messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[8, 11, 15, -13, -6, -5],\n [0, 1, -12, 15, -12, 1],\n [0, 0, -11, 6, 8, -10],\n [0, 0, 0, 4, 6, 0],\n [0, 0, 0, 0, -6, -13],\n [0, 0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex... | 258 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 1, 11, -7, -7, 7],\n [0, 3, 13, -1, -11, -1],\n [0, 0, 14, 9, 12, -14],\n [0, 0, 0, -1, 9, -6],\n [0, 0, 0, 0, 10, 14],\n [0, 0, 0, 0, 0, -13]]\n\nP... | 1595 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[4, 0, -14, -6, -13, -5],\n [0, 5, 5, 6, -3, -9],\n [0, 0, 14, -14, -4, 9],\n [0, 0, 0, 11, -5, 0],\n [0, 0, 0, 0, 5, 11],\n [0, 0, 0, 0, 0... | 1569 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -1, 0, -6, -4, 12],\n [0, -12, -9, 6, -14, 10],\n [0, 0, 11, -1, 15, -8],\n [0, 0, 0, 7, -2, 15],\n [0, 0, 0, 0, 14, -5],\n [0, 0, 0, ... | 976 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, 4, 13, 4, 9, -10],\n [0, -12, -14, 6, 0, 2],\n [0, 0, -12, 14, -3, 3],\n [0, 0, 0, -5, 14, 6],\n [0, 0, 0, 0, 4, -1],\n [0, 0, 0, 0, 0, -10]... | -13 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, 4, -1, -1, 9, 4],\n [0, -12, 2, 2, -11, 4],\n [0, 0, -5, -11, 6, 10],\n [0, 0, 0, -14, -3, -6],\n [0, 0, 0, 0, -12, 3],\n [0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex f... | 94 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[12, -15, -1, 12, 5, -6],\n [0, -14, -6, 8, -12, -4],\n [0, 0, -5, -8, 2, -5],\n [0, 0, 0, -4, -13, -6],\n [0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest intege... | 1008 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 3) of the inverse. Round your answer to the nearest integer:\n[[12, 9, 13, -6, 12, -6],\n [-8, -15, -3, 8, -7, 6],\n [-6, -1, -11, 6, 0, -3],\n [6, 9, 4, 2, -5, 11],\n [-7, 0, -14, 10, 9, -14],\n [-4, -8, -7, -4, 10... | -192 | MATH |
[
{
"content": "Find the inverse of 1/180 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[[-6, 10, -3, -1, 8, -8],\n [10, -14, -4, -6, 8, -7],\n [-3, -4, 11, 0, 14, 4],\n [-1, -6, 0, -1, -6, -11],\n [8, 8, 14, -6, 8,... | -11 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -12, 12, -10, -4, -2],\n [-12, -12, -2, -8, 6, -7],\n [12, -2, 13, -12, 2, 7],\n [-10, -8, -12, 4, 6, -9],\n [-4, 6, 2, 6, 0, 7],\n [-2, -7, 7, -9, 7, -2]]\n\nPresen... | -11 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 15, -2, -10, -4, 0],\n [0, -3, 7, -2, 13, -9],\n [0, 0, -4, 1, -7, 6],\n [0, 0, 0, -11, -3, 11],\n [0, 0, 0, 0, -2, -1],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the an... | 2119 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[12, 3, -2, 6, 14, 7],\n [-8, -3, 11, 4, -13, -11],\n [-7, 13, -10, 15, 9, 15],\n [6, -14, -3, -11, 12, 11],\n [9, -8, 7, -15, 4, -4],\n [7, -5, -9, -1, 6, 8]]\n\nPresent the ans... | 94 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-5, 8, 6, 7, -8, -8],\n [8, -2, -7, -12, 1, 3],\n [6, -7, -15, -4, -1, 8],\n [7, -12, -4, 13, -6, 0],\n [-8, 1, -1, -6, -11, 8],\n [-8, 3, 8, 0, 8, -7]]\nRound your answer to the nearest int... | -23 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 0, 6, 2, -2, -2],\n [0, -3, 0, 2, -4, 4],\n [6, 0, 12, 0, 4, 1],\n [2, 2, 0, 3, -4, 8],\n [-2, -4, 4, -4, 3, 2],\n [-2, 4, 1, 8, 2, 4]... | 374 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 1, -3, -3, -2, 4],\n [1, 15, 9, -6, 4, 7],\n [-3, 9, -5, -6, -14, 0],\n [-3, -6, -6, 4... | 90 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 6) rounded to the nearest integer?\n[[-5, 0, 9, -2, 9, -6],\n [0, -10, -6, -4, 0, 0],\n [9, -6, -2, 7, 7, 5],\n [-2, -4, 7, 13, -3, 0],\n [9, 0, 7, -3, -5, 6],\n [-6, 0, 5, 0, 6, 6]]\n\nPresent the answer in LaTex f... | 3 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, 1, 5, -3, 0, 5],\n [1, -1, 6, 12, 12, 7],\n [5, 6, -15, 0, 1, 4],\n [-3, 12, 0, 1, 0, 2],\n [0, 12, 1, 0, -3, -6],\n [5, 7, 4, 2, -6, -6]]\n\nPresent the answer in LaTex format: \... | 287 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, -6, 3, 8, 8, 11],\n [-6, 7, 6, -8, -2, -4],\n [3, 6, 1, -4, -10, -9],\n [8, -8, -4, 13, -6, -4],\n [8, -2, -10, -6, -4, -4],\n [11, -4, -9, -4, -4, -5]]\n\nPres... | 2748 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[6, 10, -12, -15, -9, 14],\n [2, -7, 13, -13, -8, 13],\n [8, 3, -12, 2, 4, 11],\n [-5, 11, -2, 9, 2, 12],\n [12, 13, 0, -13, -1, 11],\n [11, 15, -12, -11, 1, -9]]\nRound your answer to the nearest integer.\n\n... | -485 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[0, -7, 3, 2, 0, -8],\n [-7, 14, 5, 10, 2, -9],\n [3, 5, 14, -10, 4, 1],\n [2, 10, -10, 13, -2, 12],\n [0, 2, 4, -2, -3, -2],\n [-8, -9, 1, 12, -2, 3]]\nRound your answer to the nearest integer.\n\nPresent the... | 19 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 2, 15, 14, -11, 14],\n [0, -6, -15, -6, -11, -4],\n [0, 0, 11, -9, -7, 6],\n [0, 0, 0, 13, -15, -5],\n [0, 0, 0, 0, ... | -94 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, 2, -4, -10, -11, 10],\n [-15, -4, 11, 15, 10, -5],\n [-12, 11, 2, -12, 1, -14],\n [13, 8, 6, -14, -4, 15],\n [-10, -6, 9, 7, 9, 5],\n [7, 11, 0, 15, -2, -9]]\n\... | 535 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[12, 11, -2, 8, -6, -10],\n [11, -3, 6, -6, 5, -10],\n [-2, 6, 11, -8, 2, -6],\n [8, -6, -8, 13, 12, -1],\n [-6, 5, 2, 12, 13, -6],\n [-10, -10, -6, -1, -6, -3]]\n\nPresent the a... | 19 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 3, -13, -8, -8, 7],\n [0, 4, -1, -12, 3, 5],\n [0, 0, -8, 7, 0, -3],\n [0, 0, 0, 12, -2, -3],\n [0, 0, 0, 0, -9, -10],\n [0, 0, 0, 0, 0, -11]]\n\nP... | 48 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, -15, -6, -5, 0, -2],\n [-8, 8, 1, 9, 2, -4],\n [9, 1, 12, 10, -2, 0],\n [-2, -7, -12, 9, 7, -5],\n [-10, -1, -11, -5, 9, 2],\n [14, -3, -5, -2, 12, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer i... | 32 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 12, 15, 9, 12, 3],\n [8, 11, -1, -7, -8, 4],\n [12, -15, -12, -2, 9, -14],\n [0, -13,... | -24 | MATH |
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/180 * A where A =\n[[2, -8, -4, -1, -3, -2],\n [-8, 15, 2, 2, -4, 4],\n [-4, 2, 7, 2, 6, -4],\n [-1, 2, 2, -2, -4, 6],\n [-3, -4, 6, -4, -15, 6],\n [-2, 4, -4, 6, 6, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in... | -28 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[3, 7, 0, -3, 1, 9],\n [7, 11, -1, -6, 4, 6],\n [0, -1, 14, 8, 2, 11],\n [-3, -6, 8, -13, 0, 0],\n [1, 4, 2, 0, 12, -4],\n [9, 6, 11, 0, -4, 12]]\n\nPresent the answer in LaTex f... | -192 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-3, 2, -8, -4, 4, -1],\n [2, 5, -2, -6, 6, 8],\n [-8, -2, -10, 7, 1, 9],\n [-4, -6, 7, 14, -9, -4],\n [4, 6, 1, -9, 5, 2],\n [-1, 8, 9, -4, 2, 2]]\nRound your answer to the nearest integer.\n\nPresent the ans... | -297 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 3, -1, -8, 3, -6],\n [-9, 2, 0, 4, 11, -10],\n [11, -7, 5, -3, 9, 15],\n [5, 10, -8, 0, -3, -3],\n [1, 7, 4, -11, 6, 5... | 111 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 8, -10, -12, 4, -2],\n [8, -10, -9, 2, 2, 4],\n [-10, -9, -13, 5, 1, -8],\n [-12, 2, 5, 2, -6, 2],\n [4, 2, 1, -6, 14... | -117 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -14, 9, 0, -14, 13],\n [3, 7, 3, 9, 0, 6],\n [3, -7, -15, -6, 3, -15],\n [-14, 0, -4, -8, 7, 2],\n [-14, 9, 13, -3, -10, 5],\n [10, -10, -7, 0, -5, -9]]\n\nPres... | 16308 | MATH |
[
{
"content": "Find the value at position (5, 5) of the inverse of matrix 1/180 * A where A =\n[[15, -2, 4, 6, 4, -4],\n [-2, 12, 4, -2, 0, -2],\n [4, 4, -12, 12, 0, -4],\n [6, -2, 12, -12, 2, 1],\n [4, 0, 0, 2, -11, 3],\n [-4, -2, -4, 1, 3, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer ... | -17 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[13, -3, -12, -6, -3, -6],\n [13, 15, -7, -8, -13, 0],\n [15, -2, -7, 14, 5, -5],\n [-13, -11, 13, -6, -3, -12],\n [8, -3, -4, -11, -6, 12],\n [8, -7, 4, -9, -14, 6]]\nRound your answer to the nearest int... | 729 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 12, 7, -9, -8, -9],\n [5, 7, 13, -2, 10, 3],\n [-11, 7, 15, 9, 15, 2],\n [4, -4, 7, 1, -3, -14],\n [9, -... | -45 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 8, 2, -8, 3, 4],\n [8, 12, 6, 10, -6, 12],\n [2, 6, -7, -12, -6, 4],\n [-8, 10, -12, 7, -6, 0],\n [3, -6, -6, -6, 14,... | 28 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -2, -4, 1, 7, 0],\n [-2, -6, 6, 12, 3, 4],\n [-4, 6, -6, -6, -2, 12],\n [1, 12, -6, 7, -4, 8],\n [7, 3, -2, -4, -2, 11],\n [0, 4, 12, 8, 11, -14]]\n\nPres... | 71 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -13, -5, -10, 13, -2],\n [0, 10, 0, 5, 6, 8],\n [0, 0, 11, -8, 3, 4],\n [0, 0, 0, -9, -7, -3],\n [0, 0,... | -8 | MATH |
[
{
"content": "Find the inverse of 1/180 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[[-8, -9, 11, -15, 11, 0],\n [0, -9, -4, 7, -7, 11],\n [0, 0, 5, -15, 2, 15],\n [0, 0, 0, 11, 15, 1],\n [0, 0, 0, 0, -13, 4],\n... | -96 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[0, 13, 13, 15, 15, 1],\n [12, 8, 4, 7, 2, 2],\n [6, -2, 2, -1, -1, -10],\n [11, -1, 2, -12, 7, -8],\n [-1, -13, 14, -1, -3, -7],\n [-14, 8, -8, 13, 14, 4]]\n\nPresent the answer... | -2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[1, -4, -4, -2, 0, 6],\n [-4, -2, 0, 2, -6, 8],\n [-4, 0, 13, 2, 2, 8],\n [-2, 2, 2, -8, 4, 6],\n [0, -6, 2,... | 113 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, -13, -11, 0, 2, 10],\n [1, -5, 1, 0, 10, 7],\n [-14, -12, 5, -9, -14, 14],\n [-10, 1, -9, 9, -11, -11],\n [4, 0, 3, -7, -11, -8],\n [-7, -11, -6, 9, -14, -7]]\n\nPres... | -29 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, -12, 6, 6, 6, -14],\n [7, 13, -10, 11, -2, -15],\n [2, -9, -15, 15, -15, -15],\n [8, -12, -12, 13, 2, 11],\n [-5, 11, -15, 12, -6, -7],\n [7, -12, 12, -10, 14, 0]]\n\nPresent the ... | -48 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 4, 2, -2, 11, 0],\n [4, -3, -2, 0, 8, 2],\n [2, -2, -5, -4, 0, -2],\n [-2, 0, -4, 7, 8, -2],\n [11, 8, 0, 8, -12, -11],\n [0, 2, -2, -2, -11, -8]]\n\nPr... | -57 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, 6, 10, -15, -12, -2],\n [1, 4, 2, -5, 13, 5],\n [10, -2, -7, 11, -1, -4],\n [-6, 3, 8, 3, -10, 4],\n [8, 11, -10, -8, -15, 6],\n [1, 1, 8, -1, -9, 3]]\nRound your answer to the nearest integer.\n\nP... | 308 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 15, 9, 7, 12, -13],\n [14, 14, 13, 6, -5, 4],\n [14, 13, 3, -7, -6, -14],\n [-15, 15, 14, 0, 2, 7],\n [10, 1, -10, -2, 7, 9],\n [-1, -2... | 648 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[7, 3, 9, -4, -14, -13],\n [0, 13, -15, 4, 5, 13],\n [0, 0, -15, 3, -15, 11],\n [0, 0, 0, ... | 135 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -9, -4, 5, -9, -4],\n [0, -14, -2, -3, -12, -2],\n [0, 0, -9, 3, -14, -6],\n [0, 0, 0, -11, -4, -10],\n [0, 0, 0, 0, 6, -1],\n [0, 0, 0, 0, 0, -10]]... | -50 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, -12, 3, -2, 5, 5],\n [-12, -1, -8, 12, 8, -2],\n [3, -8, -3, -4, 0, -2],\n [-2, 12, -4, 7, 8, -8],\n [5, 8, 0, 8, 0, -8],\n [5, -2, -2, -8, -8, 7]]\n\nPresent the an... | 32 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[13, -12, -12, -8, 4, -4],\n [-12, -13, 2, 3, -5, -6],\n [-12, 2, -15, 4, 2, 4],\n [-8, 3, 4, -9, 12, 0],\n [4, -5, 2, 12, 12, 0],\n [-4, -6, 4, 0, 0, -... | 2 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -4, 8, 0, -7, -1],\n [14, 11, 12, 1, -2, 11],\n [2, 10, -14, 15, -12, 2],\n [-9, -3, -1, 9, 7, 12],\n [6, 15, 10, -15, -5, -6],\n [9, -11, 0, -5, 5, -10]]\nRound your answer to the nearest integer.\n\... | 993 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, -3, 8, -8, -2, 8],\n [0, 1, 8, -11, 9, -14],\n [0, 0, 14, 8, -7, -12],\n [0, 0, 0, 2, 0, 14],\n [0, 0, 0, 0, 5, 2],\n... | -7111 | MATH |
[
{
"content": "Find the inverse of 1/180 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, -6, 0, 4, -11, -3],\n [2, 1, -7, -2, 1, 13],\n [15, -12, 2, 11, 4, 8],\n [8, -1, -5, -4, -7, -3],\n [-1, 11, -1, 12, -11, 7],\n [3, 10,... | 1400 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[10, -2, 12, 1, 2, 5],\n [-13, -14, -15, -6, 3, 1],\n [-4, -15, -4, 1, 8, 15],\n [-13, -5, 1, 7, 10, -13],\n [-8, 4, -12, 5, 6, -9],\n [-2, -2, -12, 0, 8, 13]]\n\nPresent the answer in... | 8 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[6, 10, -12, -4, 4, -1],\n [10, 0, 6, 2, -8, 14],\n [-12, 6, -10, -1, -6, -6],\n [-4, 2, -1, -5, 10, 7],\n [4, -8, -6, 10, 9, -8],\n [-1, 14, -6, 7, -8,... | -8 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[10, -5, -14, -2, -4, 14],\n [1, -4, 10, -4, -15, -3],\n [-2, 8, 14, -14, -4, 10],\n [5, 12, 0, -12, -8, -14],\n [-6, -7, 7, -1, -3, 7],\n [1, 14, 0, 12, -14, 4]]\nRound your answer to the nearest integer.\n\n... | -18 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 11, -2, -13, 7, -4],\n [0, -14, -12, -2, 0, 3],\n [0, 0, 13, -2, -10, -3],\n [0, 0, 0, -4, 4, 11],\n [0, 0, 0, 0, -8, -9],... | 259 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-5, -11, 0, -9, 11, -11],\n [0, -1, -13, 10, -11, 7],\n [0, 0, -7, -1, -13, 13],\n [0, 0, 0, 5, -8, 5],\n [0, 0, 0, 0, -6, 8],\n [0, 0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent... | 10903 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 2) rounded to the nearest integer?\n[[-6, -4, -10, -4, 7, -2],\n [0, -7, -6, 10, 1, 1],\n [0, 0, 15, 3, -15, -4],\n [0, 0, 0, -3, -14, -6],\n [0, 0, 0, 0, 2, -11],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in La... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (2, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -8, 13, 3, -5, 15],\n [9, 15, -4, -7, -14, -8],\n [10, -5, 12, 5, -12, -6],\n [5, 4, 0, -8, -12, 13],\n [-6, -... | 15 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[14, -8, 8, 11, -2, -2],\n [-8, -15, 3, 0, -1, 7],\n [8, 3, 6, -7, -2, -2],\n [11, 0, -7, 1, -2, 4],\n [-2, -1, -2, -2, 8, 0],\n [-2, 7, -2... | 176 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-9, 8, -15, 11, 2, 8],\n [12, 9, 4, -4, 0, -6],\n [11, -6, -2, 9, 4, -6],\n [-6, 10, 9, -5, 7, -14],\n [9, 4, -8, 14, 7, 13],\n [15, -9, -8, -15, 5, -14]]\nRound your answer to the nearest integer.\n\nPr... | 171 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[2, -1, -15, -11, -14, 4],\n [0, 3, 2, 13, 6, 2],\n [0, 0, 8, -8, 13, 14],\n [0, 0, 0, 7, 4, 1],\n [0, 0, 0, 0, -12, -15],\n [0, 0, 0, 0, 0, -6]]\n\nPre... | 26 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 4, -2, 12, 0, 10],\n [4, 11, -4, 0, -6, 3],\n [-2, -4, 5, -1, 2, 6],\n [12, 0, -1, 10, 0, 10],\n [0, -6, 2, 0, 10, -6],\n [10, 3, 6, 10, -6, -14]]\n\nPresent the answ... | 58 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 4) rounded to the nearest integer?\n[[-5, 1, 11, -3, -3, -9],\n [1, -4, -2, 14, -11, -2],\n [11, -2, 8, 4, -2, 2],\n [-3, 14, 4, -7, -4, -4],\n [-3, -11, -2, -4, 4, -2],\n [-9, -2, 2, -4, -2, -6]]\n\nPresent the ans... | -14 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/180 * A where A =\n[[8, 15, -9, -8, 12, -13],\n [15, -1, 0, -12, 5, -10],\n [-15, -12, -5, -4, 10, 13],\n [-11, 7, 13, 5, 0, -3],\n [-3, 1, 11, -9, -8, -3],\n [7, 11, 0, 14, 13, 15]]\nRound your answer to the nearest integer.\n\nPresent ... | -4 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, -8, 0, 15, 5, -6],\n [0, -4, -4, 10, -11, 0],\n [0, 0, -7, -4, -11, 6],\n [0, 0, 0, 8, -13, -11],\n [0, 0, 0, 0, -9, -6],\n [0, 0, 0, 0, 0... | -113 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, -12, 5, -15, -9, 8],\n [-7, -8, -11, 3, -6, -5],\n [9, -1, -10, -1, -11, 13],\n [3, 6, 3, -6, -4, 6],\n [-12, 15, 2, 0, -8, -12],\n [... | 831 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, -7, 13, 5, 2, -5],\n [0, 14, 15, 9, 7, -14],\n [0, 0, -12, 13, -7, 15],\n [0, 0, 0, 12, -6, 0],\n [0, 0, 0, 0, -6, -15],\n [0, 0, 0, 0, 0,... | -15 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -13, -2, -6, 6, -9],\n [10, 1, 14, -10, 7, 6],\n [-12, 1, 11, -7, -12, -9],\n [7, -14, 1, 8, -8, 7],\n [14, 15, -1, 15, -1, -8],\n [0, 3, -5, -14, 7... | -13 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 4, 3, 3, 5, 7],\n [4, -1, 12, -5, -2, 5],\n [3, 12, -12, -2, 6, 8],\n [3, -5, -2, 2, 6, 11],\n [5, -2, 6, 6, 8, -2],\n [7, 5, 8, 11, -2, 6]]\n\nPresent the answe... | 249 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 4, -1, 7, 12, 0],\n [0, 5, -1, 1, 2, -11],\n [0, 0, 14, -3, 2, -2],\n [0, 0, 0, 4, 4, 3],\n [0, 0, 0, 0, -4, 5],\n [0, 0, ... | -55 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 2, -2, -6, -8, 2],\n [2, -6, 0, -6, 6, 8],\n [-2, 0, -8, -5, 0, 7],\n [-6, -6, -5, 14, 8, -4],\n [-8, 6, 0, 8, 9, 2],\n [2, 8, 7, -4, 2, -5]]\n\nPresent the answer i... | -92 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 0, -6, -4, -5, 2],\n [0, 8, -14, 12, 12, 0],\n [-6, -14, 10, -10, 4, 10],\n [-4, 12, -10, -9, 5, 0],\n [-5, 12, 4, 5, 8, 2],\n [2, 0, 10, 0... | 147 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, -11, 8, 5, 2, -1],\n [-10, 9, 13, 3, -15, -15],\n [-3, -13, -6, 5, -13, -7],\n [-8, -13, 9, 15, -3, -10],\n [-3, 7, 4, 4, -4, -3],\n [-14, 5, 8, 7, 0, 7]]\n\nPresent... | 16 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-10, 3, 5, -3, 1, 7],\n [0, 1, 13, -14, 3, 3],\n [0, 0, 6, 15, -6, -6],\n [0, 0, 0, 1, 11, -1],\n [0, 0, 0, 0, 3, 1],\n [0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPre... | -31650 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 1, -9, -12, -8, -3],\n [0, -10, 9, -11, 14, -4],\n [0, 0, 13, -7, -12, 3],\n [0, 0, 0, 2, -6, 9],\n [0, 0, 0, 0, 14, 8],\... | -2300 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[12, 3, -2, -2, 0, 12],\n [3, -13, 5, 2, 8, 4],\n [-2, 5, -15, 2, 4, 0],\n [-2, 2, 2, 11, 6, 12],\n [0, 8, 4, 6, 0, -6],\n [12, 4, 0, 12, -6, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex for... | 66 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, 8, -7, -5, -2, 10],\n [8, -14, 1, -10, 0, 10],\n [-7, 1, 15, 4, 12, 2],\n [-5, -10, 4, 3, 0, -1],\n [-2, 0, 12, 0, -12, -12],\n [10, 10, 2,... | -69 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 6) rounded to the nearest integer?\n[[-2, 10, 12, 0, 6, 2],\n [10, -10, -4, -12, -2, 11],\n [12, -4, -9, 2, 3, -4],\n [0, -12, 2, 2, -2, 0],\n [6, -2, 3, -2, -14, -2],\n [2, 11, -4, 0, -2, -12]]\n\nPresent the answe... | -4 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 12, -2, 0, -4, 3],\n [12, 7, -10, 2, -6, -4],\n [-2, -10, -3, 4, -5, 0],\n [0, 2, 4, -2, -12, 8],\n [-4, -6, -5, -12,... | -37 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, -4, 9, -8, -3, -12],\n [0, -2, -3, 11, -10, 1],\n [0, 0, 1, -13, 1, -7],\n [0, 0, 0, 4, -14, 4],\n [0, 0, 0, 0, 6, -1],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer i... | 206 | MATH |
[
{
"content": "Find the inverse of 1/180 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, 8, -11, 4, -9, -9],\n [0, -7, 9, 5, -3, -4],\n [0, 0, -6, -15, 9, -8],\n [0, 0, 0, -13, -13, 8],\n [0, 0, 0, 0, -9, 5],\n... | 125 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 15, -5, -3, -9, -3],\n [-14, -10, -7, 15, 4, 9],\n [-14, 2, 0, 9, -4, -9],\n [-9, 1, -3, -5, -10, 13],\... | 31 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, -1, -10, 8, 0, -12],\n [-1, 2, 2, -8, -4, -6],\n [-10, 2, 5, -6, 10, -6],\n [8, -8, -6, -6, -2, 6],\n [0, -4, 10, -2, 0, -4],\n [-12, -6, -6, 6, -4... | -15 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -7, 0, 11, -11, 7],\n [12, 5, -9, -3, 4, 8],\n [13, 11, 14, 10, -3, 11],\n [10, -9, -6, -1, 5, 11],\n [-10, -11, 7, 1... | 85 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[13, 6, 13, 10, 3, -9],\n [0, 14, -13, 8, 13, 4],\n [0, 0, -10, 10, -5, 11],\n [0, 0, 0, 15, -10, -2],\n [0, 0, 0, 0, -1, 2],\n [0, 0, 0, 0, 0, 15]]\nRound your answer to the nearest integer.\n\nPresent t... | 862 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -9, -15, 9, -5, -10],\n [0, -13, 15, 3, -14, 2],\n [0, 0, 13, -6, -11, -7],\n [0, 0, 0, -10, 13, 15],\n [0, 0, 0, 0, 6, 5],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex ... | 160 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -11, -2, 10, 13, 5],\n [-3, 10, -10, 15, -4, 10],\n [-8, -11, 14, -1, 11, 0],\n [-15, 0, -11, -13, 4, -1],\n [15, -3, 8, 0, 7, -5],\n ... | 401 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 4, 0, -2, 6, 4],\n [4, -8, -2, -4, 4, 2],\n [0, -2, -8, 4, 8, 12],\n [-2, -4, 4, -8, 12, -4],\n [6, 4, 8, 12, 0, 3],\... | 36 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[0, -3, 2, -2, 10, -4],\n [-3, -9, -2, -1, 2, 7],\n [2, -2, 12, -8, -1, 5],\n [-2, -1, -8, 9, -5, 10],\n [10, 2, -1, -5, 10, 12],\n [-4, 7, 5, 10, 12, -8]]\nRound your answer to the nearest integer.\n\nPresent... | 269 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, 0, -1, -6, -11, -10],\n [0, -7, 2, 2, -6, -2],\n [-1, 2, 5, 8, -1, 8],\n [-6, 2, 8, 9, 8, 8],\n [-11, -6, -1, 8, -10, 6],\n [-10, -2, 8, 8, 6, -14]]... | -56 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 6, -11, 4, -9, 8],\n [0, 4, -15, -15, 1, 11],\n [-15, 5, 4, -3, 14, -7],\n [-1, -13, ... | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 2, -11, -6, 3, 2],\n [2, 6, -3, -2, 0, 8],\n [-11, -3, -15, -6, -2, -3],\n [-6, -2, -6, -13, -6, ... | 457 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, -9, 1, 10, -15, -11],\n [0, -1, -14, -7, 15, -9],\n [-12, 4, 2, 5, -12, 12],\n [-3, -15, 12, 8, -13, 0],\n [14, 6, -12, 9, 7, 9],\n [0, 10, 3, -15, -11, 3]]\n\nPrese... | -28 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/180 * A where A =\n[[6, 6, 0, 2, 2, -5],\n [6, -12, -5, -13, -10, 2],\n [0, -5, 2, 2, 3, 7],\n [2, -13, 2, -12, 1, 3],\n [2, -10, 3, 1, 10, 4],\n [-5, 2, 7, 3, 4, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in L... | 20 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, -2, 1, -11, -14, 4],\n [0, -2, -2, 11, -15, -13],\n [0, 0, 10, -1, 3, 4],\n [0, 0, 0, 3, 11, -11],\n [0, 0, 0, 0, 13, -9],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answe... | 194 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, -6, -6, -5, 1, -11],\n [-3, -6, -7, 1, -15, -12],\n [-12, 2, -7, 14, 9, 13],\n [13, 2, -2, 9, -1, -10],\n [8, -6, 13, -1, 13, -12],\n [2, 2, 9, 1, ... | 56 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[0, 4, 4, -2, -6, -6],\n [4, -6, 2, -6, 3, -1],\n [4, 2, 4, 4, 2, -1],\n [-2, -6, 4, -12, -2, 2],\n [-6, 3, 2, -2, -8, -8],\n [-6, -1, -1, 2, -8, 15]]\n\nPresent the answ... | 9 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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, 2, 0, 6, -10],\n [4, 2, 4, 0, -11, -2],\n [2, 4, 14, -4, 3, 0],\n [0, 0, -4, -12, -2, 4],\n [6, -11,... | -4 | MATH |
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