messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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, 4, 6, 11, -1, 6, 3, 8, -8],\n [4, 11, 2, -5, -10, -15, 8, -16, -12],\n [6, 2, -24, -4, -10, -2, -9, 12,... | 634 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[17, 11, 8, 17, 0, 8, 11, -12, -16],\n [11, -12, 11, -6, -14, -4, 4, 20, 14],\n [8, 11, -6, 2, 4, -1, -20, -6, 10],\n [17, -6, 2, 20, -2, -2, -12, -8, 12],\n [0, -14, 4, -2, 1, 18, 15, -1, 4],\n [8, -4, -1, -2... | 68 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 1, 10, -9, 23, -5, 11, 5, 19],\n [0, 1, -3, 6, -9, -15, -25, 2, -8],\n [0, 0, -6, -19, 11, -10, 13, 19, 19],\n... | 0 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/450 * A where A =\n[[-10, -25, 16, -8, -4, 0, -12, 11, 23],\n [-12, 0, 24, 10, -3, -24, 13, -19, 13],\n [19, 25, -4, 2, 12, -6, 23, -8, -2],\n [7, 19, 0, -7, 22, 16, -13, -16, -12],\n [-17, -15, -23, 14, -14, 9, 13, 20, 13],\n [6, 13, -1... | 6 | 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[[-5, 5, 8, 4, -10, -3, -1, 16, -4],\n [5, -23, 16, -12, 9, 22, 10, -4, 10],\n [8, 16, 16, -6, -4, -2, 16, -8, 10],\n [4, -12, -6, 21, 18, 18, 6, -18, -7... | 82 | 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[[-21, 19, -20, -4, -9, -11, 13, 14, 2],\n [0, -8, 1, -5, -3, -19, 22, -7, -17],\n [0, 0, 4, -19, -24, -9, -15, 24, -14],\n [0, 0, 0, -11, 25, 16, 15, -1... | -8088 | 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[[11, -12, 17, -10, 2, -1, -1, -4, 14],\n [-12, 6, 0, -6, -2, 0, -2, -12, -11],\n [17, 0, 12, 18, -7, 3, 20, -20, -10],\n [-10, -6, 18, -17,... | 1383 | 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[[9, 6, 9, 9, 2, -22, 2, -1, 4],\n [6, 13, -3, -12, -1, -8, 8, -12, 4],\n [9, -3, 6, -14, -4, -14, -6, -2, 6],\n [9, -12, -14, ... | -47 | MATH |
[
{
"content": "Find the value at position (8, 9) of the inverse of matrix 1/450 * A where A =\n[[-7, -10, -14, 10, 8, -4, -7, 5, -6],\n [-10, 3, 16, 0, 2, -6, -2, 14, -5],\n [-14, 16, 17, 0, 4, 4, 5, -4, -8],\n [10, 0, 0, 21, 8, -2, 5, 8, 0],\n [8, 2, 4, 8, 21, -14, 4, 4, 6],\n [-4, -6, 4, -2, -14, 10, 2, 4, 6],... | -7 | 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, 8, -3, -10, 23, -21, 18, 21, 2],\n [-20, -13, 17, 4, 0, -9, -17, -10, 23],\n [-8, -13, 3, 17, 19, -2, 19, 18, 20],\n [-13, -1, 15, 20, -25, -17, -22, 2, -14],\... | 1146 | 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[[23, 21, -17, -21, -18, -5, 7, 13, 17],\n [0, 19, -4, -13, 13, -15, -8, 4, 7],\n [0, 0, -25, 10, -20, 11, 3, -15, -13],\n [0, 0, 0, -1, -11, -13, 16, 7, -13],... | -728 | 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, -3, -1, -10, -2, 5, -15, -3, 15],\n [13, -4, 7, 15, 16, 22, -8, -12, 2],\n [-15, -2, 10, -7, -13, 7, -7... | -58 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[17, 3, -7, -1, -22, 25, -13, 6, 1],\n [25, 8, 2, -17, -18, -5, 20, 4, 3],\n [-17, -13, -8, 12, -4, 5, 9, 16, 16],\n [-16, -17, 5, 18, 14, -2, 15, 23, -18],\n [24, -6, -9, 2, -20, 16, 7, 2, -25],\n [15, 9, -2,... | -62 | 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[[-5, -6, -23, 9, -2, 4, 8, -12, 0],\n [-6, 15, -5, 2, 18, 7, -8, -15, -3],\n [-23, -5, 5, -4, 12, 7, 20, -14, 14],\n [9, 2, -4, 0, 10, 10, 5, -9, 0],\n [-2, 1... | -448 | 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[[-11, 0, -4, 6, -24, 15, -10, 0, 14],\n [0, 7, -14, -10, 2, 14, 22, -14, 7],\n [-4, -14, -... | -173 | 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, -6, 10, -13, 14, -15, -2, -7, -3],\n [5, 11, 11, -23, 8, 3, -23, -11, -19],\n [-23, ... | 143 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (6, 2) rounded to the nearest integer?\n[[20, 21, 22, 2, -22, -7, -2, 14, -20],\n [0, 6, 4, 9, -18, -21, 11, -14, -1],\n [0, 0, -2, -15, 16, 9, 14, -25, -18],\n [0, 0, 0, -15, -19, 4, 22, 13, -13],\n [0, 0, 0, 0, 17, -1... | 0 | 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[[-23, -23, 1, -24, -23, -9, 20, 13, 12],\n [0, -7, -7, 18, -21, -21, -12, 1, 23],\n [0, 0, 14, 9, -5, -21, -2, 13, 24],\n [0, 0, 0, 20, 24, -13, 12, 19, -25],\n [0, 0, 0, 0, -10, 11, -... | 1560 | 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[[-4, -15, 10, 18, 3, 16, 6, -12, -8],\n [12, 11, 8, 19, -3, 6, 20, -23, 17],\n [-4, -3, -22, -13, 6, 3, 14, 14, 19],\n [-16, -... | -69 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 7) rounded to the nearest integer?\n[[-11, -10, 11, -15, 3, 25, -20, 4, -16],\n [-10, -22, 2, -10, 10, 2, -10, -2, -16],\n [11, 2, -25, -13, 4, 7, 12, 2, 8],\n [-15, -10, -13, -18, -14, 18, 4, -8, 4],\n [3, 10, 4, -... | -5 | 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[[-17, -6, -9, -16, -12, 2, -16, -6, 4],\n [-6, -12, 10, -8, -4, 5, -18, -14, 14],\n [-9, 10, 22, -12, 10, -10, -14, 2, 16],\n [-16, -8, -12, 14, 22, 7, -1, 11, 14],\n [-12, -4, 10, 22,... | -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[[-10, -1, -8, 8, 12, -23, -6, -7, -13],\n [-9, -12, 4, -4, 17, 22, 17, 3, 24],\n [-24, -18, -12, 8, -13, -16... | -9 | 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, 6, -12, 9, -15, -16, -9, -13],\n [0, 19, 25, -21, 22, -16, 6, -14, -13],\n [0, 0, 7, 15, 22, 25, 21, 24, 6],\n [0, 0, 0, 10, 12, 22, 2, -13, -14],\n [0, 0, 0, 0, -13, 9, -13, 8, -7],\... | -6206 | 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[[-2, -22, -5, 13, -19, -3, 14, -5, -25],\n [15, -1, 5, 18, 12, 19, -21, 5, 25],\n [-25, 4, -8, -18, 0, 14, -11, -7, -16],\n [-... | -97 | 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, -24, 15, -10, 4, 21, 20, 10, -22],\n [-15, -2, -8, 1, 11, -24, -11, -15, 1],\n [23, 22, 21, -3, 9, 4, 21, -2, -7],\n [3, -13, 22, -3, -14, 23, 22, ... | -50 | 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[[24, 13, 16, -3, 20, -6, -6, -15, -24],\n [0, -13, 15, 23, -11, 5, -3, -4, -10],\n [0, 0, -6, 2, 1, 18, 3, -21, 23],\n [0, 0, 0, 18, 25, -24, 19, -6, 17],\n [0, 0, 0, 0, 20, -18, 2, 15... | -417 | 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[[14, 8, 12, 15, 17, 2, -11, 8, -8],\n [8, -23, -8, 24, -10, 8, 16, 5, 6],\n [12, -8, -16, 1, 1, 16, 2, 2, -1... | 9 | 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, -11, -4, 1, -16, 12, 3, 8, 2],\n [-11, 13, 4, 0, -13, 8, -15, 2, -2],\n [-4, 4, 1, -4, 4, -4, 4, -6, -1],\n [1, 0, -4, 9, 8, -6, -2, 3... | 3381 | 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[[-12, 4, 22, 16, -2, 20, 17, 8, -7],\n [0, -22, -15, -13, 24, -8, -7, 18, 7],\n [0, 0, 23, 9, -25, 9, 10, 12, 13],\n [0, 0... | 6136 | 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, -10, 8, 9, 2, -2, 8, -3, 16],\n [-10, -20, 4, 2, -19, 6, -8, -18, -4],\n [8, 4, 17, -1, -6, 18, -9, -2... | 63 | 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[[4, 0, 14, 8, -24, -2, -12, 15, 16],\n [-13, 3, -25, 20, 8, -22, 2, -7, -25],\n [10, 17, -13, 24, 16, -21, 7, -12, -10],\n... | -70 | 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[[-13, 6, 12, 20, -9, -1, 6, -3, 16],\n [6, -7, 12, 12, 16, -17, 25, -4, 13],\n [12, 12, -21, 17, 18, -1... | 345 | 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, 4, 0, -14, -2, 15, -7, 18, -10],\n [0, -3, 7, 16, 4, -3, -16, 10, 5],\n [0, 0, 17, 17, 12, 21, -24, -3, 9],\n [0, 0, 0, -14, 9, 15, -... | 3039 | 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[[7, -1, 4, 11, -23, -22, 3, 6, -3],\n [-7, -11, 25, -10, -3, 14, 20, 11, -25],\n [-7, 11, 9, 4, -9, 13, 23, 0, -13],\n [-4, 20, -3, 18, 17, 7, 1, 9, -14... | -181 | MATH |
[
{
"content": "Find the value at position (8, 6) of the inverse of matrix 1/450 * A where A =\n[[19, -20, -20, 24, 11, 23, -23, 11, 5],\n [0, 19, -11, -9, -11, -21, -4, 20, -15],\n [0, 0, 13, -23, 16, -15, 4, 12, -21],\n [0, 0, 0, 25, 25, -5, 11, -1, -5],\n [0, 0, 0, 0, 21, 9, -3, -19, 20],\n [0, 0, 0, 0, 0, -22... | 0 | 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[[-19, -4, 10, -24, -2, 25, -24, 22, -14],\n [21, 16, 0, 12, 19, -20, -3, -24, 0],\n [-12, -8, 12, 6, 25, -12, 4, -13, 14],\n [... | 18 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-10, 8, 9, 13, 10, -2, -2, -8, -4],\n [8, -13, 17, -8, 6, 14, 4, -3, -8],\n [9, 17, 3, -14, 13, 17, 10, -6, -13],\n [13, -8, -14, -23, 3, 11, -10, 14, 9],\n [10, 6, 13, 3, 18, 16, -11, 16, 2... | 60 | 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[[-23, 3, -6, -10, 4, 4, 12, 6, -14],\n [3, -25, -4, -12, 2, -17, -14, 7, 6],\n [-6, -4, 18, 3, -13, 1, 16, 3, 8],\n [-10, -12, 3, 16, 16, -11, -4, 17, -... | -4 | 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[[19, -2, 2, -2, 6, -9, -8, 2, 13],\n [-2, 18, -2, -20, 10, 14, -3, 8, 18],\n [2, -2, 14, 6, -10, 21, -6, -6, -4],\n [-2, -20, 6, -8, -12, -7, 4, -8, 12]... | -139 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, 19, -4, -25, -1, 15, 2, 11, -15],\n [-4, -1, -5, 10, -6, -10, 2, 3, 24],\n [0, 14, -24, 23, -16, -13, -11, -17, 1],\n [-18, -20, 10, 24, -2, -23, 0, 10, -5],\n [-13, -15, -18, 20, 20, 22, -12, 7, -24],\n [-25, -15, -20... | -30 | 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[[-15, 0, 14, -8, 16, 2, 0, -20, 2],\n [0, 24, -5, -2, -9, -23, -13, 7, -6],\n [14, -5, -18, -3, -16, -21, -12, 6, -2],\n [-8, -2, -3, -5, -17, -5, -4, -5, -5]... | -185 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (9, 7) rounded to the nearest integer?\n[[-18, 5, -15, -18, -1, 23, -6, 12, -19],\n [0, 13, 17, -16, -18, 16, 17, -6, -9],\n [0, 0, 11, 16, 6, 0, 11, -17, 9],\n [0, 0, 0, -19, -24, -1, 14, -14, 4],\n [0, 0, 0, 0, 25, -3... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (1, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 12, 20, 9, -16, -17, -3, 4, 25],\n [0, 21, -17, -7, -18, -22, -21, -7, 20],\n [0, 0, -7, -20, -21, 17, -21, -18... | -50 | 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[[11, 1, 20, 16, 0, 18, -2, 0, -24],\n [1, -6, -15, -19, 14, 14, -2, 12, 8],\n [20, -15, 17, 12, 6, -7, 12, -14, 20],... | 15 | 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[[-2, 9, 2, 16, 3, -5, 22, -1, 13],\n [5, -11, 21, 16, 9, 12, 24, -4, -21],\n [22, -13, 6, -23, -11, 1, 1, 4, -20],\n [-1, 2, -... | -24 | 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, 7, -8, -10, 16, -16, -3, -14, -12],\n [7, 13, 2, 2, -10, -2, 1, -2, -6],\n [-8, 2, -4, 6, -6, 3, -5, 6, -7],\n [-10, ... | 423 | 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, 8, 23, -3, -16, 25, 4, -4, -21],\n [18, 24, -17, 17, -22, 16, -25, 8, 15],\n [0, -8, -10, -3, 20, 10, 0, -24, 18],\n [-21, 3, -22, 21, 9, -4, 23, -18, 18],\n [-5... | 1452 | MATH |
[
{
"content": "Find the value at position (9, 3) of the inverse of matrix 1/450 * A where A =\n[[-17, 16, -12, -10, -10, 14, -8, 5, -6],\n [16, -22, -10, -14, -8, 18, 2, -10, 2],\n [-12, -10, -6, -13, -10, 8, 4, 5, -11],\n [-10, -14, -13, -23, -7, -3, -7, -18, 2],\n [-10, -8, -10, -7, -9, 2, 17, -8, 2],\n [14, 1... | -20 | 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[[-15, 0, -2, 2, -9, 4, -10, 8, -16],\n [0, -23, -16, -6, 12, 3, -5, 8, 16],\n [-2, -16, -3, 10, -10, 6, -4, -8, 2],\n [2, -6, 10, -25, 13, 2, 5, 19, 1],\n [-9, 12, -10, 1... | 241 | 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[[13, -2, 18, 10, -14, -12, -18, -2, -18],\n [-2, -11, -4, -10, -15, -2, -6, -10, 18],\n [18, -4, -2, -2, -8, -19, -7, -6, 11],\n [10, -10, -2, -... | -140 | 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[[1, 1, -8, 4, 19, 20, 5, 16, -23],\n [0, -19, -8, -10, 23, 6, 12, -1, 18],\n [0, 0, -23, 9, 24, 3, -15, -20, -7],\n [0, 0, 0, -21, 0, 9, -7, -9,... | 547 | 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[[-20, -2, 0, 2, -4, 6, 13, 10, 7],\n [-2, 17, 2, -2, -12, -4, 0, 2, -12],\n [0, 2, 24, 2, 2, 18, 1, -10, -6],\n [2, -2, 2, -11, -12, -18, 10, -13, -8],\n [-4, -12, 2, -12, -25, -7, 14,... | 150 | 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[[-25, -4, 0, 2, -12, -12, 6, 16, -15],\n [-4, 11, 13, -4, -16, 14, 16, 16, 7],\n [0, 13, 13, -10, -6, 19, -1... | 145 | 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[[20, 0, 22, 1, 2, 7, -4, 1, -6],\n [0, -18, -6, 14, 2, 11, -18, -6, 4],\n [22, -6, 23, 4, -4, -6, 4, 11, -10],\n [1, 14, 4... | -70 | 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[[22, 0, -20, 12, -6, -15, 0, 4, -16],\n [0, -22, -12, 6, -18, -22, 0, -14, 6],\n [-20, -12, 12, 13, -1, 2, -6, -15, -12],\n [12, 6, 13, -18, 6, 6, 6, -18, -13],\n [-6, -1... | 118 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[19, 21, -2, 20, 14, -5, 4, -15, -17],\n [-14, 0, 12, 25, -23, 7, -11, 21, -21],\n [-2, -15, 7, -3, -16, 17, 2, 13, -9],\n [18, 0, -1, 10, -14, -23, 24, 3, 18],\n [-2, -7, -13, -... | -61 | 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, 9, 21, 21, 24, -19, 11, -18, -1],\n [0, -16, 4, 7, -15, 9, 1, -23, 21],\n [0, 0, -18, -13, 16, -23, -6,... | -75 | MATH |
[
{
"content": "Find the value at position (2, 7) of the inverse of matrix 1/450 * A where A =\n[[5, -3, -12, 2, -12, -25, 17, 6, 15],\n [0, -21, 16, -11, 16, -10, 10, 10, 14],\n [0, 0, -3, -15, -1, 19, 25, 17, -24],\n [0, 0, 0, -13, 16, 11, 4, -15, -3],\n [0, 0, 0, 0, 19, -23, -17, -18, 21],\n [0, 0, 0, 0, 0, -2... | 96 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[6, -14, -6, 21, 19, -14, -18, -4, 1],\n [15, 15, -9, 6, 7, 5, -20, 13, -17],\n [16, 6, 10, -10, -14, 15, -23, 1, 1],\n [-17, -9, 20, -21, 0, -5, -25, -25, 9],\n [-17, -3, 12, 15, -22, -7, 11, -21, 2],\n [20, ... | -261 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[17, 19, 9, -25, 10, 25, -8, -20, -3],\n [-16, -19, 18, -18, -13, 4, -8, -12, -15],\n [16, 12, -13, 16, 18, 7, 24, -13, -1],\n [-2, 3, 10, -20, -8, 2, -21, -8, 11],\n [-19, -17, 9, -14, 20, 14, 18, 13, -2... | 2385 | 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, -14, -21, -10, 12, 2, 10, 3, 8],\n [-14, 0, -4, -12, -4, -2, 4, -15, 14],\n [-21, -4, 16, 20, -20... | 902 | 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, 11, -15, -19, 9, -15, 23, 17, 21],\n [25, 14, 22, -5, 21, -23, 4, -2, 12],\n [-23, 11, 7, -4, 5, 20, -14, 19, -12],\n [-14, 1, -13, -2... | 695 | 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[[9, 2, -5, -18, 6, 5, 14, 6, -4],\n [2, 3, 6, 0, -10, 2, -20, -6, -2],\n [-5, 6, 6, 2, 8, 2, 14, -3, -10],\n [-18, 0, 2, -19, 8, -7, -2, -20, 6],\n [6, -10, 8... | 1610 | 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[[6, -8, 7, -12, -20, -15, 20, -6, 3],\n [0, -10, 22, -19, 14, 10, 18, 18, 5],\n [0, 0, 17, 17, 21, -20, 3, 1... | -22 | 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[[-13, 21, -1, -1, -9, -14, 25, -15, -16],\n [0, 19, -10, -6, 23, -21, 15, 6, 1],\n [0, 0, ... | 8004 | 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[[19, 0, 23, 21, -24, -20, 3, 0, 2],\n [-19, 8, 19, -16, 22, 15, 14, 21, -4],\n [1, 13, -4, -7, 10, -17,... | 1379 | 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[[18, 3, -25, 5, 1, 18, 10, 1, -11],\n [0, 22, -11, 14, -7, 21, 24, -15, 15],\n [0, 0, -3, -14, -24, 17, -5, -12, 8],\n [0, 0, ... | -125411 | 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[[-20, -10, 13, -16, 0, -17, 8, 14, 15],\n [-10, 19, -16, 10, 10, 13, 6, -22, -10],\n [13, -16, 5, -17, -18, ... | -1985 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-23, -4, 6, -4, 20, -12, 13, -23, 2],\n [-4, -2, 10, 22, -2, 6, 6, 7, -5],\n [6, 10, 4, -14, -11, -1, -11, -4, 7],\... | 2 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[16, 4, 6, -4, 12, -12, 8, 17, 21],\n [0, 14, -13, 4, -7, 16, 15, 24, 13],\n [0, 0, -14, -11, 19, 12, 14, -12, 9],\n [0, 0, 0, -9, -8, 16, -9, -10, -5],\n [0, 0, 0, 0, 1, 13, -9, -1, 25],\n [0, 0, 0, 0, 0... | 73334 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[0, -6, -6, 1, 12, -10, -1, 20, 12],\n [-6, -6, 5, -8, -23, 12, 0, 8, -19],\n [-6, 5, 13, 17, 2, 5, 10, -6, 18],\n [1, -8, 17, 0, 14, -2, -6, 2, -8],\n [12, -23, 2, 14, 21, 11, -8, 13, -6],\n [-10, 12, 5,... | 1626 | MATH |
[
{
"content": "Find the value at position (8, 8) of the inverse of matrix 1/450 * A where A =\n[[-21, 13, 3, 18, 20, 7, -2, -16, -1],\n [0, -16, 13, -10, 2, -14, 18, 6, 25],\n [0, 0, 24, 1, 0, -23, 0, 13, -25],\n [0, 0, 0, -22, -7, -4, -20, -17, -15],\n [0, 0, 0, 0, 17, -16, 8, 5, -4],\n [0, 0, 0, 0, 0, -11, -7,... | 25 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (9, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-21, -1, -7, 21, -6, -19, 0, 2, -12],\n [-1, -11, -5, -4, -10, -10, 10, 5, -4],\n [-7, -5, -21, -18, -14, 5, -17, -... | -19 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (3, 5) of the inverse. Round your answer to the nearest integer:\n[[-1, 22, -6, 11, -7, 16, -13, 21, -14],\n [23, -11, -22, -11, -9, 1, -15, -3, -11],\n [5, 0, -19, -13, -13, -6, 8, -16, 24],\n [11, 25, 1, 8, 10, -10, -... | 10 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-13, 7, 5, -1, 22, 14, -3, 12, -23],\n [0, -24, -3, 8, 4, 21, -16, -25, -4],\n [0, 0, -1, -4, -10, 4, -8, -2, -21],\n [0, 0, 0, 1, -14, -16, 8, 7, -10],\n [0, 0, 0, 0, 10, 1, -16, -16, -15],... | 34165 | 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[[7, 4, 11, -10, -1, 12, 16, -16, -21],\n [0, 7, 11, -25, 5, -19, 21, -3, -2],\n [0, 0, -17, -18, -18, -23, 6, -22, 23],\n [0, 0, 0, 20, -25, 23, -15, 3, 0],\n... | -25446 | 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[[9, -18, 20, -1, 16, 12, 22, 8, -5],\n [-18, -11, -4, -2, 2, -16, 0, -8, 9],\n [20, -4, 22, -3, 6, -14, -12, -8, 24],\n [-... | 229 | 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[[-19, -4, 0, -2, -8, 1, 6, -5, 7],\n [-4, -15, 0, -2, -8, -18, -6, 6, 7],\n [0, 0, 9, -9, ... | 62 | 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[[-16, 0, -4, -7, -2, -10, -4, 6, 3],\n [0, 9, -12, 6, -20, 13, 15, -1, -9],\n [-4, -12, -4, 20, 4, 12, -6, 23, 20],\n [-7,... | -47 | 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[[17, 19, -16, 0, -18, -2, -4, -4, -18],\n [19, -3, -20, 2, -8, 4, 10, -11, -12],\n [-16, -20, -1, -2, 4, 4, 14, -13, -10],\n [0, 2, -2, 23, 8, 2... | -34 | 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, 13, -6, 2, 4, 17, -12, -20],\n [4, -3, 11, 0, 4, -18, -6, -2, -4],\n [13, 11, 22, 4, 13, -22, -6, 12, 2],\n [-6, 0, 4, 10, 8, 8, -5, -10, -17],\n [2, 4, 13, 8, 15, 7, -6, -4, ... | -743 | 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[[25, 13, 18, 19, 3, 19, 20, 21, 5],\n [0, -20, -17, -11, -6, 22, -24, -23, 4],\n [0, 0, -5, 13, 17, -13, 14,... | 324 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[24, -22, -8, 8, 6, -14, -13, 8, 4],\n [-22, -18, -4, -1, 14, 2, 15, -7, -2],\n [-8, -4, -24, -16, 6, 2, -6, 16, 0],\n [8, -1, -16, -14, 24, -8, -13, -15, 14],\n [6, 14, 6, 24, -20, 4, 4, 14, 9],\n [-14, 2, 2, -8, 4, 20, 2,... | 136 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[19, -22, 24, -2, 22, 16, -24, 20, -24],\n [24, -25, -13, -20, -4, -9, 23, -4, 17],\n [-20, -23, 20, -20, -9, 9, 23, 25, 24],\n [11, 21, 9, -3, -18, -19, 24, -16, 0],\n [-16, -7, -3, 5, 7, -24, 2, 6, 7],\n [-17, 3, -11, -8,... | -7 | 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[[-25, 0, -16, 14, -7, -10, 19, 11, 24],\n [15, -22, -12, 4, -19, -14, -2, 13, 17],\n [-4, 21, 4, 13, -6, 0, ... | 95 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-12, -15, -17, -2, -16, 12, 17, 15, 11],\n [16, 6, -6, -12, 12, -22, -2, 6, -16],\n [17, -10, 13, 6, -8, -1, -19, 21, 25],\n [-8, 21, -8, -23, -25, 7, -19, -16, 18],\n [-18, 6, -3, -9, -12, -9, -1, -5, -20],\n [-6, 23, -6,... | -107 | 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, 12, 10, 4, 6, 8, 8, 2, 2],\n [12, 6, -18, -16, 14, 12, 4, -10, -14],\n [10, -18, -19, -10, 15, 0, -7, 10, -6],\n [4, -16, -10, -9, -22, -14, -8, 20, -2],\n [6, ... | 637 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[9, 4, -8, -4, -4, 3, 8, -4, 1],\n [4, -3, -1, 12, 18, -20, -18, 11, 8],\n [-8, -1, -17, -2, 18, 4, -11, -10, -10],\n [-4, 12, -2, -19, 0, 5, 10, -12, -... | 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[[-1, -17, -8, 6, 5, 18, -6, -3, 6],\n [-17, 8, 11, -11, -6, 10, 20, -16, -1],\n [-8, 11, -15, -7, 9, -3... | 29843 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[-21, -20, -16, 17, -24, -19, 20, -22, 11],\n [0, 2, -6, 4, 16, 12, -24, -23, 21],\n [0, 0, 13, -1, -24, 13, -11, -23, -21],\n [0, 0, 0, 25, 14, 12, 11,... | 0 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[12, -16, 2, 4, -16, 14, 2, -18, 9],\n [-16, 0, 2, -10, 11, -4, 15, -11, -8],\n [2, 2, -24, 0, -12, 2, 1, -5, 4],\n [4, -10, 0, -9, 2, -5, -2, 2, -19],\n [-16, 11, -12, 2, -1, 6, -4, 20, -16],\n [14, -4, ... | 1082 | 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[[-20, -10, -24, 20, -14, 1, -7, 2, 9],\n [25, 17, -22, 23, 23, -19, 11, 25, -1],\n [25, 15, -9, 15, -12, 11, -24, -2, -11]... | 1216 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 2) of the inverse. Round your answer to the nearest integer:\n[[-22, -15, 5, 15, 10, 24, 0, -12, -18],\n [-15, 15, -16, 0, 6, 10, -4, 12, 0],\n [5, -16, 25, -1, -10, 15, 4, -14, -4],\n [15, 0, -1, -8, 5, 14, -9, 7, ... | 195 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (9, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -10, -13, 4, 10, 2, 14, 11, -20],\n [-10, -10, -8, -7, 0, -10, -6, -7, 16],\n [-13, -8, 3, -5, -2, -8, -11, -5, ... | -12 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[6, 4, -25, 6, -6, -5, -7, 4, 24],\n [0, 6, 4, -3, 1, 11, 0, -23, 5],\n [0, 0, 12, -7, 5, 3, -1, 6, -9],\n [0, 0, 0, -3, -8, -15, -6, -13, -2],\n [0, 0, 0, 0, 2, 9, -5, -20, -19],\n [0, 0, 0, 0, 0, 6, -16... | 34104 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[8, 3, 4, 8, 8, 0, -20, -18, 10],\n [3, -7, -12, -22, 8, -7, 6, -14, 14],\n [4, -12, 2, 1, 1, 2, 12, 10, -2],\n [8, -22, 1, 18, -24, 10, -16, -8, 8],\n [8, 8, 1, -24, 12, 0, 8, -2, -6],\n [0, -7, 2, 10, 0, 20, -10, -17, 4],... | 95 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (7, 3) of the inverse. Round your answer to the nearest integer:\n[[0, -12, 22, -5, 2, -11, 4, -1, 25],\n [-15, 18, -15, 2, -21, 2, -18, 0, -20],\n [6, 22, 6, -14, -20, -13, 13, 14, 18],\n [8, -3, 15, 19, -9, 19, 22, -2... | -61 | 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[[20, 11, 12, 19, 19, -2, 12, 20, -15],\n [0, 19, 18, 22, 12, 15, -9, 22, 0],\n [0, 0, -8, -17, -23, -16, 17, -24, -18],\n [0, 0, 0, 5, -12, 13, ... | 246 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 9) of the inverse. Round your answer to the nearest integer:\n[[20, 7, 0, -10, -17, -3, -11, -7, 16],\n [0, -1, 9, 25, -13, 20, -19, 8, -12],\n [0, 0, -9, -13, 1, -24, 11, 4, -22],\n [0, 0, 0, -15, 14, -3, 15, 22, 6... | -32 | 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[[21, -2, -4, 3, 8, -1, -22, 20, -14],\n [-2, 17, -4, -4, 9, -1, -14, -15, -16],\n [-4, -4, 20, 2, 6, 16, -4, -19, 18],\n [3, -... | -79 | MATH |
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