messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1 value |
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[
{
"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[[13, 3, -11, 17, -18, -5, 13, -7, -3],\n [0, -15, -2, 10, 14, -2, -23, -4, -24],\n [0, 0, 4, 12, -24, -5, 7, -14, -4],\n [0, 0, 0, 1, 16, 2, -10, -11, 21],\n ... | -1868 | 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[[-3, 13, 19, -11, 17, 3, 10, -13, 6],\n [0, 25, -4, 2, -24, 16, 19, -20, 2],\n [0, 0, 18, -6, 4, -15, 2, -1,... | -119 | 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, -20, -4, -15, 22, -10, 7, -17, -20],\n [-10, 3, -23, -6, 10, -7, 0, -23, -7],\n [-6, 6, -19, 15, 7, 14, 13, -8, 14],\n [-25, -15, 2, -1... | 607 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 7) of the inverse. Round your answer to the nearest integer:\n[[7, -22, 7, -12, -5, 22, -6, -18, -19],\n [0, -9, 7, 22, -14, 25, -4, -4, 20],\n [0, 0, 12, 19, 25, -18, 1, 1, 8],\n [0, 0, 0, 2, 21, 7, -21, 22, -7],\n... | -88 | 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[[7, -17, 17, 22, 13, 3, 16, 0, 9],\n [24, -1, -2, -13, -19, 10, 19, -6, -25],\n [-18, 20, -10, -12, -14, 25, -3, -11, 2],\... | 747 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 13, -21, -4, 3, -23, -14, 0, -10],\n [25, 11, -4, 3, -12, 2, -21, 21, 23],\n [4, 20, -21, -14, -10, 0, 0, 22, ... | -11 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 4) rounded to the nearest integer?\n[[-9, 0, -18, 3, 0, -16, 0, 8, 25],\n [0, -19, -22, 24, 19, -15, 3, 10, -1],\n [0, 0, -16, 11, -17, -2, 9, 23, 9],\n [0, 0, 0, 23, 13, 6, -2, -3, 6],\n [0, 0, 0, 0, -3, -1, 9, 15,... | 0 | 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[[-21, 9, -3, 3, 17, -15, -8, 21, -14],\n [0, -16, 18, -9, 12, -19, 20, -13, 14],\n [0, 0, 24, 1, -24, -21, 3, 11, 12],\n [0, 0, 0, 19, -25, -4, ... | 98 | 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, -8, 21, 15, 23, -12, -11, 5, -25],\n [-23, -10, -3, -15, -14, -16, 6, -10, -18],\n [12, -14, -2, 2, -18, 2, 10, 0, -18],\n [24, 2, 2, 11, 15, 10, 1, -9, -17],\n [7, -6, -13, 2, 22, 3, -1... | 39 | 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, -6, -1, 8, -2, 4, 12, 12, -6],\n [-6, -7, -11, -12, -16, -11, 22, -9, 2],\n [-1, -11, -22, -6, 14... | 818 | 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[[8, 0, -23, 6, -2, 2, 13, -3, 12],\n [0, -3, -6, -1, -20, -5, 0, -16, -5],\n [-23, -6, -23, 0, -22, 10, 12, 14, 22],\n [6, -1, 0, -21, 4, 2, 4, -4, -2],\n [-2... | 120 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, 4, 8, -1, 20, -14, -4, -4, 2],\n [4, -1, 14, 8, -17, 6, -14, -5, -14],\n [8, 14, -1, 5, 0, 1, 10, 2, -11],\n [-1, 8, 5, -8, 22, 14, 0, 0, 5],\n [20, -17, 0, 22, 18, -14, 10, 14, -2],\n [-14, 6, 1, 14, -14, 11, -4, 4, -... | 473 | 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[[4, 16, 10, -20, -16, -20, -4, -8, 4],\n [16, 18, 1, -5, -2, -6, -2, 1, -4],\n [10, 1, -14, 4, -20, -8, -4, -1, 13],\n [-20, -5, 4, 17, -2, -1, 2, 16, -2],\n [-16, -2, -20, -2, -... | -1 | 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[[-21, -7, -12, 0, -22, -1, 19, 16, -1],\n [0, 14, -18, 13, 14, -12, 6, 25, 12],\n [0, 0, -11, 7, -1, -9, 7, 21, -24],\n [0, 0, 0, 25, 13, 25, -20, -20, -23],\n [0, 0, 0, 0, -11, 21, 3,... | 1171 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 10, 10, 0, 17, 1, -21, -6, -15],\n [-16, 14, 12, -20, -18, -3, 21, 0, 20],\n [17, -14, 0, -13, 14, -8, -1, 7, 2... | -8 | 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[[17, 18, 25, -2, -1, -19, -20, -2, 7],\n [0, 3, 17, -4, 0, 2, 24, -5, 23],\n [0, 0, -6, 15, 23, -6, -4, 2, 14],\n [0, 0, 0, 6, -13, 4, -3, 25, -7],\n [0, 0, 0... | 159 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-2, -3, -18, 21, 11, -23, 25, 7, 2],\n [0, -18, 8, 9, 6, -2, -12, 6, 20],\n [0, 0, -22, 11, -5, -12, 5, 22, -8],\n [0, 0, 0, 7, -3, -5, -7, 22, -7],\n [0, 0, 0, 0, -25, 21, -21, -6, -15],\n [0, 0, 0, 0, ... | 3696 | 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[[17, 20, -22, 0, 3, 19, 8, -3, 11],\n [-15, -20, -8, -5, 16, 10, 15, 12, 8],\n [-9, 11, -1, 12, -14, -3, 16, -4, -5],\n [1, 5, -20, 1, 14, ... | 1399 | 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[[14, 0, -8, 10, 7, 2, -2, -10, 9],\n [0, -23, 5, -2, 14, 9, 8, -6, 8],\n [-8, 5, -7, 0, 4, 19, -6, 4, 18],\n [10, -2, 0, -2, -14, 0, 2, 8, 0],\n [7, 14, 4, -14, -18, 0, -... | 115 | 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[[-2, -15, -13, 8, -1, -19, -22, -18, -6],\n [0, 25, 19, 20, -16, 17, 8, 0, 15],\n [0, 0, -20, -21, -21, 21, ... | -353 | 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[[-9, 16, 2, 9, 16, 4, 0, -9, -2],\n [16, 14, 8, 2, 12, 0, -7, 3, -12],\n [2, 8, 2, 8, 10, 12, -13, 8, 17],\n... | -72 | 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[[3, -4, -22, -6, 6, 10, 24, -22, 1],\n [0, -14, -4, -9, -16, -25, -4, 0, -8],\n [0, 0, 21, 3, -14, 10, 9, -14, -19],\n [0, 0, 0, -20, 21, -11, 6... | -169 | 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[[-2, -14, -8, -11, 18, -10, 1, -18, 20],\n [0, -9, 3, -18, -11, 1, 20, 24, -19],\n [0, 0, 18, -2, -23, ... | 9344 | 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[[-24, 7, 7, 15, -13, 4, 7, -13, 0],\n [-4, 13, -24, 12, 13, 0, 20, 24, -11],\n [8, 16, 18, 23, 14, -15, -23, -20, -17],\n [-20, -17, 13, 5, 6, 15, 24, -... | -32 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (4, 6) of the inverse. Round your answer to the nearest integer:\n[[-16, 14, 2, 6, 7, 8, -16, -13, 12],\n [14, -5, 2, -13, -10, 6, -17, 8, -3],\n [2, 2, 24, 6, 1, -6, -4, 4, 8],\n [6, -13, 6, 8, 14, -5, 12, 5, 18],\n [7... | 39 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[19, -3, 21, 5, -15, -16, -23, -12, -10],\n [-16, 3, -16, -14, 4, 15, -25, -21, -6],\n [-18, 17, -14, -25, -6, 2, 17, 11, 21],\n [11, -14, 11, 23, 23, 18, 2, 21, -11],\n [-20, 18, -6, 24, -12, -24, -17, 11, -6],\n [0, 3, -2... | -48 | 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, -4, -16, -18, -4, -6, 14, -20, -2],\n [-4, 21, 0, -13, 11, 12, -16, 6, 11],\n [-16, 0, 0, 1, 0, 14, 0, -11, -9],\n [-18, -13, 1, -22, 11, -... | -60 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 4) rounded to the nearest integer?\n[[-11, -5, -7, 3, -1, 7, 23, 6, 23],\n [9, 18, 12, 0, -15, 9, -18, 20, -12],\n [-16, -24, 20, -17, -23, -5, 0, -18, 22],\n [-24, -20, 2, 3, 0, -1, -14, -21, 8],\n [22, 11, -11, 18... | -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[[4, -12, 0, 21, -6, 0, 6, -11, 0],\n [-12, -19, 10, 17, -16, 6, -14, 13, 2],\n [0, 10, 16,... | 1187 | 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[[-16, -12, 4, 4, 3, -3, 14, -14, -13],\n [-12, -23, 4, 12, -2, 12, -19, 11, -8],\n [4, 4, -22, 7, 14, 1... | 2314 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 5) rounded to the nearest integer?\n[[-14, -9, -10, -14, -18, -6, -23, -10, 4],\n [0, -3, 2, 25, 14, -21, -6, 14, 18],\n [0, 0, -5, -6, -20, -4, -8, -18, 13],\n [0, 0, 0, -14, 12, 8, -12, 10, 7],\n [0, 0, 0, 0, 15, ... | 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, -24, 1, -24, 9, -8, -12, -6, -8],\n [0, -1, -24, -1, 7, 10, 5, -12, -25],\n [0, 0, 20, -23, 9, 15, -20, -1, -13],\n [0, 0, 0, 8, -22, -1, -11, -22, 19],\n [0, 0, 0, 0, -13, 5, -12, -6, -8... | 14617 | 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[[13, 14, -9, 11, 13, 3, 10, 12, 13],\n [24, 11, 9, -19, 1, 2, -4, -12, -19],\n [11, -4, -21, -24, 1, -5, 12, -11, -5],\n [-16, -3, 13, -21, -25, -13, -5, 0, 24],\n [... | 826 | 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[[-4, -18, 23, -11, -9, -3, -2, 19, -7],\n [-21, 6, 18, -25, -3, 11, -18, -13, -18],\n [-3, 17, -25, 19, 25, -2, 9, -2, -9],\n [-21, -6, -5, 14, 5, 20, 10, -15... | -19 | 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[[-10, 6, 6, 8, -15, -16, -11, -9, 14],\n [-8, -17, -1, 14, -12, -1, 24, -4, 4],\n [-6, -5, 18, 6, 25, 20, 23, -5, 9],\n [6, 4, 13, 23, -14, 15, 21, -8, -5],\n [-13, ... | 913 | 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[[-1, 11, 21, -18, 16, -10, -18, -25, 18],\n [0, -23, -25, -22, 14, 9, 6, 16, 8],\n [0, 0, -16, -5, 20, 13, 1, 1, -24],\n [0, 0, 0, -17, 10, -4, 16, 0, -14],\n [0, 0, 0, 0, -6, -15, -10... | -5886 | MATH |
[
{
"content": "Find the value at position (8, 9) of the inverse of matrix 1/450 * A where A =\n[[-8, 6, 8, 6, 6, 0, -14, 10, 4],\n [6, -14, 4, 10, -8, -3, -8, 0, 0],\n [8, 4, 23, -1, 6, 24, 10, 12, -8],\n [6, 10, -1, -20, -17, -14, 24, 16, -10],\n [6, -8, 6, -17, -15, 0, -12, -3, 2],\n [0, -3, 24, -14, 0, 17, 20... | -14 | 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[[-2, 10, -20, 15, 20, 18, 5, -6, -2],\n [0, 10, -5, 4, -2, 18, 16, 4, -4],\n [0, 0, 9, 2, -12, -16, -10, -10, 5],\n [0, 0, 0, -20, 18, -17, 19, 10, 17],\n [0,... | -331 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[-15, -24, 21, 18, 18, -17, -5, -2, 8],\n [0, -23, -14, 2, 4, 0, 22, -5, 2],\n [0, 0, -5, 9, 8, 15, 25, 21, -8],\n [0, 0, 0, -4, -9, -21, 18, -15, 4],\n... | 44 | 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, 3, -8, 6, -3, -3, -12, 13, -16],\n [3, 23, 10, 4, 4, -2, -12, 8, 10],\n [-8, 10, -7, ... | 51 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-22, 3, -8, 6, 8, -10, -20, 0, 21],\n [3, 21, 7, 6, -18, 1, 0, 6, 1],\n [-8, 7, 3, -13, 5, -4, 12, 10, 3],\n [6, 6, -13, -19, 10, 7, -10, 5, 4],\n [8, -18, 5, 10, -24, -11, -5, -6, 18],\n [-10, 1, -4, 7, -11, -4, -4, 0, 7]... | -1461 | 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[[-24, 25, -15, -13, -16, -12, -8, 25, -17],\n [0, 2, -23, -6, -20, 1, -24, 3, 12],\n [0, 0, 4, 14, -24, -9, 15, -14, 9],\n [0, 0, 0, -11, 0... | 159189 | 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[[18, -5, 18, -15, 13, -22, 25, -25, 2],\n [0, 9, -13, 21, 8, -15, 10, 25, -9],\n [0, 0, 14, -4, -2, -7, 11, ... | -12 | 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, 19, 9, 22, -17, -18, 19, -9, -9],\n [23, 7, 6, -18, -7, 12, -23, -21, -13],\n [21, 20, 5, -10, 24, 6, ... | 0 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 6) rounded to the nearest integer?\n[[-23, -12, -13, 19, 6, 8, 19, -7, 12],\n [0, -24, 14, -9, 8, 16, -10, 12, -24],\n [0, 0, -13, 21, 5, 8, 13, -23, -18],\n [0, 0, 0, 3, 13, 13, -25, -9, 15],\n [0, 0, 0, 0, -7, -1,... | -23 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[0, -8, 6, -4, 12, -9, -3, -2, 24],\n [-18, 15, -20, -21, 18, 3, 2, -15, -25],\n [17, -7, -17, 1, 8, 18, -22, 10, -8],\n [-11, 25, -13, -7, 23, -20, 22, -14, 25],\n [11, -9, -3, 0, 3, 7, 1, -1, -16],\n [21, -3, -5, -5, 17, ... | 13 | 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[[18, 10, -4, -2, -6, -12, -6, 4, 5],\n [10, -24, 4, -4, -2, 15, -10, 4, 10],\n [-4, 4, -3, 6, -3, 14, -13, -6, -22],\n [-2, -4, 6, -23, 6, ... | 942 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[2, -14, 1, 16, 21, 4, 15, 8, 11],\n [-20, -19, 6, 6, -1, 7, -19, -14, -10],\n [-10, 17, 10, -13, -19, 10, 21, 25, -17],\n [6, -15, -18, 7, -3, -1, -18, 19, -4],\n [-22, 14, -23,... | -15 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[2, -15, 17, -25, 23, 21, 12, -2, 21],\n [5, 15, 20, 24, 0, 23, 24, -21, -6],\n [15, -15, 7, 24, 12, 1, 8, -11, 6],\n [-5, 20, -21, -20, 12, -4, -8, -12, -16],\n [20, -13, 5, 4, ... | -21 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[8, -9, 17, 17, -10, -24, 8, -18, -13],\n [0, -18, 4, 6, 10, 21, 4, -25, 17],\n [0, 0, -6, -2, 24, -4, 3, -4, 18],\n [0, 0, 0, 10, 11, 2, 2, 16, 17],\n [0, 0, 0, 0, -24, -18, 22, 1, -4],\n [0, 0, 0, 0, 0,... | 124056 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (7, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -22, -25, 24, -25, 0, 19, -6, -3],\n [0, -15, 15, 15, -21, -25, -9, -4, 8],\n [0, 0, 3, -22, -21, -15, 25, -5, ... | 0 | 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, 5, 15, -20, 11, -16, 14, -19, 13],\n [0, -5, -6, -23, 25, -4, 21, -22, 2],\n [0, 0, 25, 10, 21, 15, -21, -13, -3],\n [0, 0, 0, -1, 22, 1, 25, -12, 22],\n [0, 0, 0, ... | -607 | 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[[-3, 13, -9, 8, 15, 3, -17, -13, -20],\n [0, -6, -23, -9, 23, -14, 22, 21, 19],\n [0, 0, -23, 0, -11, 10, 6, 6, -22],\n [0, 0, 0, 17, 9, 14, -12, 7, -12],\n [0, 0, 0, 0, ... | -805 | 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[[7, 23, -14, -15, -21, 1, -14, -9, -20],\n [0, -21, 2, -12, -21, 7, 24, 22, 15],\n [0, 0, -21, -24, 4, 21, 13, -22, 7],\n [0, ... | -10656 | 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, 15, -6, 18, -7, -6, 9, 21, -24],\n [4, 8, -4, -23, -20, -11, 1, -16, -17],\n [7, 6, 22, -20, 15, 10, -24, 3, -22],\n [-25, -7, 0, -1, -... | 1398 | 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[[-7, 8, -15, 1, 12, -1, 18, 6, 6],\n [8, 13, 20, -6, 4, 16, 22, 10, 14],\n [-15, 20, 22, 0, 17, 2, 13, -4, 2],\n [1, -6, 0... | 330 | 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[[-2, -22, 2, -11, -25, -23, -12, 12, 24],\n [0, 12, 12, -5, 22, 3, -21, 23, -16],\n [0, 0, 24, -19, -23, 19, 21, -6, -7],\n [0, 0, 0, -25, ... | 11282 | 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[[21, 22, -3, 19, -9, 14, -5, -24, 11],\n [-20, 18, -8, 4, -4, 7, 4, -9, 17],\n [6, 16, 25, -12, -16, 21, 25, 10, 8],\n [-1... | 256 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[17, -1, -23, -11, 3, 17, 6, 0, -10],\n [-1, 2, -17, -25, 3, -4, -10, 15, 25],\n [18, 25, 15, -19, -12, 3, -7, -7, -24],\n [15, 19, -11, -23, -15, 20, 4, 14, -8],\n [25, 22, -24, 6, -18, -4, -20, -14, 21],\n [14, 10, -11, 2... | -88 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[-1, 10, -18, -17, 11, 22, 19, 13, 6],\n [-9, 9, 11, -7, 18, 3, -19, 2, -17],\n [2, -20, 3, -9, -10, -3, 5, -23, -5],\n [0, 10, 16, 11, -4, 16, -14, 16, -13],\n [-15, -10, -18, 1... | 3 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (3, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -11, -11, -22, 6, -3, -20, -2, -6],\n [11, -6, -14, 7, 2, -18, -25, 11, -4],\n [-20, -5, 6, 9, -11, -21, 20, 24... | -10 | 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[[-23, -8, -12, -5, -14, -6, -4, -13, 14],\n [-8, 17, -13, -15, 1, 8, -16, 23, 8],\n [-12, ... | -123 | 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[[12, -23, 2, 0, 4, -13, -13, -24, 11],\n [23, 12, -24, 10, 0, -15, -18, 18, 14],\n [17, -4, -6, -18, 3, 14, 0, 4, -9],\n [-6, -10, 20, 17, -19, -10, 19, 21, 22],\n [1, -3, -2, -17, 9, ... | -600 | 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[[-18, 9, 14, -4, -1, -20, 10, -14, 2],\n [9, -16, 6, -11, 18, 8, 4, -2, 6],\n [14, 6, -4, -8, 12, -2, 2, 6, -4],\n [-4, -11, -8, -15, 0, 18, 16, -17, 2]... | 27 | 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[[12, -4, -13, -2, 20, -10, -16, 0, -8],\n [-4, 6, 0, -4, 14, -2, 11, 15, -22],\n [-13, 0, 0, 0, -2, -6, 14, -1, -6],\n [-2, -4, 0, 12, -1, -6, -9, 13, -18],\n... | -350 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[19, -3, 20, -18, -18, 0, 21, -13, 13],\n [11, 23, 2, -1, -10, -24, -8, -9, 4],\n [13, -13, 6, 24, 3, 20, 4, -8, -13],\n [17, -5, 4, -5, 22, -9, 14, -7, -11],\n [-17, -16, 18, 5, -3, 4, 7, -1... | -28 | 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[[24, 12, 11, 19, 25, -18, 15, 23, 9],\n [25, -15, -2, 23, -5, 25, -24, 14, -7],\n [13, 2, -9, -20, -7, ... | 1282 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (8, 3) rounded to the nearest integer?\n[[-2, -21, -23, 1, -10, 23, -11, 9, -14],\n [15, 18, 0, 21, 8, -3, 5, 24, -6],\n [-14, -3, -22, -3, 22, 22, -25, -1, -24],\n [4, -23, -5, -1, -6, 23, -4, -5, 7],\n [12, -11, 20, -... | 0 | 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, 4, -15, 2, 18, -14, 13, 0, -13],\n [-18, 2, 4, -17, 13, 5, -5, 21, 8],\n [5, -1, -14, -25, -4, 14, 11, 21, -25],\n [-25, 16, 16, -5, -11, -9, -4, 12, 9],\n [19, -10,... | -60 | 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[[-12, -13, -19, 18, -11, -7, 17, 21, 18],\n [9, -9, 9, -7, -6, 10, 9, 6, 22],\n [18, 14, -2, -9, -19, 17, 24, -25, 9],\n [6, 10, -13, -20, -12, 11, 22, -11, 21],\n [-22, 14, -10, 2, -1... | 176 | 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[[-20, 20, 18, -22, 3, -3, -20, 6, 16],\n [0, -11, 14, 6, -17, 11, -16, -6, -20],\n [0, 0, 16, -15, 17, -9, 6, -22, -22],\n [0, 0, 0, -21, 6, -4, -20, 9, -4],\... | -1678 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, 10, -24, -4, 6, -10, -8, -21, 10],\n [0, 19, -7, -3, 8, -13, 17, 3, 10],\n [0, 0, 10, -17, 13, 25, -7, 12, -20... | 12 | 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[[0, 21, 24, -14, 5, -9, 7, -15, 2],\n [6, -25, 21, 2, 16, -19, -24, 16, -2],\n [-22, 18, -7, 0, -15, 14, 24, 17, -15],\n [19, -23, -14, -23, 16, 1, 23, ... | 81 | 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[[25, 0, 9, -10, -9, 6, 0, -18, 10],\n [0, -14, 0, 6, 0, 16, 2, -12, -4],\n [9, 0, 11, 6, 8, -11, -2, 3, -12],\n [-10, 6, 6, 10, 3, -16, -15, 8, 9],\n [-9, 0, 8, 3, -... | 810 | 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, 7, 5, 9, -9, 2, -7, 20, -3],\n [6, 14, -13, -6, 9, -21, -17, 3, -20],\n [-1, 5, -4, -24, 19, -21, 1, -1, -18],\n [-25, -6, 18, -3, 6, -15, 13, 21, -2],\n [-15, ... | 1435 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-4, 17, -7, -18, -18, 16, 0, 22, 25],\n [0, -3, 17, -13, 2, -17, -6, -7, 22],\n [13, 25, -14, -11, 5, -12, -15, 0, 16],\n [1, -15, 12, 8, 17, -7, -20, 20, 12],\n [23, 16, 2, -25, 9, 14, -18,... | 42 | 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, -8, 18, -8, 6, -6, 6, -5, 1],\n [-8, -10, 16, -2, 8, 18, -14, 6, -5],\n [18, 16, 16, 6, 6, -2, -2, 9, -3],\n [-8, -2, 6, 23, 11, -19, -12, -8, 22],\n [6, 8, 6, 11, -... | -196 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, 4, 4, -4, -15, -24, 18, -14, 4],\n [0, -8, 0, -19, -25, 0, -3, 0, 19],\n [0, 0, 18, -18, -2, -4, -7, 11, -8],\... | 0 | 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[[25, 20, -12, 16, -13, -8, -6, 7, -15],\n [20, 6, -16, 0, 7, 2, 9, 6, -12],\n [-12, -16, 2, 3, -8, -4, -12, 3, 20],\n [16, 0, 3, -7, -23, -... | 1206 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 6) of the inverse. Round your answer to the nearest integer:\n[[-20, 21, -21, 17, -1, -8, -13, 17, -12],\n [0, -8, 2, 25, 1, 6, 21, -17, 14],\n [0, 0, 2, 7, -22, 20, 8, 22, -23],\n [0, 0, 0, -10, -2, 22, 13, 4, 19],... | 94 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 9, 14, -10, 12, -13, -3, -4, -10],\n [2, 22, 9, 19, 20, -18, 18, -4, -5],\n [0, 14, -5, -1, 15, -25, -20, -3, 25... | -7 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-15, 12, -20, 19, -15, -12, -24, 14, -23],\n [9, 7, -2, -7, -8, 23, -2, 19, 9],\n [-25, 10, -1, 19, 23, 17, 8, -1, -10],\n [8, 3, -7, -3, -7, -1, -10, ... | -3 | 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[[21, -24, 3, -13, -22, 16, 19, -16, 5],\n [0, -18, -23, 22, 20, -17, 4, -15, 9],\n [0, 0, -13, 10, -13, -14, 11, -16, -17]... | 18681 | 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[[23, -6, -1, 10, -4, 14, 0, -14, 8],\n [-6, -7, 13, -9, 2, -16, -22, 1, -16],\n [-1, 13, -1, 0, 5, 8, 0, -22, 10],\n [10, ... | -191 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[9, 22, -21, 22, 6, -23, 21, 9, -12],\n [0, 5, 5, -9, -2, -3, -8, 24, -12],\n [0, 0, -11, -20, 1, -11, 24, 10, -18],\n [0, 0, 0, -13, 15, 8, -2, 14, 6],\n [0, 0, 0, 0, -25, 8, -1... | -220 | MATH |
[
{
"content": "Find the value at position (9, 6) of the inverse of matrix 1/450 * A where A =\n[[-9, 13, -1, -21, -21, -6, -10, 25, 15],\n [0, 14, -17, -21, 16, -24, -17, 17, 10],\n [0, 0, -4, 8, 3, 12, 20, 7, -8],\n [0, 0, 0, -25, -2, -22, -22, -8, 1],\n [0, 0, 0, 0, 16, 15, 10, -20, -10],\n [0, 0, 0, 0, 0, 23,... | 0 | 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[[3, -5, 0, -12, -17, 21, -14, 16, 25],\n [25, -20, -6, -2, 1, 12, -18, -25, 23],\n [23, -2, 21, -19, -7, -4,... | -2 | 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[[8, 6, 12, -2, -6, -2, -10, -19, -3],\n [6, -24, 0, 16, -4, 0, -18, -22, 1],\n [12, 0, -6,... | -54 | 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, -5, -9, 7, -16, 25, 21, 16, 25],\n [0, -10, 15, 6, -11, 1, 2, -9, 20],\n [0, 0, 10, 24, -19, -13, -11, -1, -3],\n [0, 0, 0, -15, -16, -1, 11, 22, 17],\n [0, 0, 0, 0,... | -45 | 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[[-6, 12, 10, 4, -4, -19, -4, 0, -16],\n [12, 11, 8, 9, -9, 11, -10, 0, 10],\n [10, 8, -8, 6, -6, -12, -2, 2, -11],\n [4, 9, 6, -14, 2, -20, 6, 2, -12],\n [-4,... | 255 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 6, -2, -18, 3, 12, 12, 8, -2],\n [6, 2, 4, -2, 17, -5, 14, -3, -10],\n [-2, 4, -3, 2, 1, -22, 8, -12, 8],\n [-18... | -26 | 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[[-12, -12, -16, -14, 12, 18, 20, 8, 15],\n [0, -9, -9, -23, 5, 25, -25, -14, 13],\n [0, 0, -13, 8, 16, -5, -... | 71 | 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[[-2, 16, 2, -2, -6, -14, -10, -4, -14],\n [16, -8, 9, 2, 4, 21, -4, 8, -15],\n [2, 9, 6, 10, 4, -2, -8, -5, 3],\n [-2, 2, ... | 3 | 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[[4, -14, 2, -7, -4, 4, 16, 4, -5],\n [-14, 18, -8, -1, 4, 0, -2, -6, -17],\n [2, -8, 0, -6, 11, 4, 0, 5, 10]... | -76 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (5, 9) of the inverse. Round your answer to the nearest integer:\n[[22, 8, -6, 4, 6, -11, 10, 16, -23],\n [8, 20, 12, -14, -2, 6, 14, 6, 0],\n [-6, 12, 12, -2, -4, -16, 12, -8, 8],\n [4, -14, -2, -11, -5, -2, -3, 10, -4... | -2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, 16, 13, 0, 23, 12, -3, -4, -22],\n [0, -17, -22, -19, -3, -24, 23, -2, 14],\n [0, 0, 5, 21, 14, 22, 25, 17, 8],... | 0 | 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[[8, -22, -10, -12, 6, 0, 18, 4, 4],\n [-22, -16, 4, -4, -6, 15, -4, -19, -8],\n [-10, 4, 13, -4, -8, -8, -6, 13, -1],\n [-12, -4, -4, 14, 10, -4, 2, 2, 19],\n... | -541 | MATH |
[
{
"content": "Find the value at position (3, 5) of the inverse of matrix 1/450 * A where A =\n[[-6, 18, 19, 8, -5, 22, -3, -20, 25],\n [0, 23, -3, -17, -9, -24, -7, -7, -19],\n [0, 0, -6, -17, -9, 1, 21, -24, 10],\n [0, 0, 0, 13, -8, -19, -9, 13, 10],\n [0, 0, 0, 0, -1, -21, 4, -14, -22],\n [0, 0, 0, 0, 0, -2, ... | 1460 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[23, 19, -25, -16, 21, 6, 13, -4, -8],\n [0, 20, 6, 1, 2, -8, 13, 23, 3],\n [0, 0, -18, 5, 8, -19, 10, -8, 12],\n [0, 0, 0, -18, 25, 9, -8, -21, -12],\n [0, 0, 0, 0, -6, -1, 2, -14, -24],\n [0, 0, 0, 0, 0... | 1438 | 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[[13, 8, -20, 24, 12, 19, 25, 8, 18],\n [-11, -12, -20, 24, 11, 24, 6, -23, -23],\n [-4, -4, -16, 25, -23, -14, 3, 22, -9],\n [-19, -13, -24, -22, -16, 13, -2, -9, -20],\n... | 12 | MATH |
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