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 value at position (1, 3) rounded to the nearest integer?\n[[-5, -1, -6, 4, 2, -13],\n [-10, 15, -4, -2, -7, -1],\n [-5, -15, 0, 11, 2, -10],\n [13, 2, -5, -11, -10, -9],\n [9, 3, -1, -12, 6, -7],\n [2, 3, -5, -7, 11, 10]]\n\nPresent the ... | -33 | 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, -4, -11, -13, -1, 1],\n [0, 6, -10, -7, 11, -5],\n [0, 0, 11, 11, 1, 13],\n [0, 0, 0, -7, -14, -9... | 584 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/180 * A where A =\n[[-7, -4, -14, 11, -6, -15],\n [14, 2, 3, -9, -11, 11],\n [-13, -8, -9, -15, -3, 14],\n [-6, -13, 3, 0, 1, 15],\n [-4, 14, 15, 9, 7, 11],\n [1, -10, 7, -9, 13, 9]]\nRound your answer to the nearest integer.\n\nPresent ... | 33 | 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, 1, 2, -13, 10, 15],\n [0, 9, -11, -15, 3, 7],\n [0, 0, 10, 10, 12, 7],\n [0, 0, 0, -13, 4, -8],\n [0, 0, 0, 0, -9, -2],\n... | -93 | 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, 14, 4, 11, 11, 9],\n [0, -6, -4, 6, -15, 1],\n [0, 0, 14, -11, -12, -9],\n [0, 0, 0, 1, -8, -12],\n [0, 0, 0, 0, 15, -6],\n [0, 0, 0, 0, 0, ... | 214 | 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[[-9, -2, -14, 13, -15, -7],\n [0, 11, 8, 8, 11, -2],\n [0, 0, -1, -1, -1, 8],\n [0, 0, 0, -14, -5, 4],\n [0, 0, 0, 0, -6, 1],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex forma... | -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[[-7, -9, 4, -6, 0, 6],\n [-9, 4, 12, 2, 5, -2],\n [4, 12, 7, -4, -3, 2],\n [-6, 2, -4, -13, 10, 5],\n [0, 5, -3, 10, -7, -6],\... | -17 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-6, 0, -2, 3, -8, 0],\n [0, -6, 10, -2, 4, 5],\n [-2, 10, 4, 14, 2, 1],\n [3, -2, 14, -12, 0, -6],\n [-8, 4, 2, 0, -6, -4],\n [0, 5, 1, -6, -4, -9]]\nRound your answer to the nearest integer.\n\nPresent ... | 30141 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-5, 7, 13, 15, 3, 13],\n [6, -14, 5, -1, -5, 8],\n [-1, -7, 10, -7, -3, -12],\n [4, -10, 2, -14, 5, -13],\n [9, 10, -1, 0, -4, -10],\n [-5, -3, -12, 6, -10, 10]]\nRound your answer to the nearest integer... | 852 | 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[[-14, -3, -1, 15, -7, -15],\n [-7, 9, -11, -4, -2, 9],\n [6, 7, -10, -14, 15, -11],\n [-2, -13, -5, -14, -3, -14],\n [10, -14, 2, -8, -2, -3],\n [-7, 7,... | -27 | 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, -7, 8, -8, 7, 11],\n [13, 10, -4, -1, 0, 4],\n [-7, -15, 3, -5, 5, -11],\n [7, -3, -3, 10, 4, 7],\n [-15, 13, -4, 13, 10, -5],\n [15, -15,... | 16 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (6, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -2, 5, -5, -9, 8],\n [0, 15, 10, -7, 15, -7],\n [0, 0, 12, 2, -3, -7],\n [0, 0, 0, -14, -9, 11],\n [0, 0, 0, 0,... | 0 | 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[[10, -6, -4, -4, 4, -2],\n [6, 14, -4, -1, 14, 14],\n [-2, -6, -12, -8, 8, -10],\n [5, 13, 4, 1, -14, -... | 141 | 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, 8, -2, 11, -4, 3],\n [8, -10, 8, 11, 4, 2],\n [-2, 8, -6, -12, -8, 2],\n [11, 11, -12, -8, -6, 10],\n [-4, 4, -8, -6, -6, -1],\n [3, 2, 2, 10, -1, 1]]\n\nPresent... | 596 | 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[[-13, -4, 5, 4, 3, 5],\n [0, 5, 15, -3, 11, -11],\n [0, 0, 1, 7, 12, -5],\n [0, 0, 0, 14, ... | -732 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[2, -9, 5, 1, 5, 3],\n [0, -1, -11, 4, 5, -6],\n [0, 0, 11, -5, 9, 14],\n [0, 0, 0, -3, 7, -10],\n [0, 0, 0, 0, 12, -6],\n [0, 0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex form... | -1952 | 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, -12, -7, -11, -13, 9],\n [-14, 15, 14, 15, 6, 6],\n [15, -4, 10, 11, 12, -1],\n [-1, 8, -12, -14, 13, -6],\n [14, 1, 9, 4... | 22 | 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[[2, -13, 13, -1, 15, 6],\n [0, 12, -3, 15, 11, 1],\n [0, 0, 3, -11, 2, 9],\n [0, 0, 0, 4, 1, -9],\n [0, 0, 0, 0, -2, -4],\n [0, 0, 0, 0, 0, -14]... | 107 | 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, 1, -8, 1, -10, -3],\n [1, -4, -4, 7, -6, 4],\n [-8, -4, -9, 1, 4, -10],\n [1, 7, 1, 3, 0, 0],\n [-10, -6, 4, 0, 8, 2],\n [-3, 4, -10, 0, 2, 7]]\n\nPresent the answer... | 116 | 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, -2, 6, -9, -4, -13],\n [15, -8, -11, 13, -3, -9],\n [-1, -10, -8, 4, 13, -4],\n [7, 8, 12, 3, -11, 3],\n [0, 15, 11, -3, -3, 10],\n [-... | 675 | MATH |
[
{
"content": "Find the value at position (6, 3) of the inverse of matrix 1/180 * A where A =\n[[7, 2, -4, 0, -3, -4],\n [2, -14, 4, 8, 0, -4],\n [-4, 4, -13, -10, 14, 2],\n [0, 8, -10, -11, 4, 5],\n [-3, 0, 14, 4, 13, 9],\n [-4, -4, 2, 5, 9, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer... | 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[[-5, 0, -13, -4, 0, -2],\n [0, 8, 2, -10, 5, 2],\n [-13, 2, -14, -3, 0, -10],\n [-4, -10, -3, -5, 1, -10],\n [0, 5, 0, 1, ... | -11 | 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, 15, -2, 3, -2],\n [14, -8, 8, -4, -4, 3],\n [-11, 12, -5, -8, -9, -13],\n [-2, 2, -3, -5, 15, -5],\n [2, 12, -14, 10, 4, 3],\n [3, -10, 5, -11, 7, 13... | 87 | 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[[-4, 12, 15, 5, 15, -9],\n [0, -13, 3, -9, 7, -1],\n [0, 0, -14, 9, -1, -8],\n [0, 0, 0, 6, -3, -4],\n [0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, -5]]\n\nPresent... | -1143 | 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, 14, -15, 4, 7, -8],\n [-7, 10, 1, -2, -11, -1],\n [13, -1, 9, 0, -7, -15],\n [-5, -7, -6, -4, -11, 11],\... | 147 | 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, -11, 5, -5, -5, -13],\n [0, 12, 3, -12, -15, 7],\n [0, 0, 14, 3, 12, 5],\n [0, 0, 0, -10, -14, -13],\n [0, 0, 0, 0, -15, 1],\n [0, 0, 0, 0, 0, 2]]\n\nPre... | -42 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-12, -6, 4, 6, 10, -10],\n [-6, 9, -5, -2, -1, 8],\n [4, -5, 7, 0, -4, 0],\n [6, -2, 0, 9, 12, 6],\n [10, -1, -4, 12, 14, 6],\n [-10, 8, 0, 6, 6, 1]]\n... | 30 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 6) of the inverse. Round your answer to the nearest integer:\n[[2, 7, 14, -9, 14, -2],\n [9, -14, 13, 12, -15, -13],\n [-10, 13, 15, 10, -4, 4],\n [1, 0, -1, 10, 9, -7],\n [-3, 10, -7, -10, -10, -14],\n [1, -8, -14,... | -8 | 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, -4, -6, -4, 10, -4],\n [-4, 3, 8, -2, 6, 10],\n [-6, 8, 12, -1, 4, 6],\n [-4, -2, -1, -8, 8, 0],\n [10, 6, 4, 8, 3, 6],\n [-4, 10, 6, 0, 6, 2]]\n\nPresent the answer... | 0 | 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[[11, -10, -3, 2, 15, -7],\n [-10, -5, -10, -6, -5, -9],\n [-3, -10, -8, 6, 4, 0],\n [2, -6, 6, -13, 8, 0],\n [15, -5, 4, 8, -10, -3],\n [-7, -9,... | -67 | 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[[-15, 8, -15, 9, 11, -10],\n [-6, 1, 1, 3, -12, 7],\n [13, 0, -3, -13, -7, -7],\n [8, -2, -11, 5, -13, -9],\n [-13, -5, -7, 12, 3, 0],\n [-1, 0, 0, -10,... | -22 | 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, 5, 10, 5, -2, -8],\n [11, -4, 7, -1, 5, -2],\n [14, 8, 4, 0, 1, -3],\n [-9, 4, -5, -9, 3, 8],\n [13, 2, -12, 8, 4, -... | -37 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -3, -10, 9, -12, -6],\n [-3, -7, -8, 0, -4, 1],\n [-10, -8, -2, -10, 4, 0],\n [9, 0, -10, 14, 6, 2],\n [-12, -4, 4, 6, -10, 4],\n [-6, 1, 0, 2, 4, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer i... | -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[[-12, 13, 9, -6, 2, -2],\n [0, -10, 15, -10, 0, -2],\n [0, 0, 5, -7, 3, -12],\n [0, 0, 0, -1, 2, 14],\n [0, 0, 0, 0, -2, -3],\n [0, 0, 0, 0, 0, -13]]\n\nPrese... | -2608 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-8, 2, -2, 0, -1, -3],\n [2, 10, -4, 4, -4, -3],\n [-2, -4, -1, -3, 14, 7],\n [0, 4, -3, -6, 0, -6],\n [-1, -4, 14, 0, 7, 0],\n [-3, -3, 7, -6, 0, -14]]\nRound your answer to the nearest int... | -40 | 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, 13, 3, 3, 9, -12],\n [-14, 12, 1, 2, -3, -10],\n [13, 11, -4, 0, -9, -7],\n [9, -10, -15, 13, 7, 2],\n [-12, -5, 1, -2, -7, 4],\n [-1, -13, -8, -1, -1, -12]]\n\nPrese... | 35 | 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, -7, -6, 11, 0, 9],\n [0, 14, -7, -9, 5, -14],\n [0, 0, 6, -13, -5, 7],\n [0, 0, 0, -6, 11, 10],\n [0, 0, 0, 0, 13, -14],\n [0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.... | -457 | 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[[2, 13, 15, 8, 4, -6],\n [0, 3, 10, 6, 5, 11],\n [0, 0, 9, 15, -9, 11],\n [0, 0, 0, -9, 10, -10],\n [0, 0, 0, 0, -9, -11],\n [0, 0, 0, 0, 0, -7]... | 104 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, -11, -4, -5, -5, 2],\n [-11, -2, 4, 0, -4, 8],\n [-4, 4, 5, 6, 5, 4],\n [-5, 0, 6, 0, 10, -4],\n [-5, -4, 5, 10, 2, 8],\n [2, 8, 4, -4, 8, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTe... | -58 | 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, -4, 6, -4, 14],\n [3, -15, 4, -4, 5, -9],\n [-4, 4, -4, -10, 0, 6],\n [6, -4, -10, 2, 2, -6],\n [-4, 5, 0, 2, -8, ... | -122 | 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, 4, 0, -11, 12, -6],\n [4, -13, 2, -7, 0, 0],\n [0, 2, 11, 1, -5, 12],\n [-11, -7, 1, 14, 3, -11],\n [12, 0, -5, 3, 1, 4],\n [-6, 0, 12, -11, 4, 8]]\n\nPresent the answer in LaTex ... | 70 | 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[[7, -12, 5, -5, -12, 10],\n [11, -4, 14, -13, 7, -9],\n [-13, 7, 9, -10, 7, 0],\n [7, 4, -1, 9, 2, -10],\n [-15, -13, -15, -2, 11, 10],\n [1, -5, 14, 9, -9, 8... | -538 | 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, 9, 8, -10, -6, -2],\n [0, -11, 13, 8, -11, 0],\n [0, 0, 10, 15, -3, -8],\n [0, 0, 0, ... | -598 | 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[[-10, 11, 11, 9, -1, -7],\n [8, -13, 4, -14, 11, -13],\n [-4, -2, 3, 5, -8, 13],\n [-8, 4, 0, -7, -1, -... | 4431 | 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[[13, 0, 2, -8, 0, 7],\n [0, -6, 2, 1, -8, 7],\n [2, 2, -15, 3, -8, 0],\n [-8, 1, 3, 1, -7,... | -27 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-9, 4, 2, 0, -2, -2],\n [4, -13, -8, 1, -7, 1],\n [2, -8, -11, -6, 3, 6],\n [0, 1, -6, -11, 6, -4],\n [-2, -7, 3, 6, -5, -4],\n [-2, 1, 6, -4, -4, -15]]\nRound your answer to the nearest integer.\n\nPresent t... | 183 | 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, -2, 0, 7, -5, 8],\n [-2, -14, 6, -12, 9, -2],\n [0, 6, -14, 3, -10, 5],\n [7, -12, 3, 12, 4, 10],\n [-5,... | -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[[4, -4, 7, 8, -2, 13],\n [-4, 15, -10, -10, 0, 1],\n [7, -10, -8, 3, 10, -6],\n [8, -10, 3, 0, 2, -8],\n [-2... | 27 | 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[[-14, 6, -4, 4, 2, 0],\n [6, -10, -6, -8, 6, -6],\n [-4, -6, -15, -2, 6, 6],\n [4, -8, -2, 2, -2, -1],\... | 274 | 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, 15, -4, -11, 9, -7],\n [0, -7, -12, -9, 12, -4],\n [0, 0, -10, 9, -7, 15],\n [0, 0, 0, 4, 3, 5],\n [0, 0, 0, 0, 10, -12],\n [0, 0, 0, 0, 0, 6]]\nRound your answer to the nearest integer.... | 775 | 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[[15, -5, -4, 0, 4, -12],\n [-5, -9, 0, 7, -2, 5],\n [-4, 0, 15, -2, -2, -2],\n [0, 7, -2, -9, 8, 10],\n [4, -2, -2, 8, -9,... | 266 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (4, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 13, 3, 7, 8, -13],\n [13, -4, 10, -12, -5, 10],\n [-6, 11, 6, 7, 7, 12],\n [-1, -11, -8, -11, 14, 11],\n [1, -9... | 6 | 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, 8, 14, 1, 0, 14],\n [0, 2, 5, -9, -2, 10],\n [0, 0, 12, 8, 4, 14],\n [0, 0, 0, -9, 1, ... | -6710 | 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[[4, 14, 7, -12, 13, -14],\n [0, -13, -2, -13, -9, -15],\n [0, 0, 11, 7, -6, 4],\n [0, 0, 0, -4, 11, 15],\n [0, 0, 0, 0, 7, -14],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in ... | -1182 | 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[[4, 3, -8, -2, 2, 0],\n [3, 3, -14, -5, 0, 6],\n [-8, -14, 1, 2, 6, -2],\n [-2, -5, 2, -15, -5, -2],\n [2, 0, 6, -5, 7, 13],\n [0, 6, -2, -2, 13, 7]]\n\... | 48 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[9, 8, 2, 4, -2, -2],\n [8, 2, 3, -4, -3, 3],\n [2, 3, 6, -8, -10, -10],\n [4, -4, -8, -8, 8, 10],\n [-2, -3, -10, 8, 15, 6],\n [-2, 3, -10, 10, 6, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in La... | -1054 | 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[[1, -2, 0, 4, 12, 8],\n [-2, 7, -10, -12, -12, 0],\n [0, -10, 11, 2, 2, 2],\n [4, -12, 2, 8, 2, 6],\n [12, -12, 2, 2, -13, -12],\n [8, 0, 2, 6, ... | 90 | 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, 8, -6, -10, -1, 6],\n [8, -7, -8, -10, 1, -12],\n [-6, -8, 12, -2, 0, -4],\n [-10, -10, -2, -8, 1, -10],\n [-1, 1, 0, 1, 10, 4],\n [6, -12, -4, -10, 4, 12]]\n\nPresen... | 33 | 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[[0, 10, -4, 0, 2, -6],\n [10, -11, -11, -11, -4, -4],\n [-4, -11, 7, 4, -4, 4],\n [0, -11, 4, 3, 10, 0],\n [2, -4, -4, 10, -1, -3],\n [-6, -4, 4, 0, -3, -7]]\n\nPres... | 14854 | 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, -9, 6, 10, -9, -1],\n [0, -9, 5, 4, 11, -3],\n [0, 0, 13, 2, 0, -12],\n [0, 0, 0, -14, 1, -15],\n [0, 0, 0, 0, -14, 3],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex forma... | -30 | 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[[7, -6, -4, 5, 15, 15],\n [-7, -9, 5, -4, 14, -11],\n [-6, 15, -10, 14, 6, -5],\n [-7, 15, 11, 11, 7, 4],\n [11, 4, 3, 11, -9, -6],\n [-8, -13, -15, 7, 1, -4]]\n\nPresent the ans... | -2 | 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, 2, -8, 1, 6, 0],\n [2, 10, -2, 2, -10, -6],\n [-8, -2, -1, 11, 0, 10],\n [1, 2, 11, 14, -11, -7],\n [6, -10, 0, -11, -... | 386 | 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, -8, 1, -6, -4, 9],\n [-8, -8, -7, -1, 0, 11],\n [1, -7, 12, 9, 2, -8],\n [-6, -1, 9, 0, -3, 1],\n [-4, 0, 2, -3, 7, 4],\n [9, 11, -8, 1, 4, 3]]\n\nPresent... | 130 | 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, -1, -5, -5, 0, 8],\n [-1, 8, 2, -4, 4, 0],\n [-5, 2, -14, 0, -1, -2],\n [-5, -4, 0, -13, 0, 4],\n [0, 4, -1, 0, -14, 6],\... | -26 | 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[[-14, -2, -14, -9, -14, 12],\n [-6, 2, -10, -12, -13, -1],\n [-15, 6, 9, 4, 10, -10],\n [-14, 7, 11, -3, -1, -4],\n [15, 9, 11, 8, 4, 3],\n [-9, 10, 6, 11, -7, 11]]\n\nPresent th... | -10 | 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[[14, 8, -14, -15, 5, -9],\n [10, -4, -1, 1, 3, -3],\n [12, -7, 3, -3, 3, -14],\n [6, 15, 2, -1, 4, -14]... | 402 | 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, -6, 3, -2, -6, -8],\n [-6, -10, 4, -8, 5, 2],\n [3, 4, 10, -6, -2, -11],\n [-2, -8, -6, 9, 4, 2],\n [-6, 5, -2, 4, -1, 2],... | -22 | 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, 2, -10, -2],\n [-2, -1, 8, -1, -4, 4],\n [2, 8, -9, -2, -2, -1],\n [2, -1, -2, -2, 3, 7],\n [-10, -4, -2, 3, 15, 4],\n [-2, 4, -1, ... | 191 | 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[[-2, 11, 14, 10, 11, -14],\n [0, 3, 1, 12, -1, -5],\n [0, 0, -3, 9, 6, -1],\n [0, 0, 0, -1, -2, 3],\n [... | 16799 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-3, 15, 8, 1, 13, 14],\n [0, 2, -5, 8, 11, 6],\n [0, 0, -10, -7, 4, 15],\n [0, 0, 0, 15, -2, 5],\n [0, 0, 0, 0, 4, 5],\n [0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPr... | -951 | MATH |
[
{
"content": "Find the value at position (4, 6) of the inverse of matrix 1/180 * A where A =\n[[-9, 0, 0, -9, -6, 2],\n [0, -13, -3, -4, -1, -8],\n [0, -3, 14, -4, -4, 1],\n [-9, -4, -4, -6, 0, -2],\n [-6, -1, -4, 0, 11, 2],\n [2, -8, 1, -2, 2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answ... | 501 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-2, 14, 12, -8, 2, -3],\n [0, 7, 0, -8, 15, 15],\n [0, 0, -6, -12, -4, 6],\n [0, 0, 0, 2, -4, 2],\n [0, 0, 0, 0, -14, -9],\n [0, 0, 0, 0, 0, -12]]\n\nP... | 0 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[15, -15, -1, 13, 14, 11],\n [-12, 10, -3, 2, 15, 15],\n [10, -13, -1, -9, -5, 12],\n [13, 11, -12, -5, -15, 2],\n [-13, 10, 8, -12, -6, 12],\n [10, 11, -6, -3, -5, -10]]\nRound your answer to the nearest... | 226 | 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, -9, 9, -12, -8, -10],\n [-6, -13, -8, 13, -10, -10],\n [3, -3, -12, 1, 9, -5],\n [-15, 15, 1, -9, -... | 1499 | 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, 11, 0, 12, 9, -12],\n [0, -12, 13, 12, 10, 0],\n [0, 0, 7, 3, -12, 5],\n [0, 0, 0, -7, 2, 3],\n [0, 0, 0, 0, -5, 1],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in ... | -276 | 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, 2, 2, 1],\n [-8, -5, 11, 15, 2, 8],\n [-7, -12, -14, -7, -6, -15],\n [4, -1... | 33 | 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, -10, 12, -6, 0, -10],\n [-10, -7, -6, 5, -14, 9],\n [12, -6, -5, 4, 0, 3],\n [-6, 5, 4, 12, -7, 3],\n [0, -14, 0, -7, -15, 12],\n [-10, 9, 3, 3, 12, 7]]... | 39 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[8, -15, 2, -13, 10, -10],\n [0, -13, -14, 13, 1, -1],\n [0, 0, -6, 14, 5, -1],\n [0, 0, 0, -2, 5, 13],\n [0, 0, 0, 0, 5, -9],\n [0, 0, 0, 0, 0, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex... | -29 | 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[[-1, -12, 10, -4, 8, 10],\n [-12, -13, 1, 0, -4, 6],\n [10, 1, -14, 0, -1, -14],\n [-4, 0, 0, 8, 0, 8],\n [8, -4, -1, 0, 1... | 9 | 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, 6, 3, 13, 9, 12],\n [2, 15, 6, 2, -7, 11],\n [0, -2, 5, 0, -8, 12],\n [11, -3, 0, -14, 7, 7],\n [15, 0, -5, 0, 10, 5... | 445 | MATH |
[
{
"content": "Find the value at position (5, 6) of the inverse of matrix 1/180 * A where A =\n[[-5, 6, 6, 7, 12, 0],\n [6, -10, 1, -2, 13, -2],\n [6, 1, -1, 9, -7, 14],\n [7, -2, 9, -2, 0, -6],\n [12, 13, -7, 0, 12, -6],\n [0, -2, 14, -6, -6, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer ... | 3 | 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[[-10, 0, 11, 6, -10, -8],\n [0, -10, 10, 8, 12, 8],\n [11, 10, 13, 13, -6, -3],\n [6, 8, 13, -8, 10, 0],\n [-10, 12, -6, 10, 12, -5],\n [-8, 8, -3, 0, -... | 131 | 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[[-1, -7, -13, -11, -12, -5],\n [0, -2, 13, -11, 10, -2],\n [0, 0, 4, -10, 11, -15],\n [0, 0, 0, -5, 1, -7],\n [0, 0,... | 442 | 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, 0, -1, 9, 11, -2],\n [0, -12, -6, -6, 0, 2],\n [-1, -6, 8, 0, -8, 8],\n [9, -6, 0, 6, 10, 5],\n [11, 0, -8, 10, 3, -4],\n [-2, 2, 8, ... | 266 | 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[[5, -15, 4, -2, -11, 15],\n [13, -8, -11, 15, 6, -1],\n [-7, 8, -5, 11, -3, -4],\n [1, -13, -8, -5, -9, -7],\n [9, 1, 15, -12, -13, 7],\n [5, -8, -3, -11, -4,... | -12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (6, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 0, -9, -9, -3, 13],\n [-1, 6, -7, 10, -11, 0],\n [2, -5, 10, 9, 13, 9],\n [-3, 14, -12, -14, 1, 14],\n [-5, 13, ... | 12 | 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[[-4, 12, 0, -4, 10, 0],\n [12, 11, 1, -2, -5, -1],\n [0, 1, 13, -1, 8, -4],\n [-4, -2, -1, -3, 8, 2],\n [10, -5, 8, 8, -12, -2],\n [0, -1, -4, 2, -2, 13]]\n\n... | 228 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 0, -3, -8, -8, 4],\n [0, -15, -1, -10, -3, -8],\n [-3, -1, 4, 3, 2, -2],\n [-8, -10, 3, 13, -12, -10],\n [-8, -3... | -16 | 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, -14, 10, -14, 8, -3],\n [-5, 0, 7, -1, 12, -3],\n [-15, -10, -13, -14, 5, 6],\n [-7, 13, -5, 13, 1... | 437 | MATH |
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/180 * A where A =\n[[-6, 11, 10, -12, 14, 13],\n [9, 5, -6, -13, 7, 0],\n [3, -15, 5, -8, -7, -10],\n [-2, 3, 9, -11, -4, -6],\n [9, -7, -4, -7, -3, 13],\n [-12, -11, 10, -1, -10, 2]]\nRound your answer to the nearest integer.\n\nPresent... | -1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -1, 15, 6, -9, 5],\n [5, 8, 8, 0, 15, -5],\n [-6, 1, -5, -10, 5, 11],\n [-8, 8, 3, -2, 12, 3],\n [10, 14, 15, -... | 34 | 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[[-13, 5, -3, 15, -11, 2],\n [0, 13, 6, 9, 6, 5],\n [0, 0, 5, 7, -5, -9],\n [0, 0, 0, 5, 13... | 94 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-5, -15, 15, -13, -8, 5],\n [0, -11, -7, 15, -2, -11],\n [0, 0, -9, -1, 5, 8],\n [0, 0, 0, -6, -3, -15],\n [0, 0, 0, 0, -8, 1],\n [0, 0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTe... | 355 | 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[[0, -5, -4, 9, 9, -14],\n [-2, 1, -10, 3, 14, 6],\n [6, 4, -8, -8, -1, -9],\n [8, -5, 6, 2, 13, -14],\n [-10, 8, 8, 13, -2, 0],\n [11, 5, -14, 9, -15, 14]]\n\... | 46 | 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, 10, -4, -3, -4, 10],\n [0, -6, -4, 6, 4, -10],\n [0, 0, 14, -4, -3, -2],\n [0, 0, 0, -14, 5, 8],\n [0, 0, 0, 0, 3, 5],\n [0, 0, 0, 0, 0, 11]... | 72 | 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, 12, 0, -14, -3, 10],\n [0, -6, -10, -2, 1, -7],\n [0, 0, -3, -12, 1, 11],\n [0, 0, 0, 9, 8, -12],\n [0, 0, 0, 0, -3, 6],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answ... | -157 | 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[[7, -4, -6, -10, -4, 10],\n [-4, -5, 2, 11, -8, 8],\n [-6, 2, 13, 3, -8, -10],\n [-10, 11, 3, -15, 2, 2],\n [-4, -8, -8, 2, -7, -11],\n [10, 8, -10, 2, -11, 1... | -45 | 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[[-11, 5, -14, 2, 14, -11],\n [0, 4, -13, -5, -7, -15],\n [0, 0, 6, 0, 1, 7],\n [0, 0, 0, 8, 15, 12],\n [0, 0, 0, 0, 3, -5],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex forma... | 245 | MATH |
[
{
"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 5) of the inverse. Round your answer to the nearest integer:\n[[-11, -3, 3, 4, 12, -2],\n [-3, -4, -4, 3, 2, -4],\n [3, -4, -2, -1, -2, 8],\n [4, 3, -1, -14, 2, 3],\n [12, 2, -2, 2, 10, 3],\n [-2, -4, 8, 3, 3, -1]]\... | 7 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-7, 15, 5, 12, 9, -4],\n [-6, 2, 6, -1, -11, 5],\n [7, 1, -9, 8, -11, 9],\n [3, 9, 12, 11, 5, -3],\n [7, 10, 7, -7, -2, 11],\n [-1, 15, -2, -5, 2, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in L... | 12 | MATH |
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