messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-3, -2, -6, -4, 12],\n [-2, 4, 4, 0, 4],\n [-6, 4, 6, 2, 2],\n [-4, 0, 2, 15, -9],\n [12, 4, 2, -9, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\... | 48 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 10, 6, 13, 1],\n [0, -13, -4, 7, -15],\n [0, 0, 5, 8, -2],\n [0, 0, 0, -10, 9],\n [0, 0, 0, 0, -1]]\n\... | -160 | MATH |
[
{
"content": "Find the inverse of 1/150 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[[3, 5, 14, 12, 11],\n [-15, -6, 3, 0, -4],\n [-11, 7, 5, 2, 2],\n [-13, 9, 2, 0, 8],\n [12, -2, -15, 13, 1]]\n\nPresent the an... | -27 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 0, -8, 12, -2],\n [0, 4, 1, -7, 10],\n [-8, 1, 5, -6, 2],\n [12, -7, -6, -8, -4],\n [... | -62 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-11, -6, -7, 1, 0],\n [-11, 10, 14, 15, -3],\n [7, -12, -12, 1, 9],\n [5, 2, 4, -15, 10],\n [-13, -4, 6, -3, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed... | 289 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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[[13, 12, 15, -3, 1],\n [0, 13, -5, -3, -5],\n [0, 0, 8, 12, 1],\n [0, 0, 0, 3, -14],\n [0, 0, 0, 0, 4]]\n\nP... | 129 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (5, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 3, -11, 8, -6],\n [12, 13, 3, -7, -6],\n [2, -1, -7, -1, -5],\n [-13, 13, 3, -2, -11],\n [4, -12, 14, 12, 8]]\... | 1 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/150 * A where A =\n[[11, -5, 9, -10, 7],\n [10, 7, 6, -15, -15],\n [13, -10, 7, -13, -10],\n [-3, 9, 14, -6, 5],\n [-12, 0, -6, 1, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 16 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the value at position (3, 5) of the inverse. Round your answer to the nearest integer:\n[[9, -2, -2, -4, -4],\n [-2, -9, -4, -2, 6],\n [-2, -4, 8, -4, 13],\n [-4, -2, -4, -7, 9],\n [-4, 6, 13, 9, 13]]\n\nPresent the answer in LaTex format: \... | -7 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, -10, -9, 2, 0],\n [-4, -13, 12, -4, 13],\n [4, -9, 3, 7, -8],\n [-6, -9, 3, -12, 3],\n [-3, 8, -12, -2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 278 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-10, -2, -2, -5, 15],\n [0, 3, 8, -11, -12],\n [0, 0, 1, 10, 7],\n [0, 0, 0, 14, 0],\n [0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 185 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 11, -11, 8, 14],\n [0, 2, -14, 12, -9],\n [0, 0, -3, -13, 8],\n [0, 0, 0, -10, -1],\n ... | -860 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -9, -14, 1, -8],\n [14, 5, -6, -1, 14],\n [-2, -1, -4, -1, -1],\n [-8, -7, 15, 3, 12],\n [2, 4, -8, -9, -11]]\n\nPresent the answer in LaTex format: \\bo... | -60 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 10, 0, -8, 0],\n [10, 2, 14, -13, 0],\n [0, 14, -12, -10, -3],\n [-8, -13, -10, -6, 2],\n [0, 0, -3, 2... | -235 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, -2, -4, 7, -8],\n [0, -4, -8, 12, -4],\n [0, 0, -15, -4, -12],\n [0, 0, 0, 7, -8],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\box... | 76 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, 9, 3, 11, 10],\n [-3, 3, -7, 3, -3],\n [2, 14, -7, -11, 0],\n [-9, -13, -5, -13, -4],\n [-15, -15, -5, 13, 4]]\n\nPresent the answer in LaTex format... | -41 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -6, 8, -9, 9],\n [-10, 14, 1, -10, 14],\n [1, -11, 0, -10, -14],\n [-12, 8, -8, -13, -5],\n [-6, 15, 3, 15, 13]]... | 26 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[-5, -11, 1, -6, -14],\n [0, 7, -10, -5, 4],\n [0, 0, 12, 8, -2],\n [0, 0, 0, -14, -7],\n [0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \... | -47 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -4, -4, 2, 2],\n [-4, 13, 8, 10, 8],\n [-4, 8, -12, 0, 3],\n [2, 10, 0, 15, 4],\n [2, 8, 3, 4, -7]]\n\nPresent the answer in LaTex for... | 160 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, 3, -11, 2, -7],\n [14, -13, 14, 6, 11],\n [11, -13, 12, 14, 15],\n [-6, -5, -9, -8, 11],\n [-12, 7, 6, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 261 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 9, 7, -10, -9],\n [0, -8, 12, 6, 1],\n [0, 0, -8, 11, 13],\n [0, 0, 0, -14, 5],\n [0, 0, 0, 0, 10]]\n\n... | -58 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 2, -6, -14, 10],\n [0, -5, -11, 11, 7],\n [0, 0, -10, -14, -4],\n [0, 0, 0, -7, -1],\n [0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\... | -113 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[5, -12, -3, -8, 6],\n [-14, -13, 11, -3, -3],\n [-14, -2, 3, 0, 13],\n [4, -4, 2, 3, 1],\n [-9, -15, 10, 12, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{... | 341 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 8, 1, -8, -10],\n [8, 10, 2, 2, -4],\n [1, 2, 15, 6, 4],\n [-8, 2, 6, -3, 9],\n [-10, -4, 4, 9, 5]]\n\nP... | 4 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-15, -4, 13, -1, -1],\n [0, -9, 14, 14, 3],\n [0, 0, -1, 1, 15],\n [0, 0, 0, -14, 8],\n [0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 143 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-14, -13, -14, -9, 15],\n [0, 11, 2, -13, 0],\n [0, 0, -10, -9, 10],\n [0, 0, 0, 6, 10],\n [0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 28 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -11, 5, 7, 1],\n [0, 9, -5, 2, 1],\n [0, 0, -12, 3, -5],\n [0, 0, 0, 12, 5],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: ... | 244 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-4, -4, -2, 2, -4],\n [-4, 13, -11, -10, -6],\n [-2, -11, -15, -1, 9],\n [2, -10, -1, 0, 2],\n [-4, -6, 9, 2, 0]]\n\nPresent the answer in LaTex format... | -15 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[15, 2, -15, -7, 2],\n [7, 9, 6, 6, -10],\n [9, -1, -6, -13, 12],\n [-8, -2, 3, -2, 0],\n [8, -3, 12, 10, -13]]\n\nPresent the answer in LaTex format: \\boxed... | -94 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, -1, 8, 6, -4],\n [-1, -8, -6, -8, 11],\n [8, -6, -10, 6, -4],\n [6, -8, 6, -13, 0],\n [-4, 11, -4, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 445 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 4, -6, -8, 5],\n [4, -12, 6, 0, 2],\n [-6, 6, 1, 9, -2],\n [-8, 0, 9, 2, -8],\n [5, 2, -2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{... | -78 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -13, 1, -11, -4],\n [0, -3, 1, 4, -15],\n [0, 0, 7, -1, 9],\n [0, 0, 0, -6, -6],\n [0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -79 | MATH |
[
{
"content": "Find the inverse of 1/150 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, 12, -3, 8, -8],\n [0, -15, -3, 11, 15],\n [0, 0, -11, 8, -12],\n [0, 0, 0, -2, -1],\n [0, 0, 0, 0, 15]]\n\nPresent the a... | -75 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -9, -7, -10, -6],\n [1, -15, 9, -1, -12],\n [2, 9, 9, -12, 11],\n [15, 4, -11, -6, -10],\n [2, -8,... | 200 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, -7, -4, -1, -8],\n [0, 2, 2, -2, -11],\n [0, 0, 11, -9, -15],\n [0, 0, 0, -1, -4],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed... | -150 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[4, 2, 1, -9, -2],\n [-15, 0, -3, -7, -1],\n [-13, -7, -3, -4, 14],\n [-7, 2, -5, -9, 3],\n [-7, -8, -14, 10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 8 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 15, 1, 9, -3],\n [6, 4, 8, -3, -12],\n [8, 3, -12, -5, 8],\n [-1, -7, 11, 15, 3],\n [-13, 5, 12, -13, 7]]\n\nPr... | -1 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 6, 1, -3, -2],\n [3, 11, 1, -7, -4],\n [-6, 7, -5, -2, -6],\n [-4, -15, 10, 12, 0],\n [-5, -4, -5, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 50 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, -11, 2, -7, 10],\n [-11, -9, -4, -4, -10],\n [2, -4, -11, 1, 10],\n [-7, -4, 1, 10, 2],\n [10, -10, 10, 2, 6]]\n\nPresent the answer in LaTe... | -58 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-14, 10, -5, -8, 6],\n [10, 14, -4, -2, 6],\n [-5, -4, -11, -3, 11],\n [-8, -2, -3, 3, 6],\n [6, 6, 11, 6, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Y... | 167 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 12, -13, -5, 8],\n [0, 7, -3, 8, 11],\n [0, 0, 10, -2, -13],\n [0, 0, 0, -6, -13],\n [0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex ... | 345 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[14, 11, -3, -13, -7],\n [0, -6, -4, 2, -13],\n [0, 0, -6, 14, 9],\n [0, 0, 0, -13, -13],\n [0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | -126 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -5, 9, 8, 1],\n [-5, 4, 1, 2, 3],\n [9, 1, 11, -2, 8],\n [8, 2, -2, -1, -5],\n [1, 3, 8, -5, -2]]\n\nPresent the answer in LaTex format: \\b... | 18 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, -12, -1, 3, -5],\n [0, 4, 11, -7, 11],\n [0, 0, 9, -3, -13],\n [0, 0, 0, 13, -15],\n [0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex for... | 46 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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[[-8, 0, -12, -3, -5],\n [0, 12, 0, -2, 4],\n [-12, 0, -5, 4, 6],\n [-3, -2, 4, 5, -6],\n [-5, 4, 6, -6,... | 146 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/150 * A where A =\n[[-9, 6, -13, -5, 7],\n [0, 7, 3, -1, -9],\n [0, 0, 13, -3, -15],\n [0, 0, 0, -15, 15],\n [0, 0, 0, 0, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -20 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[14, -2, -1, 15, -8],\n [9, 4, -5, 4, 11],\n [4, 1, -3, -6, 7],\n [-8, 12, 5, 14, 0],\n [-9, -14, -8, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{... | -166 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, 14, -8, 10, -4],\n [10, -7, -10, -13, 6],\n [9, 10, -10, -2, 9],\n [-7, -11, 12, 9, 7],\n [6, -5, -10, -14, -4]]\n\nPresent the answer in L... | 1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 7, -8, 6, 7],\n [0, -9, -11, 15, -3],\n [0, 0, -13, 14, 6],\n [0, 0, 0, 3, -3],\n [0, 0, 0, 0, 9]]\n\nPresent the ans... | 21 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 0, -6, -13, -11],\n [7, -1, 11, -9, 6],\n [-4, -7, -4, -2, 0],\n [-10, 3, -7, -8, -10],\n [1, -6, 9, -1... | -15 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/150 * A where A =\n[[-14, -7, 8, 5, 6],\n [-7, -11, -8, 8, -7],\n [8, -8, -9, 1, 11],\n [5, 8, 1, 1, -1],\n [6, -7, 11, -1, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -4 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[11, -11, 12, 4, 4],\n [0, 14, -7, 0, 15],\n [0, 0, 1, 6, -6],\n [0, 0, 0, -14, -6],\n [0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 816 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, -1, 12, 8, -8],\n [-1, -15, 10, 6, -3],\n [12, 10, -12, -2, -6],\n [8, 6, -2, -10, 1],\n [-8, -3, -6, 1, -11]]\n\nPresent the answer in LaTex forma... | -16 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -13, 4, 12, -5],\n [-7, -6, -8, -1, -8],\n [6, -8, 0, -13, -4],\n [-7, -9, 8, 11, 1]... | 88 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -1, 1, 14, 1],\n [0, -7, -1, 3, -11],\n [0, 0, 11, 1, -13],\n [0, 0, 0, -4, -15],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex f... | 1010 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -14, 11, -1, 11],\n [0, -13, 7, 9, -11],\n [0, 0, -14, 7, -9],\n [0, 0, 0, 2, -2],\n [0, 0, 0, 0, 8]]\n\nPresent the a... | 240 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 14, 4, 14, -5],\n [14, -13, 3, 6, -1],\n [4, 3, 9, -4, -8],\n [14, 6, -4, 10, 2],\n [-5, -1, -8, 2, -9]]\n\nPresent the answer in LaTex for... | -19 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-9, -6, -13, 4, 14],\n [-7, 9, -7, -8, 12],\n [-6, -1, 11, -14, -1],\n [-9, -12, -7, -9, 5],\n [-12, -6, -4, 15, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed... | 4 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 6, -15, 4, -6],\n [6, 7, -4, 13, -11],\n [-4, 13, -2, -6, 4],\n [8, -2, -2, 13, 3],\n [-9, -14, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 15 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[-14, -14, -1, 15, -3],\n [5, -8, -5, 5, 6],\n [-5, -13, -7, -1, -15],\n [8, 5, 14, -7, -2],\n [-1, -11, 12, -1, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{... | -1069 | MATH |
[
{
"content": "Find the inverse of 1/150 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, 11, 4, 6, 7],\n [-2, -3, 4, 6, -4],\n [2, -2, 10, 12, 11],\n [-7, -6, 0, -6, -9],\n [-12, 0, -15, 1, -6]]\n\nPresent the... | -20 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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[[9, 1, 1, -5, 0],\n [1, -4, 1, 2, -4],\n [1, 1, -7, -12, 3],\n [-5, 2, -12, -15, 13],\n [0, -4, 3, 13, ... | 508 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, 8, -2, -5, 3],\n [8, 12, 0, 11, 2],\n [-2, 0, -6, 2, -8],\n [-5, 11, 2, 11, 2],\n [3, 2, -8, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 46 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 12, 7, -11, 12],\n [5, -14, -10, -15, 9],\n [9, -14, -7, -7, -15],\n [10, -7, 2, 7, -12],\n [2, 1, -9, -14, 6]]\n\nPresent the answer ... | 158 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, -7, 6, 5, -11],\n [0, -6, -6, -2, 10],\n [0, 0, -13, -13, 9],\n [0, 0, 0, -3, -13],\n [0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format... | -45 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -2, -9, -3, 1],\n [-2, -7, -3, -10, -1],\n [-9, -3, -12, 12, 8],\n [-3, -10, 12, -15,... | 44 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-11, 2, -2, 8, 6],\n [2, -14, -2, -7, -4],\n [-2, -2, 15, -3, 0],\n [8, -7, -3, 9, 0],\n [6, -4, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | -4 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -5, 4, -10, 12],\n [-5, 4, 8, 2, 0],\n [4, 8, -11, -12, 2],\n [-10, 2, -12, 6, 9],\n [12, 0, 2, 9, -5]]\n\nPresent th... | 88 | MATH |
[
{
"content": "Find the inverse of 1/150 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, -5, -6, 8],\n [1, -7, 4, 0, -5],\n [-5, 4, -1, 5, -2],\n [-6, 0, 5, -14, 10],\n [8, -5, -2, 10, -12]]\n\nPresent the an... | -83 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 1, 8, -9, -1],\n [1, -2, 12, 8, 6],\n [8, 12, -6, 2, 10],\n [-9, 8, 2, -5, -14],\n [-1, 6, 10, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 27 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 6, -8, 8, -2],\n [6, 14, -7, 11, -6],\n [-8, -7, 1, 12, -4],\n [8, 11, 12, -3, -2],\n [-2, -6, -4, -2, -... | -423 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/150 * A where A =\n[[-13, -3, 10, 11, -6],\n [0, 1, 8, -15, -6],\n [0, 0, 15, 14, -2],\n [0, 0, 0, 12, -12],\n [0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -35 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/150 * A where A =\n[[-10, 15, 2, 1, -2],\n [-1, 5, -9, 13, -2],\n [3, -2, 6, 14, 11],\n [14, 7, 0, 4, -9],\n [14, -5, 8, 8, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 83 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 4, -5, 15, 11],\n [-14, -8, 13, 2, 13],\n [-6, -13, -1, -3, -8],\n [-13, -8, 11, -7, 0],\n [5, 3, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 74 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -7, 2, -1, 8],\n [-7, -4, 9, -2, 0],\n [2, 9, 7, 4, -6],\n [-1, -2, 4, -14, -6],\n [8, 0, -6, -6, 7... | 312 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -7, -2, -9, -1],\n [-7, -10, 7, 0, 0],\n [-2, 7, 5, 0, -3],\n [-9, 0, 0, -8, 3],\n [-1, 0, -3, 3, 10]]\n\nPrese... | 8 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -6, -5, -7, -5],\n [13, 4, 11, 11, -5],\n [-13, 10, -10, 6, -7],\n [8, -6, 2, -4, 8],\n [-11, 2, 14, -15, -15]]\... | 50 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 8, -14, -3, -8],\n [8, 13, -4, 6, -4],\n [-14, -4, 10, -8, 6],\n [-3, 6, -8, -3, 4],\n [-8, -4, 6, 4, -11]]\n\nPrese... | 55 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 6, 7, -14, -10],\n [0, -12, 13, 2, -15],\n [0, 0, -4, -11, 8],\n [0, 0, 0, 9, -11],\n [0, 0, 0, 0, 4]]\n\nPresent the... | 5 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/150 * A where A =\n[[5, -10, 4, 7, -6],\n [-10, -15, 12, -13, -4],\n [4, 12, -6, 2, 3],\n [7, -13, 2, -3, 6],\n [-6, -4, 3, 6, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 147 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-13, -4, 15, 5, 7],\n [0, -5, -3, -9, 15],\n [0, 0, -4, -15, -8],\n [0, 0, 0, -12, -3],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | -82 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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[[-5, -7, -6, -10, -15],\n [6, -9, 2, 12, -7],\n [-14, 6, 15, 12, 15],\n [-12, -3, -11, -2, 8],\n [-13, ... | 133 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 15, 10, 11, 15],\n [-3, 10, -10, 10, -14],\n [-7, -2, 14, -5, 0],\n [-7, -6, -1, -8, 7],\n [-3, -14, -15... | 219 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -11, -12, -12],\n [0, 7, 2, -3, -10],\n [0, 0, -14, 5, 15],\n [0, 0, 0, 5, 11],\n ... | -200 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value at position (4, 4) rounded to the nearest integer?\n[[-13, 2, -2, -9, -9],\n [2, -7, -6, -10, 2],\n [-2, -6, -13, 10, 9],\n [-9, -10, 10, -15, -2],\n [-9, 2, 9, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the inverse of 1/150 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, 0, 2, -2, -8],\n [0, -3, 10, 4, -3],\n [2, 10, 12, 1, -1],\n [-2, 4, 1, -11, 2],\n [-8, -3, -1, 2, -13]]\n\nPresent the answer in LaTex... | 126 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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[[12, -6, -6, -4, 5],\n [-6, 6, 2, -10, 4],\n [-6, 2, 6, -3, 2],\n [-4, -10, -3, -9, -10],\... | 28 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/150 * A where A =\n[[-10, -12, -13, -5, -3],\n [0, -2, 5, 11, -1],\n [0, 0, 15, -3, -3],\n [0, 0, 0, -12, 13],\n [0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{You... | 902 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, -1, -4, -4, -2],\n [-1, -13, 14, -5, 10],\n [-4, 14, 15, -2, 0],\n [-4, -5, -2, 8, -13],\n [-2, 10, 0, -... | 49 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, 0, -6, -2, -6],\n [0, 8, -7, 4, 8],\n [-6, -7, -11, -1, -12],\n [-2, 4, -1, 3, 8],\n [-6, 8, -12, 8, 2]]\n\nPresent the answer in LaTex format: \\b... | -44 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 1, 10, -6, 4],\n [1, -8, -4, -4, -4],\n [10, -4, -12, 0, -11],\n [-6, -4, 0, 2, -7],\n [4, -4, -11, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 563 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 times the following and determine the value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 2, 14, -15, 1],\n [0, 13, -3, -9, -15],\n [0, 0, -6, 9, -12],\n [0, 0, 0, -7, -13],\n [0, 0, 0, 0, -15]]\n\nPr... | -12 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, 1, 5, -8, 0],\n [1, 5, 2, -2, 4],\n [5, 2, 9, 4, 6],\n [-8, -2, 4, 2, -2],\n [0, 4, 6, -2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 42 | MATH |
[
{
"content": "Find the inverse of 1/150 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-7, 8, -10, 1, 5],\n [8, 11, 3, -8, 6],\n [-10, 3, 7, 8, 4],\n [1, -8, 8, -6, -2],\n [5, 6, 4, -2, -8]]\n\nPresent the answer in LaTex format: ... | -35 | MATH |
[
{
"content": "Find the inverse of 1/150 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, -2, -6, -2, -1],\n [-2, -10, -13, 0, 3],\n [-6, -13, -11, -2, -1],\n [-2, 0, -2, -8, -6],\n [-1, 3, -1, -6, -12]]\n\nPresent the answe... | 275 | MATH |
[
{
"content": "For the inverse of 1/150 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, 9, -4, 2, -1],\n [9, -3, 1, 6, 4],\n [-4, 1, -11, -6, 1],\n [2, 6, -6, -11, -10],\n [-1, 4, 1, -10, 0]]\n\nPresent the answer in LaTex format: \\bo... | 15 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 12, 13, 2, -4],\n [-8, -13, 4, -15, -1],\n [12, 4, 10, -11, 3],\n [13, -15, 3, -5, -2]... | 10 | MATH |
[
{
"content": "Find the inverse of 1/150 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, 2, -10, -5, 12],\n [1, 3, -11, -12, 7],\n [12, 8, 12, 11, -12],\n [3, -6, 15, -11, -5],\n [-6, -12, -9, 4, 4]]\n\nPresent... | 24 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/150 * A where A =\n[[15, -5, -2, 14, 2],\n [-5, -14, -4, 4, -14],\n [-2, -4, -8, -6, 6],\n [14, 4, -6, 7, 4],\n [2, -14, 6, 4, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex forma... | 24 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/150 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, 11, -8, 0, 9],\n [12, 7, -10, -10, -15],\n [12, 14, -6, -9, 9],\n [-13, -14, -7, -15, -11],\n [9, -10, ... | -5 | MATH |
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