6],\n [0, 0, -17, 6, -1, 5, -1],\n [0, 0, 0, -13, -3, 4, 9],\n... | 21 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, 10, 2, 11, -6, 10, -4],\n [10, -12, 1, 10, -12, -14, 8],\n [2, 1, -18, 6, 4, -5, 2],\n [11, 10, 6, 6, -9, 1, -6],\n [-6, -12, 4, -9, -13, 6, 3],\n [10, -14, -5, 1, 6, -15, -6],\n [-4, 8, 2, -6, 3, -6, -14]]\nRound your... | -94 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 6, -18, -16, 2, 9, -16],\n [13, 13, 11, -6, 15, -15, -1],\n [13, -5, 13, -13, -2, -11, 16],\n [5, -16, -2, 17, ... | -45 | 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, 8, 5, 16, -15, 7, 17],\n [0, 15, -6, -18, -18, -10, -8],\n [0, 0, 17, -4, -17, -9, -8],\n [0, 0, 0, 17, 10, 13, 14],\n [0, 0, 0, 0, 18, -5, 3],\n [0, 0, 0, 0, 0, -1... | 10 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-9, -16, -7, -6, 15, -18, 6],\n [0, 6, -13, -15, 7, 7, 7],\n [0, 0, 9, -17, 2, -5, 18],\n [0, 0, 0, -18, 3, 6, 11],\n [0, 0, 0, 0, -16, -11, 6],\n [0, 0, 0, 0, 0, -9, 8],\n [0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the... | 39 | 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[[6, 1, -2, 3, 14, 7, 8],\n [0, 4, -3, -5, -5, 7, 8],\n [0, 0, 8, -4, 6, -1, 11],\n [0, 0, ... | 2035 | 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[[18, -14, -1, -8, -11, 1, -8],\n [8, 10, 6, 0, -17, -17, -12],\n [12, 14, -8, -6, -9, 1, 2],\n [-5, 5, -12, -14, -13, 16, -10],\n [-18, 1, ... | 713 | 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, -5, 4, 5, -3, 2, -2],\n [-5, -10, 14, 6, -8, -10, 10],\n [4, 14, 15, -5, 16, -6, 14],\n [5, 6, -5, -10, -2, -14, 11],\n [-3, -8, 16, -2, -18, 8, 6],\n [2, -10, -6, -14, 8, 9, -12]... | -126 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -7, -5, -11, -17, 15, 5],\n [0, -9, -12, -18, -9, -14, 2],\n [0, 0, 12, 8, -13, 12, 17],\n [0, 0, 0, 3, -6, 0, ... | -9 | 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[[-8, 3, -5, 9, -15, -3, 4],\n [-6, 1, -14, 0, 2, -14, -5],\n [17, -13, -14, 5, 10, 10, -17],\n [-13, 15, -7, 3, -15, -13, ... | -24 | 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, -15, -9, 13, -18, 4, -2],\n [0, 8, -4, -12, 14, -14, 15],\n [0, 0, -17, -3, -2, -7, -14],\n [0, 0, 0, 1, -10, -3, 16... | -2297 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[5, 4, 1, 14, 8, 10, -12],\n [4, 6, 2, -2, -4, -8, 1],\n [1, 2, 3, 6, 10, 0, 0],\n [14, -2, 6, -11, 10, 4, -8],\n [8, -4, 10, 10, 12, -2, 2],\n [10, -8, 0, 4, -2, 11, -1],\n [-12, 1, 0, -8, 2, -1, 9]]\nRound y... | -57 | 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[[3, 0, 5, 9, -6, -10, -10],\n [2, 5, 12, 10, -9, -15, -16],\n [-6, 2, -11, -10, -18, -5, -7],\n [17, 3, 17, ... | -237 | 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, 18, 17, -9, -13, -3, 6],\n [0, 12, -11, -2, -5, 11, -1],\n [0, 0, 12, 14, 4, -14, -4],\n [0, 0, 0, 9, -13, -14, 6],\n [0, 0, 0, 0, 12, -4, ... | 22 | 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[[0, 4, 6, -12, -11, -16, 4],\n [14, 9, 3, 16, 15, 11, 17],\n [-5, -10, 3, 9, -5, -4, 18],\n [5, 15, -16, 4, 1, -4, -3],\n [-12, 14, 0, -1, -1, -16, -16],\n [17, -3, 4, 4,... | -46 | MATH |
[
{
"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[0, 0, -14, 0, 10, -2, 4],\n [0, -12, 2, -9, 6, -6, -14],\n [-14, 2, 5, -2, 3, 8, -13],\n [0, -9, -2, 12, 2, -10, 10],\n [10, 6, 3, 2, 12, -13, -16],\n ... | -2 | MATH |
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