messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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[[15, -4, -1, -14, 2, -3],\n [0, -11, 10, -6, -4, -6],\n [0, 0, 15, 9, -14, -11],\n [0, 0, 0, -10, 6, 7],\n [0, 0, 0, 0, 9, 14],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the... | 242 | 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[[1, -6, -4, 1, -12, -14],\n [-5, -9, -14, 10, 2, 5],\n [-12, -8, 4, -2, -4, 6],\n [5, 11, 14, 2, -5, 15],\n [13, 12, 14, -8, -... | -28 | 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[[3, -2, -1, -4, -4, -2],\n [-2, 11, -3, -2, 6, 2],\n [-1, -3, -6, 8, -1, 3],\n [-4, -2, 8, -11, -3, -2],\n [-4, 6, -1, -3, 10, 0],\n [-2, 2, 3, -2, 0, -... | -30 | 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, 11, -4, 2, 0, 0],\n [11, -15, -2, -1, -12, -8],\n [-4, -2, 5, 0, -2, -3],\n [2, -1, 0, 10, 0, -4],\n [0, -12, -2, 0, -10, 0],\n [0, -8, -3, -4, 0, 11]]\n\nPresen... | 800 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-7, -8, 12, -6, 1, 7],\n [14, 13, 10, -10, -2, 6],\n [6, -10, 10, -9, -4, -13],\n [-2, 6, 3, 7, 0, -9],\n [-8, 2, 9, -3, 5, -7],\n [-6, 5, 7, 11, -7, -1]]\nRound your answer to the nearest integer.\n\nPr... | 512 | 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, -14, 9, -3, -14, 3],\n [10, -14, -13, -10, -13, 15],\n [-6, 8, 11, -10, 7, 0],\n [1, 3, -13, 2, -9, -7],\n [4, -4, -11, -1... | -116 | 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[[-14, -10, 15, 3, -8, 10],\n [0, -13, 10, -2, 9, 0],\n [0, 0, -13, 6, 10, 2],\n [0, 0, 0, 5, 9, -15],\n [0, 0, 0, 0, -10, 7],\... | 36 | 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, -8, 10, 4, -13, -4],\n [0, -4, -14, 8, -2, 6],\n [0, 0, -11, -7, 5, -5],\n [0, 0, 0, 1, -14, 8],\n [0, 0, 0, 0, -2, -11],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the a... | 32735 | 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, -14, -8, -7, 11, -13],\n [0, -9, -11, 5, 10, -11],\n [0, 0, 5, 13, 4, 15],\n [0, 0, 0, 2, 9, -14],\n [0, 0, 0, 0, 9, -13],\n [0, 0, 0, ... | 3554 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-4, -2, 3, 7, 4, 0],\n [-2, 14, -1, -5, -4, -4],\n [3, -1, -1, 10, -10, 7],\n [7, -5, 10, -11, 8, -2],\n [4, -4, -10, 8, 2, 0],\n [0, -4, 7, -2, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent t... | -7 | 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[[12, 7, 0, -13, 10, 2],\n [0, 7, 5, -2, -1, 1],\n [0, 0, 5, 1, 7, 9],\n [0, 0, 0, -2, 13, 4],\n [0, 0, 0, 0, 8, -3],\n [0, 0, ... | 146 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-8, 2, -9, -10, 12, 3],\n [2, 3, -2, -1, 0, 0],\n [-9, -2, 4, 7, 0, -3],\n [-10, -1, 7, -5, 12, -6],\n [12, 0, 0, 12, 15, 6],\n [3, 0, -3, -6, 6, 0]]\n\nPresent the answer in La... | 20 | 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[[-8, 14, -4, -13, 1, 5],\n [0, -5, -12, 0, 1, -7],\n [0, 0, 11, 4, 9, -14],\n [0, 0, 0, 13, -10, -13],\n [0, 0, 0, 0, 7, -15],\n [0, 0, 0, 0, 0, -1]]\n\nPrese... | -1529 | 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, 10, 9, -2, 10, 6],\n [-9, -2, 15, 10, 15, 8],\n [11, 15, 13, -6, 1, -2],\n [-8, -12, 10, 0, 8, -3],\n [... | -22 | 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, -13, -8, 4, 6, -6],\n [0, 3, 14, 5, 12, -13],\n [0, 0, -5, 15, 1, 0],\n [0, 0, 0, 7, 3, -4],\n [0, 0, 0, 0, -11, -1],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format... | -233 | 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[[4, -1, 4, -12, 6, 2],\n [-10, 7, 11, 10, 3, -5],\n [12, 8, -14, 11, -8, 13],\n [-5, -11, 2, 7, 14, 2],\n [-2, 6, -6, -13, -7, -13],\n [-5, 15, -4, -4, -13, 5]]\n\nPresent the answer i... | 52 | 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[[-9, -2, 8, 12, -5, -9],\n [9, 5, -6, -5, -1, 3],\n [0, 6, 5, 12, 4, -4],\n [2, 7, -3, -11, -12, 12],\n [-2, -8, -7, 9, 3, -13],\n [-11, 5, 10, ... | 9 | 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[[3, 1, 1, -5, 15, -14],\n [-10, 6, -2, -13, -4, -12],\n [-4, -3, -14, -14, -1, 7],\n [13, 1, -9, 14, 12, -2],\n [-4, 14, 1, -2, -10, 3],\n [8, -... | -24 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[8, 4, -4, -11, -6, -4],\n [4, -5, 1, 9, 7, -2],\n [-4, 1, -4, 0, -6, 12],\n [-11, 9, 0, 7, -4, -6],\n [-6, 7, -6, -4, 4, 6],\n [-4, -2, 12, -6, 6, 2]]\nRound your answer to the nearest integer.\n\nPresent the... | 132 | 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, 6, -12, 4, -2, -6],\n [6, -8, -6, 5, 2, 0],\n [-12, -6, -14, 12, -8, 3],\n [4, 5, 12, 9, 0, -8],\n... | 290 | 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[[3, 2, -7, 0, -3, -6],\n [0, 4, -2, -4, 9, 3],\n [0, 0, -1, 0, 11, -8],\n [0, 0, 0, 3, 3, ... | 2754 | 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[[-11, -7, 2, -5, 0, -14],\n [-4, 6, -10, -5, 11, -8],\n [-4, 13, 11, 14, -14, -7],\n [-1, -14, 13, -15, -6, -14],\n [-4, 7, -8, -11, 6, 12]... | 348 | 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[[-3, 3, 11, -15, -5, 4],\n [0, 14, -8, -11, 1, 14],\n [0, 0, -6, -14, -7, 8],\n [0, 0, 0, ... | 592 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[6, -9, -6, -6, -2, 4],\n [-9, 1, 4, 2, -1, 4],\n [-6, 4, 12, -4, -7, 6],\n [-6, 2, -4, -15, 6, -2],\n [-2, -1, -7, 6, -7, -5],\n [4, 4, 6, -2, -5, 10]]\n\nPresent the answer in ... | -4 | 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[[5, -11, -6, -10, 8, 3],\n [0, -3, -15, 4, 9, -1],\n [0, 0, -6, -7, 1, -7],\n [0, 0, 0, -6, 9, 1],\n [0, 0, 0, 0, 6, -12],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in ... | -32 | 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[[-8, 0, 12, 3, -14, 2],\n [0, -4, -1, -11, 4, 8],\n [12, -1, -5, 6, 0, 6],\n [3, -11, 6, 13, 3, 0],\n [-14, 4, 0, 3, -9, -5],\n [2, 8, 6, 0, -5, 14]]\n\nPresent the answer in LaTex for... | -32 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[0, 4, 0, 3, 4, -9],\n [4, -3, 2, 4, -10, -1],\n [0, 2, 1, -1, -2, 4],\n [3, 4, -1, 12, -2, 3],\n [4, -10, -2, -2, 4, -7],\n [-9, -1, 4, 3, -7, 0]]\n\nPresent the answer in LaTex... | 5 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[-2, 4, 8, 0, -3, 4],\n [4, 15, -11, -6, 12, 0],\n [8, -11, -3, 6, -4, 12],\n [0, -6, 6, -9, -9, -9],\n [-3, 12, -4, -9, -11, 4],\n [4, 0, 12, -9, 4, 4]]\n\nPresent the answer in... | -1 | 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[[11, -15, -2, 1, -6, -4],\n [0, -2, 14, 11, 0, -8],\n [0, 0, -6, 13, 1, 11],\n [0, 0, 0, 4, 0, 1],\n [0, 0, 0, 0, -8, -10],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer i... | -63 | 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[[15, -2, 10, -4, 8, 0],\n [-2, -7, -9, -6, 3, -6],\n [10, -9, 2, 2, 0, 10],\n [-4, -6, 2, -13, 0, 2],\n [8, 3, 0, 0, -11, 6],\n [0, -6, 10, 2, 6, 4]]\n\nPresent the ... | 487 | 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[[6, 6, -8, -3, 6, -2],\n [6, 5, 10, -2, 7, 0],\n [-8, 10, -7, 4, 4, 10],\n [-3, -2, 4, 6, -8, 2],\n [6, 7, 4, -8, -11, -6]... | 96 | MATH |
[
{
"content": "Find the value at position (3, 5) of the inverse of matrix 1/180 * A where A =\n[[11, 8, 2, -2, -1, -2],\n [8, 1, -2, 2, 10, 0],\n [2, -2, 6, 6, 7, -8],\n [-2, 2, 6, -14, 6, -4],\n [-1, 10, 7, 6, -6, -1],\n [-2, 0, -8, -4, -1, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer i... | -11 | 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[[14, 11, 1, -12, 15, 7],\n [0, -5, -10, -10, 11, -7],\n [0, 0, -14, -12, -11, 1],\n [0, 0, 0, -4, 5, -8],\n [0, 0, 0, 0, 3, 3],\n [0, 0, 0, 0, 0... | 69 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[4, 0, -5, -9, 1, 1],\n [0, -3, -6, -9, -2, 7],\n [0, 0, -12, 5, -11, 4],\n [0, 0, 0, -9, 15, -6],\n [0, 0, 0, 0, -15, -9],\n [0, 0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\... | -102 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 6) of the inverse. Round your answer to the nearest integer:\n[[15, -12, -12, 12, 9, -3],\n [7, 3, -6, -11, -9, 8],\n [0, -15, -4, -14, -9, -5],\n [15, 13, 14, -3, 15, -14],\n [-9, -1, 9, -5, -14, -9],\n [-12, -5, 1... | 17 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-9, -3, -11, 1, 5, -4],\n [0, 3, -9, -10, -8, -3],\n [0, 0, -7, 14, -5, 8],\n [0, 0, 0, -9, 9, -9],\n [0, 0, 0, 0, -5, -9],\n [0, 0, 0, 0, 0, 1]]\nRound your answer to the nearest integer.\n... | -4077 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -11, 13, 12, 14, -9],\n [-7, 9, -15, 15, -15, 3],\n [-10, 2, -6, 12, -5, -15],\n [-15, -3, -11, 4, -15, 4],\n [-... | -29 | 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[[10, 5, 1, 6, 13, 9],\n [0, 7, 6, -11, -12, -12],\n [0, 0, 5, -3, 6, -11],\n [0, 0, 0, 7, -9, 4],\n [0, 0, 0... | 330 | 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[[13, 12, -8, 8, -13, 9],\n [0, -15, -14, -1, 6, 12],\n [0, 0, 6, -2, 1, 11],\n [0, 0, 0, 10, -3, 11],\n [0, 0, 0, 0, -1, 3],\n [0, 0, 0, 0, 0, 15]]\n\nPresent... | -260 | 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[[-2, -2, 8, -5, 4, 2],\n [-2, -8, -2, 0, 2, 2],\n [8, -2, 9, 10, -4, -8],\n [-5, 0, 10, -10, -2, -1],\n [4, 2, -4, -2, 11, -2]... | -396 | 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[[2, 6, -7, 8, 9, 13],\n [0, 10, -8, 3, 8, 0],\n [0, 0, -10, 6, -13, -6],\n [0, 0, 0, -12, 10, -4],\n [0, 0, ... | 153 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-3, 2, -7, 10, 8, 8],\n [-7, 15, 7, 13, -7, -6],\n [12, -14, -10, -1, -13, -5],\n [15, -10, -13, 8, 15, -5],\n [-1, -3, 4, 12, -6, -10],\n [-1, 9, 2, 2, -9, -1]]\nRound your answer to the nearest integer.\n\n... | 71 | 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[[2, 2, 4, -7, 8, -14],\n [0, 4, -14, -5, 10, -9],\n [0, 0, -6, -11, -5, -15],\n [0, 0, 0, ... | 1364 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[14, 14, -15, 8, -2, -12],\n [-11, -5, 8, 12, 15, 7],\n [-3, 0, 8, -3, 8, 6],\n [10, -14, 0, -10, -2, -15],\n [1, -5, 3, -13, -5, 13],\n [-11, 1, 10, 6, -9, -6]]\nRound your answer to the nearest integer.... | 432 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/180 * A where A =\n[[12, 13, -5, -13, 4, -6],\n [0, -6, -2, -4, -1, -6],\n [0, 0, 10, 3, -15, 8],\n [0, 0, 0, -14, 1, 14],\n [0, 0, 0, 0, 11, -7],\n [0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in... | 0 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[4, 1, 0, -4, 0, -2],\n [1, -12, -6, -4, 3, 4],\n [0, -6, -5, 2, -11, -10],\n [-4, -4, 2, -1, -3, 6],\n [0, 3, -11, -3, -11, -4],\n [-2, 4, -10, 6, -4, 10]]\nRound your answer to the nearest integer.\n\nPresen... | 58 | 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, 14, -8, 13, 13, -15],\n [-14, 14, -1, 4, 12, 2],\n [-5, 9, -6, 8, 8, -12],\n [-11, -12, -3, 9, -3, 2],\n [13, 11, 8, -14, ... | -51 | 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, 13, -6, -15, -6, 5],\n [-7, 12, -1, -1, -13, 9],\n [-11, -7, 10, 6, -7, 7],\n [-9, 8, 7, -4, 9, 11],\n [-7, -10, 7, -14, 15, -7],\n [12, 13, 1, -15, 3, 12]]\n\n... | 455 | 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[[-5, 1, 1, -14, -3, -2],\n [0, 12, -6, -13, 13, 11],\n [0, 0, -1, -7, -6, -8],\n [0, 0, 0, 2, -11, -10],\n [0, 0, 0, 0, 4, 0],\n [0, 0, 0, 0, 0,... | -81 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[6, 8, 12, -14, -8, 1],\n [8, -4, 0, -10, -2, -7],\n [12, 0, -10, 1, -6, 4],\n [-14, -10, 1, -4, -9, 2],\n [-8, -2, -6, -9, -1, -3],\n [1, -7, 4, 2, -3, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer i... | 27 | 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[[3, -1, -10, 11, -5, 5],\n [0, 4, 4, 5, 2, 9],\n [0, 0, -14, 10, 14, -7],\n [0, 0, 0, -6, 7, -12],\n [0, 0, 0, 0, -12, 10],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format... | 128 | 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, 0, 0, 12, 5, 4],\n [0, 14, 8, -7, 2, -6],\n [0, 8, 6, 1, -6, 1],\n [12, -7, 1, -12, -4, -4],\n [5, 2, -6, -4, 0, -5],\n [4, -6, 1, -4, -5, 15]]\n\nPresent the answer ... | 30 | 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[[5, 6, -14, -8, 11, -7],\n [0, -14, -10, 6, -8, 10],\n [0, 0, -7, -15, -7, -6],\n [0, 0, 0, 14, -6, -1],\n [0, 0, 0, 0, -3, 1],\n [0, 0, 0, 0, 0... | -75 | 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[[-13, 13, 2, 4, -1, -2],\n [0, 1, 6, 15, 10, -8],\n [0, 0, 2, 14, 9, 15],\n [0, 0, 0, 12, -8, 15],\n [0, 0, 0, 0, 6, 1],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer... | 5247 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (5, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, 5, -4, -11, -5, 4],\n [-13, 5, -1, -2, -5, 4],\n [-8, -12, 11, -4, -8, -10],\n [-1, 14, -4, 0, 0, 11],\n [5, 4,... | 4 | 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[[-3, 14, 11, -1, 0, 0],\n [0, 1, -5, -8, 4, -13],\n [0, 0, 4, 0, -2, 0],\n [0, 0, 0, 15, 14, -5],\n [0, 0, 0, 0, 14, 11],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: ... | 4022 | 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[[7, -2, 14, -15, -3, 14],\n [0, -9, -1, 4, -6, -2],\n [0, 0, 8, 9, 6, -4],\n [0, 0, 0, 14, 9, 4],\n [0, 0, 0, 0, -14, 6],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in ... | 2 | 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, 9, 7, -11, 7, 13],\n [9, -8, 0, 6, 0, -3],\n [4, 13, -1, -15, 6, -13],\n [-10, 6, -2, -12, 2, -1],\n [-7, 2, -13, -6, 1, -9],\n [-1, ... | 388 | 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[[1, -11, -9, 3, 9, 8],\n [13, -1, -13, -1, -11, 7],\n [-4, 14, 4, -11, -13, -7],\n [10, -7, -9, 10, -14, 7],\n [7, 11, 5, 0, -7, -3],\n [12, 11, 3, 4, 1, -10]]\n\nPresent... | -97 | 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[[-12, -15, 2, 15, 3, -7],\n [-3, -8, 7, -3, -1, -5],\n [-4, -2, -12, -15, 8, -12],\n [3, -7, -6, -12, 4, 14],\n [-7, -3, -... | -210 | 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[[4, 9, -4, 5, 9, -5],\n [0, 14, 2, 14, 15, 9],\n [0, 0, 1, -2, -15, 1],\n [0, 0, 0, -11, -11, -7],\n [0, 0, 0, 0, 6, 14],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answe... | 8995 | 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, 10, 9, -2, 0, 7],\n [10, -1, -2, -7, -5, 9],\n [9, -2, 7, 5, 8, -7],\n [-2, -7, 5, -6, -3, 10],\n [0, -5, 8, -3, -12, -8],\n [7, 9, -7, 10, -8, -12]]\n\nPresent the... | 60 | 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[[15, -15, 1, 10, 1, -9],\n [0, 4, -1, -3, 12, -14],\n [0, 0, 8, -3, 8, -5],\n [0, 0, 0, -6, -7, 11],\n [0, 0, 0, 0, -15, 1],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the an... | 511 | 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[[13, 2, -1, -10, -9, 1],\n [0, -8, -4, 5, -2, -4],\n [0, 0, 6, 4, -1, 15],\n [0, 0, 0, -6, -6, 0],\n [0, 0, 0, 0, -11, 7],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: ... | -96 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-11, 8, -4, -12, -1, -7],\n [0, -6, 13, 12, 7, 15],\n [0, 0, -8, -4, 6, 8],\n [0, 0, 0, 14, -15, 0],\n [0, 0, 0, 0, 2, -5],\n [0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.... | 340 | 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[[14, -9, 7, 6, -6, -5],\n [9, -3, -7, 15, -9, -7],\n [-3, 10, -13, -13, -15, 5],\n [15, 4, -14, 9, -13, -1],... | -23 | 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[[6, 0, 2, 6, 6, 2],\n [0, -1, -12, 6, 2, 1],\n [2, -12, -10, 6, -4, 4],\n [6, 6, 6, -7, 4,... | 72 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, 8, 4, 3, -2, 8],\n [8, -3, 0, -2, 8, 6],\n [4, 0, -6, 13, 8, -6],\n [3, -2, 13, 11, 0, -11],\n [-2, 8, 8, 0, -1, -2],\n [8, 6, -6, -11, -2, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex ... | 58 | 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, 4, 10, -9, 8, -14],\n [0, 7, 0, -3, -8, -10],\n [0, 0, -12, 11, -5, -11],\n [0, 0, 0, -9, 11, -1],\n [0, 0, 0, 0, -5, 12],\n [0, 0, 0, 0, 0... | -19 | 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[[-7, -2, 0, 6, 4, 4],\n [-2, -5, -3, -3, 11, -9],\n [0, -3, -7, -1, 7, 0],\n [6, -3, -1, 6, -4, 0],\n [4, 11... | -13 | 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[[-11, -10, 14, 11, -9, 15],\n [-1, 10, -15, 8, -12, 13],\n [9, -15, -5, 2, -2, 6],\n [-5, -6, 11, 14, 1, -12],\n [8, -1, 10, 0... | 16 | 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, -3, 6, 8, 15, 6],\n [0, -1, 11, 2, 4, -2],\n [0, 0, -11, 10, -12, -14],\n [0, 0, 0, -6, 2, 1],\n [0, 0, 0, 0, -15, -15],\n [0, 0, 0, ... | 1937 | 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[[11, 12, -15, -11, 15, -7],\n [14, 9, 1, 0, -8, 1],\n [-1, 8, -15, -4, -11, 8],\n [-10, 9, -15, 9, -15, -6],... | -222 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 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[[12, -2, -12, 13, 1, 1],\n [-4, 12, 4, 2, -13, -5],\n [9, 2, -12, 1, 2, -11],\n [-2, -6, -1, -15, 0, -5],\n [7, 4, -... | -59 | 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[[-7, 6, -4, 1, 14, 9],\n [0, 13, -1, 14, 3, 11],\n [0, 0, 13, 10, 15, 11],\n [0, 0, 0, -7, 11, -3],\n [... | 816 | 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, 10, -5, 2, 1, -4],\n [10, 6, 10, 5, 1, 4],\n [-5, 10, -13, -4, -12, 8],\n [2, 5, -4, 3, 0, -12],\n [1, 1, -12, 0, 0, 2],\n [-4, 4, 8, -... | 1269 | 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[[1, 6, 2, 6, 4, 1],\n [6, 8, 0, -1, -2, -8],\n [2, 0, -14, -3, 2, 2],\n [6, -1, -3, -3, -10, 4],\n [4, ... | 566 | 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, -9, 8, -13, 14, 4],\n [0, 3, -9, -7, 3, -3],\n [0, 0, 6, 2, 13, 7],\n [0, 0, 0, -5, 15, -15],\n [0, 0, 0... | 67 | 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[[-2, 12, 5, -5, 0, 3],\n [1, 11, 10, -10, -5, 1],\n [-7, 2, 1, 15, -4, 7],\n [6, 6, 14, -11, -5, -12],\n [11, -12, -13, 10... | 108 | 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, -15, 5, 3, 5],\n [4, 2, -5, 4, -13, 13],\n [1, -4, -6, -8, -1, -11],\n [-12, 10, 12, 5, 4, 3],\n [5... | -114 | 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, -13, 5, 10, 15, 11],\n [0, -15, -13, -13, -11, 3],\n [0, 0, -15, -12, 13, 13],\n [0, 0, 0, 1, -2, 2],\n [0, 0, 0, 0, -13, 7],\n [0, 0, 0, ... | 114 | 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[[-5, 15, 5, 10, -7, 10],\n [-13, -10, 8, -5, -7, 13],\n [-1, 7, 12, -13, -15, 4],\n [13, 6, 3, -2, 1, 6],\n [-2, 1, 9, 11, -2, -4],\n [0, -15, -... | 22 | 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[[7, 3, -10, -9, -15, -15],\n [13, -11, -10, 15, 0, 15],\n [9, 0, -2, -15, -3, 4],\n [-6, 8, -6, -7, 15, -3],\n [-13, 11, 2, 4,... | 13 | 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[[-14, -15, 8, -11, 8, -13],\n [0, 12, -9, 8, 15, 6],\n [0, 0, 7, 14, 12, 2],\n [0, 0, 0, -15, -11, 1],\n [0, 0, 0, 0, 4, -12],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex fo... | 58 | 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[[-14, 8, 5, -2, -9, 2],\n [8, 10, -5, -4, -6, 4],\n [5, -5, -3, 4, -4, 12],\n [-2, -4, 4, 14, 4, -2],\n [-9, -6, -4, 4, -7, -10],\n [2, 4, 12, -... | 0 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[0, -3, -6, 4, 2, -2],\n [-3, -15, -4, 4, -2, 3],\n [-6, -4, 0, 10, -2, -6],\n [4, 4, 10, -5, -10, -4],\n [2, -2, -2, -10, -11, -2],\n [-2, 3, -6, -4, -... | -165 | 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[[4, -6, -7, -6, 13, -10],\n [0, 12, 9, -10, -12, 14],\n [0, 0, 7, 3, 2, 10],\n [0, 0, 0, 1, 15, -11],\n [0, 0, 0, 0, -3, -12],\n [0, 0, 0, 0, 0, -11]]\n... | -77 | 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[[-9, -15, 15, 7, 13, -4],\n [-5, 8, -8, 9, -10, 12],\n [6, -14, 3, 4, 4, 8],\n [-2, -15, -6, 0, 14, -12],\n [11, 12, 13, -5, 0, 11],\n [4, -15, 0, 3, 5,... | -94 | 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, 2, 9, 2, -8],\n [1, -3, -12, -6, -6, 12],\n [2, -12, -15, 4, -4, 1],\n [9, -6, 4, 0, 4, 6],\n [2, -6, -4, 4, 13, -10],\n [-8, 12, 1, 6, -10, 7]]\n\nPresent the answer in LaTex ... | 54 | 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, -3, -8, 8, -11, -4],\n [0, -13, -13, -15, 9, 6],\n [0, 0, -4, -7, -7, 2],\n [0, 0, 0, 11, -12, -3],\n [0, 0, 0, 0, -13, -1... | 281 | 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, 13, 7, 11, 6, -6],\n [9, -3, 0, -7, -14, 7],\n [-11, 13, 6, 1, 7, 6],\n [-12, 1, -7, 4, -14, 8],\n [2, ... | 26 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[5, -3, 15, 13, -7, 11],\n [14, -9, 7, 8, 15, -11],\n [-11, 1, 14, -7, -10, 9],\n [3, 0, 5, -14, -6, 0],\n [-11, -1, -3, -3, -3, -1],\n [-2, -8, -5, 2, 8, -12]]\nRound your answer to the nearest integer.\... | 16181 | MATH |
[
{
"content": "Find the value at position (5, 6) of the inverse of matrix 1/180 * A where A =\n[[10, -6, 15, -15, 13, -11],\n [0, -15, 7, -8, -13, -13],\n [0, 0, -13, -1, -8, -13],\n [0, 0, 0, 2, -5, -5],\n [0, 0, 0, 0, -15, 13],\n [0, 0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\n\nPresent the a... | -12 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-12, -1, 2, -2, -2, -1],\n [-1, -3, 4, 4, -4, 0],\n [2, 4, -15, -6, -6, 6],\n [-2, 4, -6, -8, -3, -8],\n [-2, -4, -6, -3, -12, 10],\n [-1, 0, 6, -8, 10, -3]]\n\nPresent the answ... | -162 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-2, 7, 12, -2, 6, -6],\n [0, 15, -11, 7, 11, -10],\n [0, 0, -3, 13, -3, 3],\n [0, 0, 0, -15, -8, 6],\n [0, 0, 0, 0, -10, 0],\n [0, 0, 0, 0, 0, -5]]\n\n... | 0 | 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[[-14, -6, -15, -12, 9, -4],\n [0, -12, -7, 15, 12, -10],\n [0, 0, 13, -2, 6, 9],\n [0, 0, 0, 2, 4, 0],\n [0, 0, 0, 0, 7, -5],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex... | 0 | 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[[6, 7, 8, 2, -3, -6],\n [7, 14, 3, 8, 2, -3],\n [8, 3, -11, 0, -10, 2],\n [2, 8, 0, -9, -8, 0],\n [-3, 2, -10, -8, -10, -4],\n [-6, -3, 2, 0, -4, -8]]\n\nPresent the... | 641 | 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[[-9, -2, 10, 7, -6, -4],\n [-2, 13, 8, -6, 9, 2],\n [10, 8, -15, -10, 2, 1],\n [7, -6, -10, -13, 4, -1],\n [-6, 9, 2, 4, 7, 2],\n [-4, 2, 1, -1, 2, -7]]... | -44 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-6, 6, 5, 0, 2, -10],\n [6, 12, 0, 13, -4, 4],\n [5, 0, 10, 6, 1, -2],\n [0, 13, 6, -15, 10, 2],\n [2, -4, 1, 10, -14, 0],\n [-10, 4, -2, 2, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex ... | 22 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[1, -4, 2, -2, 0, 6],\n [-4, -13, 5, -1, 1, 4],\n [2, 5, 9, 2, 4, 0],\n [-2, -1, 2, -12, -4, 2],\n [0, 1, 4, -4, -13, -6],\n [6, 4, 0, 2, -6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answ... | -46 | MATH |
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