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[[1, -10, 15, -4, -4, -12],\n [-10, -10, -2, 0, -4, 0],\n [15, -2, 4, 0, 0, 1],\n [-4, 0, 0, 6, 11, 0],\n [-4, -4, 0, 11, -15, 4],\n [-12, 0, 1, 0, 4, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in ... | 25 | 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[[-13, -2, 10, -8, 9, 14],\n [-2, 9, -3, 8, 2, 9],\n [10, -3, -10, -2, 3, 8],\n [-8, 8, -2, 0, 14, 6],\n [9, 2, 3, 14, 0, 2],\n... | 14 | 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[[7, 3, 0, -4, -2, 2],\n [3, -5, -8, 6, 8, 9],\n [0, -8, 7, 9, 5, -6],\n [-4, 6, 9, -14, 10, -12],\n [-2, 8, 5, 10, -2, 3],\n [2, 9, -6, -12, 3, -6]]\n\nPresent the a... | 216 | 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, 11, -10, 15, 7],\n [-10, 0, 5, -8, -11, 15],\n [7, -11, 8, -6, -10, -13],\n [11, 5... | -29 | 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, 2, 2, -12, -8, 10],\n [0, -15, 5, 11, 10, -2],\n [0, 0, -2, 12, 15, 12],\n [0, 0, 0, -5, 8, -10],\n [0, 0, 0, 0, 8, -15],\n [0, 0, 0, 0, 0,... | -120 | 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, 5, 3, 5, 8, -15],\n [0, 10, 6, 5, -10, -10],\n [0, 0, 1, -5, 11, 0],\n [0, 0, 0, 5, -9, 3],\n [0, ... | 1203 | 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[[-2, -6, 4, 12, 9, 6],\n [0, 8, 11, -14, -5, 9],\n [0, 0, -12, 0, 11, -8],\n [0, 0, 0, -14, -3, -5],\n [0, 0, 0, 0, 7, -14],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the an... | 2200 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[12, 10, -3, -13, -7, 6],\n [-12, -11, -12, -15, -4, -7],\n [-14, 0, -5, 4, 8, 2],\n [2, -3, 2, 13, 10, 13],\n [4, -6, 9, 7, -2, 7],\n [12, 14, -12, -2, 8, 10]]\nRound your answer to the nearest integer.\n\nPresent the answ... | -68 | 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[[-13, -3, 1, 6, 0, 6],\n [-3, 15, 6, -5, 1, 0],\n [1, 6, 5, -2, -6, -9],\n [6, -5, -2, 13, -6, 10],\n [0, 1, -6, -6, -14, -1],... | 16 | 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, -12, -13, 8, 3, 14],\n [0, 8, -14, -10, 8, 3],\n [0, 0, -2, 6, -13, 11],\n [0, 0, 0, -7, -1, -2],\n [0, 0, 0, 0, 5, -2],\n [0, 0, 0, 0, 0, ... | -104 | 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, -8, -12, -7, 2, 8],\n [7, -13, 3, -13, 8, 1],\n [15, 3, 1, -11, -10, -6],\n [-11, -10, -5, -12, 15, 14],\n [-15, 8, 15, -5, 5, 2],\n [-14, -10, -8, -14, 6, -6]]\nRound your answer to the... | -30 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 11, 8, 12, -8, 4],\n [10, 9, -2, -7, 4, 4],\n [-9, -11, 8, 4, 9, 15],\n [4, 13, 15, -3, -11, 0],\n [-6, -3, -1... | 68 | 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, -11, 6, -8, -12, -2],\n [-2, -8, 2, -6, -13, -9],\n [7, -7, -9, 1, 6, -11],\n [7, 7, ... | -25 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[13, 2, -7, -2, -7, 2],\n [2, -13, 2, 2, 8, 4],\n [-7, 2, -9, 0, -8, 0],\n [-2, 2, 0, -8, 4, 5],\n [-7, 8, -8, 4, -13, 0],\n [2, 4, 0, 5, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer... | -172 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[6, -1, 0, -1, 8, -1],\n [0, 4, 1, -9, 6, -15],\n [0, 0, 9, 7, 6, 8],\n [0, 0, 0, -14, -15, -4],\n [0, 0, 0, 0, 14, 14],\n [0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer i... | 131 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-2, 1, -2, 1, -14, 2],\n [-1, -6, 2, 4, -15, -1],\n [-13, 9, -2, 9, -13, 5],\n [9, 12, 5, 3, 4, 7],\n [-7, -8, 11, -2, -8, -1],\n [10, 12, 13, 1, 3, -9]]\nRound your answer to the nearest integer.\n\nPre... | 220 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[5, 9, 7, -11, -4, -13],\n [13, 6, -10, -15, 1, -1],\n [12, -11, -1, -14, 11, -9],\n [3, -1, -6, 15, 7, -11],\n [1, 13, 8, 9, -3, 10],\n [-7, 3, -15, 9, -12, 2]]\nRound your answer to the nearest integer.... | 399 | 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[[-1, 8, -1, 7, 5, 6],\n [-12, 0, 13, -6, 4, 3],\n [-15, 15, 14, -8, 4, -9],\n [-7, -9, 7, 4, -12, -10],\n [-7, 6, 1, 13, -15, -7],\n [6, 3, 4, 11, 6, 14]]\n\nPresent the answer in LaTe... | 18 | 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[[-11, 0, 9, 0, -8, 1],\n [0, -9, -6, 4, 4, 0],\n [9, -6, -4, 5, 0, -12],\n [0, 4, 5, 2, 12, 4],\n [-8, ... | 406 | 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[[0, 1, -5, -1, 7, 4],\n [-1, -4, 3, 14, 0, -1],\n [10, -15, -4, 1, 9, 9],\n [-2, -15, -11, 14, -13, -7],\n [-4, 3, 1, 10, ... | 33 | 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[[-6, 9, 10, 2, 0, -6],\n [9, -4, 12, 5, -7, 7],\n [10, 12, -1, -10, -1, 8],\n [2, 5, -10, -14, 1, -2],\n [0, -7, -1,... | 22 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/180 * A where A =\n[[-1, -3, -4, -9, 5, 5],\n [0, -12, -3, 14, -12, 6],\n [0, 0, 3, 2, 7, 4],\n [0, 0, 0, -15, 3, 0],\n [0, 0, 0, 0, 2, 6],\n [0, 0, 0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex f... | 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[[10, 15, -7, 2, 5, 14],\n [0, 8, -6, -2, -11, -9],\n [0, 0, -13, -5, -14, 0],\n [0, 0, 0, -5, -9, 9],\n [0, 0, 0, 0, -1, -2],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the an... | 1544 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/180 * A where A =\n[[-14, -8, 0, 2, -10, -6],\n [0, 15, -14, 12, -13, 7],\n [0, 0, 3, -12, -8, 2],\n [0, 0, 0, 4, -6, -7],\n [0, 0, 0, 0, 4, 7],\n [0, 0, 0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in ... | 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, 10, -3, -7, -4, -12],\n [0, -10, -4, 8, 7, 1],\n [0, 0, -2, 14, 4, 15],\n [0, 0, 0, -5, -1, 1],\n [0, 0, 0, 0, -13, 1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the ans... | 1410 | 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[[-11, -4, -5, 9, 0, 13],\n [-9, 9, 0, 13, -14, 4],\n [-3, -9, -1, 15, -5, -14],\n [13, 4, 10, -9, -13, -12],\n [11, -3, 15, 1, 14, -3],\n [-10, 8, 0, -3, 2, 3... | -37 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -4, -3, -4, -2, -7],\n [-4, 5, 1, 6, 3, 10],\n [-3, 1, 9, -5, -1, -9],\n [-4, 6, -5, -14, -2, 0],\n [-2, 3, -1, ... | -4 | 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, -12, -3, 7, -6, -11],\n [5, 12, 5, 15, 12, -9],\n [4, -9, 2, -7, -7, 12],\n [13, -15, -9, -6, -14, 7],\n [-10, 5, -4, 1, 6... | 26 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -14, 3, -2, -4, 15],\n [0, 4, 14, 6, -6, -2],\n [0, 0, -8, 14, -10, -11],\n [0, 0, 0, -15, -13, 4],\n [0, 0, 0, ... | 1320 | 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, -2, 10, -12, 9, 10],\n [0, 5, -2, 5, 13, -12],\n [0, 0, -4, -6, 15, -12],\n [0, 0, 0, -3, -3, 0],\n [0, 0, 0, 0, -13, -2],... | -863 | 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, -13, 7, -12, 1, -4],\n [-11, -13, 1, -14, -10, 5],\n [3, -5, -7, -12, -15, 6],\n [1, 10, -6, 4, -7, -1],\n [-13, 10, -14, -6, -1, -3],\... | 392 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 2, 10, 8, 9, -10],\n [-3, -8, -14, 12, -2, 3],\n [-8, 8, 14, 5, -5, -10],\n [-13, -13, 8, 13, 12, 3],\n [-10, 1... | 7 | 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[[12, -4, -1, 6, 4, 6],\n [-4, 5, -2, 0, 3, 2],\n [-1, -2, -6, -4, 6, -10],\n [6, 0, -4, -13, -3, -10],\n [4, 3, 6, -3, -13, 9],\n [6, 2, -1... | 1732 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, 4, -5, 0, -5, 3],\n [0, -12, -15, -1, 15, -4],\n [-13, 2, 2, -2, -15, -5],\n [5, 13, -6, 1, -4, -10],\n [-9, 6, 12, 7, -1, -15],\n [-3, -8, 14, -4, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer... | -157 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[13, 1, -2, -4, 4, 4],\n [1, 15, 7, -8, -1, 2],\n [-2, 7, -6, 2, -12, 6],\n [-4, -8, 2, 8, -4, -6],\n [4, -1, -12, -4, 4, -2],\n [4, 2, 6, -6, -2, 15]]\nRound your answer to the nearest integer.\n\nPresen... | 475 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[9, -6, 2, 11, 5, 10],\n [0, 6, 0, -13, 13, -12],\n [0, 0, -3, -4, 15, -12],\n [0, 0, 0, -9, 12, -6],\n [0, 0, 0, 0, -3, 0],\n [0, 0, 0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the ans... | -110 | 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[[9, -2, 11, -4, 6, -3],\n [-2, -4, -10, -2, 10, -14],\n [11, -10, 8, -4, -1, 1],\n [-4, -2, -4, 0, -2, -4],\n [6, 10, -1, -2, -9, -3],\n [-3, -14, 1, -4, -3, 1]]\n\nPrese... | 72 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/180 * A where A =\n[[-8, -13, 6, 10, 9, -6],\n [0, -11, 7, -13, -13, -12],\n [0, 0, 12, -15, -14, 4],\n [0, 0, 0, -7, 12, -3],\n [0, 0, 0, 0, -15, 2],\n [0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answe... | 0 | 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, 6, 9, 3, -4, 5],\n [-7, 8, 0, 9, -11, 2],\n [-1, -9, 11, -4, 14, -6],\n [15, -7, -5, 10, 10, -7],\n [-15, -14, -9, 10, 14... | -244 | 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[[-10, -6, 1, 5, -10, 15],\n [6, 13, -3, 6, -11, 6],\n [6, 8, -5, -5, 13, -14],\n [-8, -5, ... | 168 | 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, -2, -3, 7, -5, -9],\n [7, -7, -13, 5, 5, -3],\n [-4, 7, -9, -12, -10, -7],\n [5, -9, 7, 7, -5, -14],\n [-2, 8, -8, -9,... | -37 | 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, -14, -7, 6, -5, 3],\n [0, -1, -7, 7, 11, -8],\n [0, 0, 6, -14, -2, 13],\n [0, 0, 0, 2, 2, 14],\n [0, 0, 0, 0, -10, 4],\n [0, 0, 0, 0, 0, 7]]\n\nPre... | -8778 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-8, 1, -10, -1, 10, 4],\n [1, -8, 9, 11, 0, 3],\n [-10, 9, -6, -6, 0, -8],\n [-1, 11, -6, -2, 2, 4],\n [10, 0, 0, 2, 10, -6],\n [4, 3, -8, 4, -6, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaT... | 28 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-1, 7, -4, 5, 1, -1],\n [13, -2, 14, 2, 11, -9],\n [14, -5, 0, 11, -3, -15],\n [1, -8, -12, 7, -14, -8],\n [-15, -12, 8, -9, 10, 12],\n [5, 9, -13, 5, 6, 15]]\nRound your answer to the nearest integer.\n\nPre... | -9 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[14, 8, -13, 8, 10, 7],\n [8, -13, 11, 5, 5, 0],\n [-13, 11, 12, -1, -4, 12],\n [8, 5, -1, 3, 6, -2],\n [10, 5, -4, 6, -10, -8],\n [7, 0, 12, -2, -8, -1... | -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[[8, -5, -6, -8, 2, -4],\n [-5, -10, -5, -8, 6, -2],\n [-6, -5, -12, -5, -10, 2],\n [-8, -8, -5, -13, -8, -4],\n [2, 6, -10, -8, 5, -6],\n [... | 211 | 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, 13, -14, 4, 1],\n [0, 12, -7, 11, 12, 0],\n [0, 0, 10, 2, 8, 1],\n [0, 0, 0, 6, -8, 5],\n [0, 0, 0, 0, -6, 4],\n [0, 0, 0, 0, 0, 8]]\... | 44 | 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, 6, -10, -4, -7, 8],\n [6, -10, 8, -9, 2, -4],\n [-10, 8, 7, 10, -6, -6],\n [-4, -9, 10, -7, 3, -7],\n [-7, 2, -6, 3, 11, ... | 135 | 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, -2, -6, -2, 2, 2],\n [-2, -9, -6, -7, 4, 5],\n [-6, -6, -9, 8, -4, -6],\n [-2, -7, 8, 15, 2, -1],\n [2, 4, -4, 2, 4, -2],\n [2, 5, -6, -1, -2, 10]]\nRound your answer to the nearest inte... | 24 | 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[[10, 8, -13, -3, 0, 12],\n [5, 14, 4, -1, -8, -5],\n [2, 12, 5, -12, 4, -11],\n [-8, -7, 12, 3, -12, -3],\n [8, -10, -15, -1, 3, 10],\n [-10, -9, 9, -11, -14, -1]]\n... | 791 | 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, -12, -3, 3, -6, 6],\n [0, -11, 3, -7, -6, 9],\n [0, 0, -12, -6, -14, 3],\n [0, 0, 0, -13, 0, -7],\n [0, 0, 0, 0, -10, 13],\n [0, 0, 0, 0, 0, -4]]\nRound your answer to the nearest intege... | -59 | 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, 8, -2, -9, 4, 12],\n [8, 13, -2, 8, -2, -4],\n [-2, -2, -2, -12, 11, -6],\n [-9, 8, -12, 15, -10, -7],\n [4, -2, 11, -10, 11, -4],\n [1... | 838 | 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[[-5, 1, -1, 10, 14, -13],\n [0, 3, -3, -4, -15, 0],\n [0, 0, -14, -12, -8, 3],\n [0, 0, 0, 4, 6, 0],\n [0, 0, 0, 0, 6, -12],\n [0, 0, 0, 0, 0, 14]]\n\nP... | 111 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 5) of the inverse. Round your answer to the nearest integer:\n[[-6, -11, 5, 8, 14, -13],\n [3, 8, -4, 8, -14, 2],\n [-14, -5, -10, 2, 13, -7],\n [11, -6, 8, -1, 1, -13],\n [1, 0, 12, -11, 6, -8],\n [9, -8, 1, -3, 12... | 2 | 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, -2, -10, 2, -8, -10],\n [-2, 1, 9, 0, 11, 6],\n [-10, 9, -15, 0, 10, -8],\n [2, 0, 0, -9, -8, -6],\n [-8, 11, 10, -8, -5, 8],\n [-10, 6, -8, -6, 8, -14]]\n\nPr... | 762 | 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, -6, -4, -9, -13, 1],\n [-1, -9, 13, -5, -15, -9],\n [3, 3, 12, 5, 0, -12],\n [7, 11, -... | 30 | 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[[9, -8, 1, 2, -4, 2],\n [-8, 2, -1, 0, -6, -4],\n [1, -1, -5, -11, 0, 4],\n [2, 0, -11, -8... | 28 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 5) of the inverse. Round your answer to the nearest integer:\n[[-7, 4, 12, 2, -5, -3],\n [-3, -10, 7, 7, -15, 7],\n [-5, 0, 0, 7, 11, 0],\n [9, 1, 2, -5, 14, 3],\n [5, -11, 2, -11, 5, -13],\n [-1, -7, 3, 7, 5, 2]]\n... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -8, -8, -3, -2, 4],\n [-8, -4, 8, 4, 8, -4],\n [-8, 8, 11, 0, 6, -7],\n [-3, 4, 0, 1, 10, -4],\n [-2, 8, 6, 10... | 3 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 1) rounded to the nearest integer?\n[[4, -9, 10, 2, 6, -6],\n [-9, 4, 8, -4, -1, 8],\n [10, 8, 1, -4, -4, 3],\n [2, -4, -4, -12, 2, 3],\n [6, -1, -4, 2, 13, 13],\n [-6, 8, 3, 3, 13, 12]]\n\nPresent the answer in LaT... | -4 | 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, 11, 5, 4, -5, -14],\n [0, -5, 9, -8, 0, 7],\n [0, 0, -12, -9, -5, -8],\n [0, 0, 0, 3, ... | -2916 | 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[[-2, -4, 11, -8, -15, -11],\n [0, 10, 3, -13, -3, 12],\n [2, 13, -1, 13, 0, -10],\n [-8, -6, 1, 13, -5, -9],\n [7, 2, -3, -11, 4, -5],\n [9, 3, 1, 5, 2, -15]]\n\nPresent the answer in ... | 244 | 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[[13, 1, 14, 6, 12, -10],\n [0, -12, 14, -14, -12, 9],\n [0, 0, 15, 6, -9, 8],\n [0, 0, 0, 5, 9, 8],\n [0, 0, 0, 0, 15, 13],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer i... | 14 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[5, -7, -15, 9, -10, -13],\n [8, 2, 5, 6, 14, 4],\n [10, 0, 7, -2, 0, 2],\n [-6, 12, -3, 6, -9, 11],\n [10, -14, -6, 5, -2, 15],\n [-7, -5, -6, -15, -10, -8]]\nRound your answer to the nearest integer.\n\... | 281 | 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, -5, 4, -2, -2, -8],\n [0, 6, -7, -6, 15, 12],\n [0, 0, -7, -11, -6, 12],\n [0, 0, 0, -14, 3, 9],\n... | 1389 | 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[[6, 8, 4, 6, 0, 4],\n [8, 12, 2, 3, -11, -3],\n [4, 2, 0, 8, -2, -6],\n [6, 3, 8, -9, -2, -4],\n [0, -1... | 1188 | 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, -13, 3, 0, 13, -13],\n [0, 1, 9, -7, -13, -1],\n [0, 0, 14, -11, 10, -5],\n [0, 0, 0, -13, -1, 9],\n [0, 0, 0, 0, -10, 11],\n [0, 0, 0... | 8220 | 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[[8, -6, 7, -10, -14, -10],\n [0, 12, -4, 15, 0, 12],\n [0, 0, 8, 5, 15, 4],\n [0, 0, 0, 9, 13, 2],\n [0, 0, 0, 0, -6, 13],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answ... | 596 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[4, 0, -10, -6, 1, 2],\n [0, -13, -6, 8, 2, 2],\n [-10, -6, 0, 3, 2, -5],\n [-6, 8, 3, -9, -6, 6],\n [1, 2, 2, -6, -1, 4],\n [2, 2, -5, 6, 4, 11]]\nRound your answer to the nearest integer.\n\nPresent the answ... | 33 | MATH |
[
{
"content": "Find the value at position (4, 6) of the inverse of matrix 1/180 * A where A =\n[[-10, 14, 8, -5, 15, 12],\n [0, -5, -12, 10, 0, 10],\n [0, 0, -9, -5, 0, 12],\n [0, 0, 0, -7, 7, -6],\n [0, 0, 0, 0, -6, 1],\n [0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in ... | 12 | 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[[2, 13, -4, -15, 10, -10],\n [0, -12, -15, 1, 10, 10],\n [0, 0, -9, 12, 15, 2],\n [0, 0, 0, 13, -12, -15],\n [0, 0, 0, 0, 9, -13],\n [0, 0, 0, 0, 0, -7]]\n\nPresent ... | 3454 | 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[[1, -2, 0, -4, 5, 13],\n [0, 2, -5, -8, 6, -10],\n [0, 0, 13, -13, 12, -15],\n [0, 0, 0, -4, -8, 9],\n [0, 0, 0, 0, -6, 14],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex... | 0 | 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, 8, -8, -4, -1, 6],\n [-14, -7, 13, -7, 13, -15],\n [2, 11, 13, 13, 8, 5],\n [11, 13, -5, 15, 13, 2],\n [-9, 13, 12, 13, -12, 6],\n [5,... | 225 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-3, 0, 4, 11, 1, 4],\n [10, -5, -1, -7, 3, 10],\n [12, 2, -12, -3, -5, 2],\n [10, -13, 9, 3, -11, -2],\n [-6, 6, -13, -3, -8, -12],\n [2, -12, 14, -6, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answ... | -144 | 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, -7, 5, -4, 4, 2],\n [-7, 2, 8, 4, -2, 1],\n [5, 8, 5, -4, 2, -11],\n [-4, 4, -4, 0, 9... | 12 | 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[[-4, 10, 10, -9, -13, -10],\n [-8, 4, 4, 7, -7, 10],\n [0, 10, -13, 11, 0, 2],\n [-4, -10, 11, -13, 0, 10],\n [-2, 7, 10, ... | 316 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 5) rounded to the nearest integer?\n[[6, 15, -2, -2, 1, -2],\n [-7, -3, -5, 6, 12, -7],\n [-7, -10, -4, 14, -4, -15],\n [7, 7, -15, -11, 8, 3],\n [4, -8, -7, 0, 11, -1],\n [-12, 10, 9, -8, -1, -9]]\n\nPresent the an... | 9 | 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[[-13, 6, 11, 1, 1, -11],\n [6, 6, 10, 12, 6, -10],\n [11, 10, -10, 5, 2, -2],\n [1, 12, 5, -2, 7, 4],\n [1, 6, 2, 7, 5, 4],\n ... | 20 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/180 * A where A =\n[[3, -9, -1, 1, 12, 15],\n [0, -12, 0, -5, -9, 7],\n [0, 0, -14, -7, -5, 10],\n [0, 0, 0, -1, -4, -9],\n [0, 0, 0, 0, 5, -15],\n [0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in... | 60 | 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[[-5, 12, 2, 10, -1, 13],\n [0, 15, -12, -9, -5, -12],\n [0, 0, 4, 2, 14, 9],\n [0, 0, 0, 3... | 137 | 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[[15, -7, 8, 4, -7, 9],\n [-5, -5, -1, 8, 4, -9],\n [9, 11, -9, -2, 5, 4],\n [-1, 10, -11, 10, -1, -2],\n [-7, -4, -8, 15, 0, -11],\n [-9, -10, -4, 3, 2, -9]]\n\nPresent the answer in L... | 262 | MATH |
[
{
"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 4) rounded to the nearest integer?\n[[0, 4, -12, 0, 0, 2],\n [4, -9, 6, 1, -2, 8],\n [-12, 6, 0, -8, 3, 4],\n [0, 1, -8, -7, 4, 5],\n [0, -2, 3, 4, 15, -2],\n [2, 8, 4, 5, -2, -1]]\n\nPresent the answer in LaTex for... | -23 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-2, -1, 12, -4, 6, -13],\n [-5, -8, -1, -5, -7, -8],\n [-4, 4, -6, -8, 6, -5],\n [4, 4, 3, 14, -9, -11],\n [-9, 0, -15, 6, -10, 8],\n [-12, 9, -4, -13, 5, -2]]\nRound your answer to the nearest integer.\n\nPresent the answ... | -34 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[9, 10, -12, -8, -12, 2],\n [9, -5, -14, -9, -10, -1],\n [-4, 8, -5, 4, 1, 6],\n [-6, -15, 7, 9, -12, -3],\n [-6, 10, -5, -14, -3, -11],\n [5, 14, 9, -14, -9, -5]]\nRound your answer to the nearest intege... | 486 | 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[[3, -1, 10, -14, 6, 9],\n [3, 3, -7, 8, 1, -10],\n [-5, 13, 7, 8, -5, 12],\n [-6, -14, 9, -6, 5, -10],\n [1, 8, -9, 15, -7, -12],\n [-5, -10, -14, -13, 1, -11]]\n\nP... | 342 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 12, 15, -8, 5, 9],\n [0, 11, 9, -10, -4, -11],\n [0, 0, 6, 6, 1, 4],\n [0, 0, 0, 5, 3, -1],\n [0, 0, 0, 0, 5, 1... | 25 | 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[[8, 4, -4, 9, -12, 5],\n [4, 13, -5, 0, -2, 2],\n [-4, -5, 15, 10, -9, 3],\n [9, 0, 10, -13, -4, 6],\n [-12, -2, -9, -4, 8, 2],\n [5, 2, 3,... | 204 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-14, 11, -8, 5, -11, -8],\n [0, -11, 8, -10, -13, 6],\n [0, 0, 14, 8, -15, 1],\n [0, 0, 0, -13, -13, 8],\n [0, 0, 0, 0, 10, 10],\n [0, 0, 0, 0, 0, 7]]\nRound your answer to the nearest integ... | -53 | 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, 6, -3, 6, -2, 3],\n [6, -15, -13, -8, -14, 4],\n [-3, -13, 14, -4, -4, -2],\n [6, -8, -4, 4, -5, -6],\n [-2, -14, -4, -5, -7, 4],\n [3, 4, -2, -6, 4, -8]]\nRound your answer to the neares... | 2011 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[15, -7, -2, -5, -4, 2],\n [3, -7, 14, 3, 3, 9],\n [-15, -13, 14, 15, 14, 8],\n [3, 11, 1, 10, -12, -11],\n [4, -4, 6, 9, -15, -15],\n [6, -7, -11, 10, 7, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer... | 119 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 4, 13, -5, -4, 6],\n [0, 12, 4, -6, -10, -3],\n [0, 0, -11, 0, -3, 3],\n [0, 0, 0, -14, -7, -8],\n [0, 0, 0, 0... | 0 | 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[[1, -3, 3, 15, 9, 6],\n [-4, 7, -13, 0, 8, 8],\n [-1, 9, -3, 5, -12, 9],\n [-9, -11, 4, 6, 10, 7],\n [-14, 2, -6, 4, -11, 1],\n [-3, -7, -11, -10, -2, 9]]\n\nPresent the answer i... | -4 | 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[[-11, 1, -1, 8, 0, 5],\n [1, 4, -2, 8, 10, 2],\n [-1, -2, 15, -7, -9, 3],\n [8, 8, -7, 12, -2, -6],\n [0, 10, -9, -2, 13, 2],\n [5, 2, 3, -6, 2, 5]]\n\n... | 33 | 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[[6, 10, -6, -6, 8, 2],\n [10, 10, -10, 2, 2, 4],\n [-6, -10, 11, -10, -4, 2],\n [-6, 2, -10, 8, 0, -12],\n [8, 2, -4, 0, -11, -5],\n [2, 4, 2, -... | -84 | 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, -4, -7, -2, 8, -9],\n [1, 5, -9, 13, -11, 0],\n [-14, 10, 5, 3, -12, 7],\n [-13, -8, 3, 9, 13, 14],\n [9, 5, 12, 10, 14, -1],\n [7, -9, 13, -2, -11, 2]]\nRound your answer to the nearest... | -200 | 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[[0, -2, -1, -13, 12, -5],\n [2, -4, -12, -5, -5, 9],\n [2, -8, -10, 15, -11, -3],\n [11, -1, -3, -7, 14... | 533 | 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[[-12, -11, 15, 12, -9, 3],\n [8, 0, 10, 14, -7, 1],\n [-8, 2, -11, -15, -1, 3],\n [-13, 14, -4, -12, 3, 8],\n [-13, 11, 1, -5, 14, 12],\n [-12, -5, -15, -1, 8... | 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[[5, 4, 4, -1, 12, 7],\n [4, 5, 8, -2, -12, -2],\n [4, 8, -3, 2, 8, 6],\n [-1, -2, 2, 11, 12, 9],\n [12, -12, 8, 12, 6, 7],\n [7, -2, 6, 9, 7, 15]]\n\nPresent the answer in LaTex format... | 62 | 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[[-11, -10, 2, 2, -5, 2],\n [-10, -12, -2, -2, -2, 1],\n [2, -2, 5, 0, -8, 4],\n [2, -2, 0, -9, 0, -1],\n [-5, -2, -8, 0, 2, 6],\n [2, 1, 4, -1, 6, -10]]\n\nPr... | 668 | 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[[4, 7, 4, -9, 3, -13],\n [0, -14, -11, 9, -1, -11],\n [0, 0, 9, 3, 8, -15],\n [0, 0, 0, -1, -2, -12],\n... | 1459 | MATH |
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