messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
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[
{
"content": "Calculate the inverse matrix of 1/450 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[[25, -6, -6, -7, 25, -8, -13, -9, 7],\n [0, -21, 2, -1, -6, -5, -13, -20, 3],\n [0, 0, 3, ... | 855 | MATH |
[
{
"content": "Find the value at position (3, 6) of the inverse of matrix 1/450 * A where A =\n[[-21, 11, -24, 12, -19, -25, -23, -6, -24],\n [0, 17, -5, 19, 6, 22, -6, 17, 24],\n [0, 0, 7, -2, -8, -6, 6, -21, -24],\n [0, 0, 0, -4, 13, -4, -15, -15, 19],\n [0, 0, 0, 0, 18, 2, 16, -4, 14],\n [0, 0, 0, 0, 0, -19, ... | -8 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[6, 11, 18, 3, -4, -24, 24, -17, 3],\n [7, -16, 2, 20, 20, 13, -14, -4, -20],\n [19, 14, -3, 8, 16, 12, -10, -16, 21],\n [-5, -16, -15, -5, -1, 8, 5, 1, -1],\n [16, 6, 18, -15, 21, 0, 10, 11,... | -327 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-25, 12, 24, 19, 8, -7, 8, 10, -22],\n [0, -9, -10, -5, 2, -18, 3, -20, 4],\n [0, 0, 5, -1, -3, 17, -5, -10, -22],\n [0, 0, 0, -20, 1, 25, 10, 10, -2],\n [0, 0, 0, 0, 15... | -66 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 8) of the inverse. Round your answer to the nearest integer:\n[[10, -17, -16, -23, 23, 3, -19, 0, -18],\n [0, -13, 9, -7, 20, -4, -10, -11, -24],\n [0, 0, 4, -19, 5, 15, 15, 23, 9],\n [0, 0, 0, -16, 4, 6, -23, -16, ... | -93 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-16, 12, 10, -7, 14, -20, -2, 5, -12],\n [12, 7, -14, -18, -4, 5, 7, 2, -1],\n [10, -14, -18, -17, 10, 6, 4, -22, -2],\n [-7, -18, -17, -6, -18... | -337 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 1) rounded to the nearest integer?\n[[1, -6, 7, 5, -2, 11, -20, -2, 14],\n [-6, -3, 2, -16, -12, 19, 2, 2, 5],\n [7, 2, -17, -16, -19, -3, -4, -8, -8],\n [5, -16, -16, -13, -2, -18, 5, -2, -8],\n [-2, -12, -19, -2, ... | 3 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[-4, 17, 2, 22, 14, 8, -4, 10, 2],\n [17, 10, -11, 17, -4, -15, 14, 2, -16],\n [2, -11, -1, -6, 12, 18, 8, 0, 18],\n [22, 17, -6, -9, 15, 2, -2, 9, -4],\n [14, -4, 12, 15, -19, 4... | 16 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-1, -5, 10, -13, 20, -17, 9, 20, 10],\n [23, 21, 18, 20, 25, -16, -21, 5, -2],\n [6, 23, 23, -23, -10, 15, 23, -6, ... | 3 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[19, 22, -24, 23, -17, 0, -3, 25, 2],\n [-20, -22, 4, 21, -8, 4, 1, 18, 5],\n [18, 23, 13, 4, 11, -14, -9, 8, 2],\n [-22, 8, 20, -12, -13, 23, 23, 24, -... | -2 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, -20, 10, 4, -8, 15, 8, -2, -2],\n [-20, 13, -4, 4, -2, -4, -12, 10, 15],\n [10, -4, 24, 0, 2, 6, -10, 14, 2],\n [4, 4, 0, -8, 7, 10, 14, -3, -2],\n [-8, -2, 2, 7, 8,... | -107 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-20, 19, -12, 2, 7, -1, 14, -8, 20],\n [8, -14, 1, -2, 7, -11, 17, 6, 24],\n [-9, 9, 21, ... | -68 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 9, -18, -12, -4, -5, 2, 0, -7],\n [9, -7, 4, 20, -16, -5, -18, 20, 4],\n [-18, 4, -8, 2, -6, 0, -20, -3, -7],\n ... | -5 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[1, -3, -10, 5, -14, 7, 12, 19, 6],\n [0, 24, 23, 25, -3, 6, -11, 14, 15],\n [0, 0, 17, 24, 23, -4, 12, 8, -25],\n [0, 0, 0, -2, 20, -2, 22, -12, 0],\n [0, 0, 0, 0, 10, -2, 0, 3, 22],\n [0, 0, 0, 0, 0, -2... | 220728 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, 24, -21, -20, 16, 25, -16, -20, -16],\n [0, -5, 18, -22, -13, -16, -10, -7, -20],\n [0, 0, 20, -16, 14, -23, 23, -7, 9],\n [0, 0, 0, -7, 24, 18, -11... | -75981 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -4, 0, 8, 12, -3, 1, -9, -3],\n [-4, 16, 19, -22, 10, -20, 16, 2, -16],\n [0, 19, 5, -9, -8, 2, -14, -12, -10],\n [8, -22, -9, 13, 2, 0, -16, -6, -18],\n [12, ... | 688 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-25, 14, -17, 5, -2, 19, 23, -4, -17],\n [0, -3, -6, 16, -5, 1, -21, -9, 8],\n [0, 0, -16, 18, -24, 21, -1, -23, 8],\n [0, 0, 0, -15, 3, -10, 13, 3, -13],\n [0, 0, 0, 0, -18, -19, -21, -20, 25],\n [0, 0, 0, 0... | -380 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-21, -18, 16, 19, -17, 13, -6, 25, -15],\n [0, -4, -10, 16, 12, 16, -16, -1, -7],\n [0, 0, -23, -9, -12, -16, -20, 5, 5],\n [0, 0, 0, 18, 20, 0, -24, 16, -22],\n [0, 0, ... | -227 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[5, 21, -18, -11, -4, 6, -21, 18, 18],\n [-17, 15, -11, 21, 18, 11, 7, -4, 25],\n [-15, 24, -20, -9, 20, 18, -21, 13, 22],\n [-17, 3, -3, 21, 10, 5, -6, -3, -19],\n [20, 10, -22, -2, -12, -1, -19, -11, 18... | 670 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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, -24, 17, -21, 2, -13, 10, -17, 13],\n [0, 1, -13, 16, 13, 24, 2, -8, 8],\n [0, 0, 19, -3, 8, 10, -17, -... | 1102 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-19, 0, -13, 16, -7, 4, -2, 6, 7],\n [0, -22, -6, -2, 9, 10, -3, 1, 4],\n [-13, -6, 8, -10, 3, 1, 16, 4, -1... | -445 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-15, 8, 1, 24, -4, -23, 24, 22, 14],\n [0, -20, -1, -24, -10, 15, 25, -5, -11],\n [0, 0, 17, -6, 18, 5, -11, 22, 2],\n [0, 0, 0, -3, -23, 19, 18, -18, -24],\n [0, 0, 0, 0, 10, 21, -22, 18, -... | 901 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[8, 4, 14, 5, 4, -15, -3, -7, -2],\n [4, -10, -1, 14, 13, 0, -18, 2, -8],\n [14, -1, 17, 6, -23, 4, 1, -2, 16],\n [5, 14, 6, 17, -10, -10, 16, 8, -16],\n [4, 13, -23, -10, 20, -12, 0, 10, -4],\n [-15, 0, 4, -1... | -29 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-3, -12, -11, 12, 1, 10, 0, 6, -6],\n [-12, 11, 10, 8, -18, -13, -14, -12, 8],\n [-11, 10, 2, 14, 4, -2, 11, -3, -15],\n [12, 8, 14, -18, 8, -14, -19, 3, -11],\n [1, -18, 4, 8, -22, 1... | 391 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -2, 7, 20, 16, 15, 2, 2, 4],\n [-2, -22, -3, -20, 0, -10, -6, -1, 6],\n [7, -3, -18, 16, 5, 10, -17, 11... | 258 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-23, 10, -10, -15, 2, -6, 8, -2, -14],\n [10, 18, 18, 0, 0, 1, 7, -7, -12],\n [-10, 18, -24, 16, 18, -3, 11, -10, 3],\n [-15, 0, 16, 7, 0, -8, 11, -14, 8],\n [2, 0, 18, 0, -6, 4, -2, -2, 4],\n [-6, 1, -3, -8, 4, -24, -8, -... | -2899 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-11, 5, 18, -4, -14, -16, -5, 21, 5],\n [0, -16, -7, -3, 20, -16, 23, 1, 17],\n [0, 0, -15, -18, -7, -10, -22, -12, -4],\n [0, 0, 0, 9, 10, 19, 23, 4, -5],\n [0, 0, 0, 0, -18, 9, 3, 16, -19],\n [0, 0, 0, 0, 0, -12, -14, -1... | -249 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, 22, 12, 0, 17, 23, -8, 1, -4],\n [22, -6, -6, 2, -8, -15, -17, 22, 6],\n [12, -6, 9, -16, 6, 10, 6, 17, -10],\n [0, 2, -16, 6, 5, -9, -4, -11, 8],\n [17, -8, 6, 5, -... | -3 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[17, 13, 20, -22, 14, 18, -13, 15, -17],\n [-24, 9, -14, -9, -22, -12, -5, 15, -18],\n [7, 19, 2, -23, -12, -7, -20, 10, -6],\n [-25, -16, -13, -14, -15, 10, -9, 21, 3],\n [-23, 3, -16, 20, -7, -22, 20, 1... | 4898 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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, 5, -13, 4, 6, -21, -14, 13, 15],\n [0, -22, 16, 22, 17, 3, 15, -21, -15],\n [0, 0, 23, 2, -4, -15, -5,... | 278 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[-11, 10, -2, 14, 3, 24, -12, -24, 22],\n [-4, 21, -20, -17, -14, 16, 13, -21, 14],\n [18, -25, -16, -15, 1, -3, -6, -21, -13],\n [24, -16, 23, 25, 10, ... | -40 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[25, 14, -4, -18, 16, 2, 24, 21, 6],\n [0, -5, 0, -12, -11, -12, -14, 10, -23],\n [0, 0, 13, 25, 20, -25, 13, -1, 5],\n [0, 0, 0, -13, -18, -17, -11, -1... | -35 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[18, 6, 2, -22, 13, 19, -18, -12, 4],\n [-23, -24, -16, -20, -19, -10, -20, -10, 1],\n [-14, -4, -11, -4, 9, 22, 24, -11, -3],\n [12, 23, -24, -24, 23, -7, -21, -22, 2],\n [-8, 14, 15, 24, 5,... | -53 | MATH |
[
{
"content": "Find the inverse of 1/450 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[[-24, -6, 21, -6, -14, -9, -8, 14, -2],\n [0, 11, 15, 4, -6, -3, 11, -16, 7],\n [0, 0, -10, 24, 2, -14, -6, 21, -8],\n [0, 0, ... | -265 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 8, 22, -18, -10, 14, -3, 6, -13],\n [0, 12, -25, -24, 13, -13, 1, -22, 15],\n [0, 0, -23, -3, -24, -10, -16, 2, 18],\n [0, 0, 0, 18, -... | 1860 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, 12, 23, -14, -19, 11, -10, 12, 14],\n [0, 14, 3, 13, -9, 25, 0, -6, 20],\n [0, 0, 13, 11, -7, -5, 6, 2, 13],\n [0, 0, 0, -11, 2, -5, -10, -3, 0],\n [0, 0, 0, 0,... | 6010 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-14, 23, -23, -6, 24, -14, -2, -10, -16],\n [0, 15, -12, -12, -4, -22, 21, 8, -8],\n [0, 0, 14, 5, 16, -6, 10, 16, -16],\n [0, 0, 0, -16, -19, -4, -3, ... | -4151 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[5, 6, -11, 13, 5, -23, 25, 6, -16],\n [0, 1, 22, 20, 14, 17, 5, 25, 8],\n [0, 0, -19, -18, -9, 18, 24, 13, 15],\n [0, 0, 0, 4, 25, 24, -11, -22, -13],\n [0, 0, 0, 0, 23, -16, 4, 0, 18],\n [0, 0, 0, 0, 0,... | 331036 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 12, 2, -17, -3, -4, 8, -11, 2],\n [12, 3, -17, -5, -6, 12, 13, 14, -19],\n [2, -17, 5, -8, 14, 3, -18, 0, -8],\n [-17, -5, -8, 3, -14, 1, 6,... | -17 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 9) of the inverse. Round your answer to the nearest integer:\n[[21, 19, -8, 23, 7, -11, -2, 10, 8],\n [0, 25, 14, -4, -10, 14, 16, -10, -21],\n [25, -20, 16, -2, 4, 11, 6, -7, 25],\n [19, 2, 21, -18, 17, -25, -22, -... | 1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[12, -22, 20, 9, -16, 12, 24, 4, 16],\n [-17, -10, -22, 0, 3, 2, -15, 2, 18],\n [6, -2, 25... | 31 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-25, -17, -4, 25, 14, 1, -17, -19, 10],\n [22, 12, 24, -24, 17, -21, -9, 11, 9],\n [25, -18, 17, -23, -23, -25, -2, 19, 4],\n [16, 0, 12, 17, 14, 25, 1... | -225 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, -4, -22, -3, -19, 18, -15, 13, 16],\n [15, 8, -21, 16, -1, 2, -12, 1, -10],\n [1, -24, -7, -3, 15, -12, 21, 25, 0],\n [-18, 1, 21, 14, 2, -... | 129 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-18, -17, -24, -24, 1, 22, 13, 10, -21],\n [-25, -4, -16, 19, -2, -11, 7, 24, -3],\n [-12, -8, -1, -4, 18, 18, 11, -19, 0],\n [-2, -13, 15, -20... | 15 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 12, 20, 4, 0, 6, 8, -6, 9],\n [12, 25, -8, -2, 16, 2, 8, 2, -8],\n [20, -8, 15, -8, 1, -11, 6, -19, -6],\n [4, -2, -8, 12, -20, -9, 4, 2, 9],\n [0, 16, 1, -20, 10, ... | 132 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (9, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, 12, 19, -5, 3, 8, -14, 13, 6],\n [0, -9, 6, -18, 12, 3, 5, -7, -17],\n [0, 0, 24, 25, 13, 14, 5, -7, 7],\n [0, ... | 0 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-9, -22, 24, -8, 2, 24, -10, 17, -18],\n [0, -8, 24, 3, 14, -10, 4, 23, 8],\n [0, 0, -4, 21, -1, -4, 2, 13, 7],\n [0, 0, 0, -14, -9, 10, -10, 13, -3],\n [0, 0, 0, 0, 21, 0, 10, -23, -16],\n ... | -5293 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-14, -2, 25, 18, -4, 0, -4, -19, -11],\n [22, 4, -22, -20, 22, 21, -24, 5, -2],\n [9, 21, 5, -1, -18, -14, -24, -11, 14],\n [6, -15, -9, -5, -4, 7, 3, -11, -5],\n [-24, 16, 12, -23, -1, -13, -2, 5, -11],\n [-20, 15, -16, -... | -38 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-1, -20, -10, 18, 2, 10, 7, 4, 10],\n [-1, -13, 13, -11, 12, 4, -12, 24, -22],\n [-25, -23, 19, 24, 10, -22, 17, -12, -1],\n [13, -23, -19, -18, 18, -19, 22, -1, -9],\n [0, -22, 23, -8, -22,... | 48 | MATH |
[
{
"content": "Find the inverse of 1/450 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, -13, -1, -2, 15, -10, 17, 15, 16],\n [0, -5, 5, -11, 19, 23, 10, 17, -25],\n [0, 0, -23, -11, 7, 6, -3, 0, 22],\n [0, 0, 0, 3, -20, 21... | 302504 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-21, -6, 25, -19, 17, -3, -25, 13, -23],\n [0, -23, -20, 5, 1, 3, -11, 10, -21],\n [0, 0, -1, 6, -5, 22, -9, -17, 0],\n [0, 0, 0, -3, -15, -16, -3, -21, 0],\n [0, 0, 0, 0, 8, -23, 24, 6, 0],\n [0, 0, 0, 0, 0,... | -340 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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, 20, -8, 20, -10, 21, -6, 13, -18],\n [0, 12, 3, -13, -9, 14, 17, -9, -17],\n [0, 0, -2, -5, 20, -... | 17694 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, -24, -8, 2, 21, 16, 23, -19, -15],\n [0, 17, -2, -11, 5, 25, -7, -16, 22],\n [0, 0, -24, 3, 16, -16, 16, -17, 24],\n [0, 0, 0, -2, 11, 17, -20, -18,... | 63347 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 22, 24, 15, -18, 17, 9, -21, 5],\n [0, 5, 11, -18, -20, -3, -10, 18, 23],\n [0, 0, 6, 23, -23, 24, -10, 8, -13],\n [0, 0, 0, -2, -23, 7, 4, ... | 27 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 9, 4, 16, 7, 9, 10, 10, 13],\n [9, -4, -12, 20, 0, -2, -4, -2, -4],\n [4, -12, -2, 15, -18, 4, -1, 0, -6],\n [16, 20,... | 45 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[20, 23, -3, -1, -1, -23, -22, 4, 7],\n [3, -22, -12, -5, -19, -5, -19, -25, 8],\n [-3, -23, -8, 17, -14, -12, 15, 2, 16],\n [19, -2, -2, -23, -17, -2, -24, 14, 2],\n [-19, -17, 19, 13, 13, 7... | 80 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[22, 23, 14, -11, 4, -5, -18, -19, 15],\n [8, 16, 11, 22, 6, 7, -20, 16, -16],\n [0, 25, 19, 0, -7, 9, 19, -22, -1],\n [-18, -14, -2, -2, -9, -1, 7, 1, -24],\n [-17, 7, -7, 23, -21, 21, -6, -2, 5],\n [18, -22, 6, 21, 9, -12... | -85 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -14, -8, 6, -15, 9, 4, 6, -2],\n [-14, 8, 6, 14, 16, 9, -5, 3, 8],\n [-8, 6, -14, -2, 8, -11, -14, -12, -7],\n [6, 14, -2, -9, -10, 2, -7, 0, 13],\n [-15, 16, ... | 579 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-22, -17, -18, 2, 6, -12, -6, -14, 3],\n [-17, -25, 7, -9, 16, -7, 2, -2, -16],\n [-18, 7, 23, 2, 10, -7, -3, -16, 2],\n [2, -9, 2, 2, -6, -3, 6, -2, 11],\n [6, 16, 10, -6, 1, -12, -2, 0, -14],\n [-12, -7, -7... | -49 | MATH |
[
{
"content": "Find the value at position (1, 5) of the inverse of matrix 1/450 * A where A =\n[[-23, 11, 12, 15, -22, 0, 13, 19, 16],\n [0, 16, -15, -15, 12, 12, -6, 0, 12],\n [0, 0, -12, 24, -1, 25, 16, 16, 13],\n [0, 0, 0, -21, -4, -15, 3, -19, -8],\n [0, 0, 0, 0, -19, 4, -22, 25, 4],\n [0, 0, 0, 0, 0, -16, -... | 47 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -7, -19, 21, 9, 0, 18, -3, 8],\n [0, -19, -15, 25, -18, -13, 6, 15, 8],\n [0, 0, 17, -2, 21, -5, -8, -12, -7],\n [0, 0, 0, 8, 23, 0, -... | 50218 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[25, -11, 9, -9, 22, -13, -4, 14, -5],\n [0, 20, -22, -19, -16, -11, 0, -10, 14],\n [0, 0, 12, -10, 8, 3, -8, -15, -14],\n [0, 0, 0, 12, 7, -17, -11, 2, -18],\n [0, 0, 0, 0, 16, 24, 24... | -1151 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, -1, 8, -6, -2, -6, 2, -2, 1],\n [-1, 2, -6, -6, -10, 6, -14, -4, 1],\n [8, -6, 9, -10, -21, -4, -2, 10, -8],\n [-6, -6, -10, -11, -8, 16, -8, -1, 15],\n [-2, -10... | 89189 | MATH |
[
{
"content": "Find the value at position (5, 2) of the inverse of matrix 1/450 * A where A =\n[[-13, 17, -5, -25, -22, -23, 24, -3, -10],\n [0, -13, 13, 5, -2, 21, -11, -21, 23],\n [0, 0, -15, -2, 19, -16, 21, 8, -15],\n [0, 0, 0, 7, -18, 23, 6, 14, 19],\n [0, 0, 0, 0, -20, -1, -1, 5, -12],\n [0, 0, 0, 0, 0, -2... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 0, 9, -16, 19, -4, -11, -2, -1],\n [0, 8, 4, -4, 6, 16, 16, -18, -2],\n [9, 4, 7, 18, 2, -2, 5, -4, -10],\n [-16... | 2 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, 2, 2, 0, 0, -1, 13, -10, 2],\n [2, 4, 10, 8, 1, 18, 0, -14, 22],\n [2, 10, 24, 0, 2, 8, -18, -16, -18],\n [0, 8, 0, -13, 16, -6, -2, 1, 5],\n [0, 1, 2, 16, 25,... | 550 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 7) rounded to the nearest integer?\n[[6, 6, 13, -5, 18, 16, 13, 20, 1],\n [0, 10, -18, -7, 3, -7, -21, -4, 9],\n [0, 0, -24, 16, -4, 22, 9, 13, -7],\n [0, 0, 0, 19, -6, 25, -19, -2, -23],\n [0, 0, 0, 0, 3, -3, -22, ... | -15 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-6, 16, 21, 1, 2, 5, 21, -19, -18],\n [0, -15, 22, 0, -1, -19, -6, 15, 25],\n [0, 0, -8, -18, 3, 14, -... | 89821 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (2, 9) rounded to the nearest integer?\n[[-19, -9, 16, -14, 4, 22, 8, -4, -5],\n [0, -14, -9, -10, -21, -7, 2, -9, -4],\n [0, 0, -11, -7, 21, 24, 0, 18, 18],\n [0, 0, 0, -16, -4, 21, -15, 0, -25],\n [0, 0, 0, 0, 19, -9,... | -284 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, -22, 6, 3, 4, -23, -21, -7, -18],\n [0, 5, 1, -13, 16, -20, -25, 4, -15],\n [0, 0, -10, -11, -21, -11, -25, -11, 10],\n [0, 0, 0, -4, 1, 8,... | -1033 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[19, 22, -25, 25, 10, -23, 8, -14, 19],\n [0, 24, 11, -1, -14, 25, 7, -17, -25],\n [0, 0, 2, -23, 12, 10, 18, 18, -21],\n [0, 0, 0, -22, -20, 25, 12, -20, -15... | -9883 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (4, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 7, -16, 18, -8, 7, 3, 5, -2],\n [0, -6, -20, -18, -12, -21, 10, 22, 12],\n [0, 0, -4, -18, -12, -19, -22, -7, ... | 143 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, -23, 14, -4, -8, 19, 4, -25, -6],\n [23, -21, -14, -15, -2, -8, -18, 3, -4],\n [19, -24, -3, -10, 18, -18, -22, -12, -17],\n [-15, 22, 12, 18, 25, -10, -13, 10, 18],... | -74 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[21, 18, 9, 25, 6, 25, 16, -10, -20],\n [-17, 14, -4, 22, -18, 6, 0, -8, 11],\n [-14, 12, 8, -22, -10, -2, -12, -9, 25],\n [5, -22, 24, 18, 8, 12, 12, -23, -18],\n [... | 2542 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (8, 1) rounded to the nearest integer?\n[[-22, 21, 4, 13, 25, -12, 22, 1, -13],\n [-6, 23, 23, -2, -16, -19, -9, -4, 18],\n [-15, 16, -3, -4, 14, 21, -8, 19, 0],\n [22, 4, -13, -22, 17, 1, 25, 14, -16],\n [18, 2, -5, -1... | -15 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (7, 8) of the inverse. Round your answer to the nearest integer:\n[[3, -16, -21, 23, 13, 8, 12, -16, -17],\n [6, -21, 9, -15, 16, -10, 1, -6, 25],\n [-25, 0, -15, -11, 13, 14, 22, -8, -2],\n [2, -1, -3, -15, 7, -10, 10,... | -21 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[15, -23, 11, -16, 16, 6, 10, 23, 1],\n [0, -7, 12, -25, 0, 20, -13, 9, -24],\n [0, 0, 2, 18, -24, -15, 22, 11, 0],\n [0, 0, 0, -23, -12, -10, 23, 25, 10],\n [0, 0, 0, 0, -15, 11, 17, 19, -5]... | -1813 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, 15, -5, 6, -14, 11, 14, 21, -19],\n [0, 19, 5, -25, -15, 19, 8, -7, -15],\n [0, 0, -18, 19, -18, 8, 14, 1, 3],\n [0, 0, 0, 11, -25, -17, -16, 4, 17],\n [0, 0, 0, 0, -2, 10, 7, 7, ... | -7045 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 4, 3, -4, -5, 17, -8, -14, 20],\n [4, 20, 0, -2, -2, -2, 10, -2, -8],\n [3, 0, -21, -3, -14, -4, 2, -5, 16],\n [-4, -... | 357 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 25, -15, 12, 25, -12, 2, 1, -4],\n [0, -2, -7, -2, 0, -1, 19, 18, 3],\n [0, 0, -15, -2, -2, -14, -19, 14, -9],\n [0, 0, 0, -11, 6, -3, -19, 12, 5],\n [0, ... | -66806 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-24, -12, -2, -4, 2, 17, -18, -11, 6],\n [-12, 13, 16, -2, -16, 6, 12, 18, -13],\n [-2, 16, -12, -4, 8, 16, 12, -1, -8],\n [-4, -2, -4, 24, -6,... | 172 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -10, 24, -16, 3, 1, 9, 16, 19],\n [0, -3, -23, 10, 19, -12, -22, 18, 22],\n [0, 0, -6, -9, 3, 13, 6, -22, -2],\n [0, 0, 0, -12, 14, 16, 12, 8, 20],\n [0,... | 151675 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-25, 4, -6, 8, 10, 4, -6, -12, 16],\n [4, 11, -8, 0, 5, -10, -1, 2, 11],\n [-6, -8, -17, 8, 10, -9, 4, -7, 2],\n [8, 0, 8, 24, -10, 11, 16, 6, 0],\n [10, 5, 10, -10, -3, 12, -6, 0, -13],\n [4, -10, -9, 11, 12, -9, -5, 18, ... | 111 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[21, 5, -9, -11, 0, 1, -8, -20, 5],\n [5, -13, -12, 10, 16, 0, 8, 1, 10],\n [-9, -12, 6, -18, 20, 4, -6... | 742 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-25, 10, 4, -3, 11, 2, 23, -21, 10],\n [0, -16, -21, -12, -2, 2, -5, 19, 25],\n [0, 0, -6, 25, 6, 25, 12, 14, 16],\n [0, 0, 0, 25, 18, 2, -24, -9, 13],\n [0, 0, 0, 0, -8, 14, 8, 17, -25],\n ... | 397 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-15, 6, -6, 11, 5, -4, 12, -12, -2],\n [6, -20, 4, -2, 12, -2, 14, 15, -12],\n [-6, 4, -7, -2, -2, -12, 0, 1, 1],\n [11, -2, -2, -15, -6, -4, 0, -1, -2... | 195 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -14, -9, -2, 10, 2, 2, 5, -4],\n [-14, -5, 13, -11, -11, -1, -22, 6, 13],\n [-9, 13, -7, -6, -4, 2, 20, -10, -6],\n [... | -36 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 14, -6, 8, -18, 6, 4, 3, -21],\n [0, -14, 13, 1, -13, 21, -16, 10, 5],\n [0, 0, 19, 10, 0, 18, -6, 8, 11],\n [0, 0, 0, 5, -24, -1, 12, -23,... | -81 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -17, 23, 24, -19, 1, -23, -4, -10],\n [-18, -21, 23, 4, 2, 25, 1, 24, -4],\n [4, 11, -19, 24, 4, -13, -4, -15,... | -11 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[20, -9, -17, 5, 9, -23, -13, 11, 12],\n [0, -20, 3, 23, -17, 10, -3, -11, 24],\n [0, 0, -19, 21, -1, 11, -3, -15, 20],\n [0, 0, 0, 13, -25... | 3634 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, -16, 18, 8, 7, -16, 16, 0, 16],\n [-1, -24, 0, -6, -23, 6, -25, -2, 24],\n [17, 18, 7, 12, 22, 9, -9, 22, 17],\n [22, 18, 7, -15, -3, 12, 6, -7, -14],\n [2, -24, -1... | 37 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[-2, -12, 23, 15, 25, -23, 21, -5, 0],\n [0, 4, 25, -22, -12, -8, -14, 12, 16],\n [0, 0, -25, -23, 13, 9, -11, 12, -10],\n [0, 0, 0, -15, 2, 1, 12, -8, 21],\n [0, 0, 0, 0, -24, -... | -96 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-24, 16, 17, 0, -23, -2, 0, -18, 21],\n [11, -18, -8, -8, -14, 10, 14, -24, -6],\n [-23, 14, 18, 8, 23, 20, 20, -20, 14],\n [-16, -2, -8, 7, 13, -19, 19, 22, 18],\n... | 943 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-19, 14, -4, 2, 16, -11, 23, 12, 11],\n [14, -8, 14, 8, 4, 4, -4, 6, -6],\n [-4, 14, -3, -14, 18, -2, -6, -4, -12],\n [2, 8, -14, 11, -4, -4, -2, 9, 14],\n [16, 4, 18, -4, 20, 0, -13, -10, 18],\n [-11, 4... | 560 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 0, 14, 3, -17, -8, -19, 16, -5],\n [-10, -23, 6, -16, 6, -18, 6, 24, -22],\n [3, -14, 11, 10, 25, -7, 11, 21, 5],\n [18, 0, 19, -20, 3, -9, -6, 16, 20],\n... | -74 | MATH |
[
{
"content": "Find the inverse of 1/450 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, -10, 0, -23, -3, -17, 25, -2, 7],\n [0, 2, -2, 17, 24, -19, 12, 18, -1],\n [0, 0, -25, -3, 21, 14, -8, 21, -18],\n [0, 0, ... | -98985 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[19, -4, 18, 8, -17, 7, 12, 8, 9],\n [21, 0, -19, 19, 22, 19, 1, -14, -9],\n [-5, 17, -4, 0, 13, -13, 16, 16, 19],\n [-3, 25, 4, -9, 1, -6,... | 3334 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 8) of the inverse. Round your answer to the nearest integer:\n[[-7, -10, -24, -25, -23, -2, 18, 12, -24],\n [-10, 3, 11, 18, -22, -12, -9, 18, 19],\n [-9, -6, 21, 3, 15, 0, 16, 12, -9],\n [-14, 2, -17, 6, 8, -10, 22... | -24 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[22, 4, 12, -18, -23, -15, -1, -21, -14],\n [4, 1, 17, -21, -6, -5, -23, 15, 24],\n [18, -22, -2, -19, -2, -15, -24, 18, 15],\n [-20, -19, 12, -8, 19, -17, 2, -7, -22],\n [-22, -13, 2,... | -18 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[20, 10, -19, -4, -20, -4, 3, -8, 22],\n [10, 12, 10, 4, 0, 8, 3, -10, 8],\n [-19, 10, -18, -2, 0, 6, 1... | 1558 | MATH |
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