messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-18, 22, 10, 0, 19, -18, 6, 6, -25],\n [0, -25, -11, 24, -6, -23, -11, 11, -5],\n [0, 0, -3, 14, 9, -8, -9, 5, 22],\n [0, 0, 0, 10, 9, -15, 1, 8, -8],\n [0, 0, 0, 0, 16, -15, -21, -8, -1],\n... | 210 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, 23, 16, -6, -6, -4, 12, -9, -1],\n [23, 25, 0, -12, -18, -2, 12, -8, 4],\n [16, 0, 8, -16, 12, -2, 0, 2, -7],\n [-6, -12, -16, -7, -1, -8, 12, 0, 1],\n [-6, -18, 12, -1, -10, 10, -10, 0, 0],\n [-4, -2, -2, -8, 10, 11, ... | -409 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-23, -2, -3, 19, 22, -25, 6, 7, 22],\n [4, -24, -8, 4, -8, -21, -21, -18, -17],\n [6, -12, -13, -8, -22, 24... | -54 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-24, -5, -14, 16, 23, 1, 24, 22, -16],\n [0, -5, -4, -13, 22, 14, -14, -9, 22],\n [0, 0, 23, 14, -14, -17, 4, -20, -1],\n [0, 0, 0, 2, 3, 10, -15, -5, 12],\n [0, 0, 0, 0, 15, -11, -3, 15, -20],\n [0, 0, 0, 0, 0, -17, 25, 4... | 781 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-7, 3, 21, 24, 22, 13, 16, -1, -10],\n [-9, 2, 13, 17, 23, -21, -25, -23, 22],\n [-2, 3, -11, -22, 18, -25, 23, -11, -2],\n [5, -6, -16, -15, -8, 8, 2, 12, -10],\n [-2, 13, 25, -14, 24, 16, -19, 10, -9],\n [23, -22, 11, 7,... | -73 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-5, 11, 2, 19, 6, 15, 1, -3, -16],\n [0, 15, -20, -2, -8, -16, -11, 19, 17],\n [0, 0, 24, 9, 1, -1, -23, -5... | -307 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, -20, -14, 16, -7, 14, -21, 1, -16],\n [0, 20, -12, 8, 23, -11, 3, 0, 1],\n [0, 0, 9, 9, 24, -20, -12, 0, -23],\n [0, 0, 0, 3, -17, 6, -4, -4, 8],\... | 2499 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[18, -12, -19, 0, 6, 3, 20, 13, -17],\n [0, -9, 23, -1, 4, 19, 3, 3, -8],\n [0, 0, -9, -20, -14, 12, -2... | 65480 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-7, 3, -24, 11, 0, 3, -21, 6, 12],\n [22, -24, -21, 21, 7, 25, 9, -7, -11],\n [9, -18, 21, -25, 12, -4, -9, -10, 19],\n [-25,... | -19 | MATH |
[
{
"content": "Find the inverse of 1/450 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, -2, 14, -9, 12, -4, -6, 2, -10],\n [-2, 6, -7, -7, 2, -6, -7, 7, -21],\n [14, -7, 14, -1, 15, 2, 14, -10, 4],\n [-9, -7, -1, -24, 2, 1... | 9977 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-3, -8, -2, 16, 3, 12, 12, -13, 6],\n [-7, -9, -24, -8, 13, 1, -12, -11, -18],\n [-17, -5, 17, 9, -12, 1, -18, 9, -8],\n [-12, -18, 23, -18, 11, 18, -24, -9, -13],\n [-12, 15, 15, -17, 1, -6, 12, -14, 16],\n [-4, 11, 24, 1... | 949 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[1, 6, -2, -16, -1, 2, -2, 2, 0],\n [6, 10, 13, 2, 20, 12, 17, 5, 1],\n [-2, 13, -16, -12, -10, -8, -8, 12, 8],\n [-16, 2, -12, 16, -10, -6, 14, -18, 16],\n [-1, 20, -10, -10, 13... | -110 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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, 10, 16, 16, 18, 19, -8, 3, -14],\n [10, -23, 4, 22, 6, -8, 6, 14, 6],\n [16, 4, 1, 8, -20, -18, -10, 5, 4],\n [16, 22,... | 788 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 21, 3, 17, -2, 14, 6, 13, -14],\n [21, -7, -6, -14, -3, -6, 14, -2, -11],\n [3, -6, -16, 10, -2, 16, -16, 18, 21],\n [17, -14, 10, -3, -4, 5... | 41 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-21, -17, 24, -16, 23, -16, -12, 10, -16],\n [0, 11, 15, 12, 22, -4, -3, -10, -15],\n [0, 0, 9, 22, -6, 11, 15, -21, 10],\n [0, 0, 0, 18, -6, 13, 7, 4, -10],\n [0, 0, 0, 0, 17, 14, -25, -23, -18],\n [0, 0, 0,... | 648 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 23, -22, 11, -8, 5, 23, 13, -16],\n [-17, 2, 2, -13, -8, -14, -18, -3, 24],\n [-21, -19, -11, -23, -8, 12, 0, 12, 7],\n [-5, -9, 17, -24, -1, 15, -7, 12, -1],\n [13, ... | -54 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -16, -20, 6, 0, 4, -14, 1, 0],\n [-16, -24, 2, -2, 5, 9, -6, 8, 8],\n [-20, 2, -4, -11, 6, -2, -12, -8, 0],\n [6, -2, -11, -20, 23, 14, -2, 8, -8],\... | -43 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[16, -2, -1, 7, 15, -14, 19, 6, -3],\n [-2, -10, -18, 14, -16, 8, 2, -6, -5],\n [-1, -18, -5, 4, 4, 7, 16, 0, -2],\n [7, 14, 4, -8, 0, -2, 12, -14, 11],\n [15, -16, ... | 807 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[13, -10, 7, 1, -25, 18, -10, -21, 20],\n [0, 15, 8, 18, -1, 16, 8, -11, -22],\n [0, 0, -1, 15, -13, 16, 20, -1, -23],\n [0, 0, 0, -12, -4, 22, -17, -2, -3],\n [0, 0, 0, 0, -12, -6, 13, 10, 1... | 6092 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 16, 6, 17, 9, 23, -15, -9, 25],\n [0, -24, -2, 20, -11, 2, -23, 3, 19],\n [0, 0, -4, 5, -19, 22, 22, 0, 5],\n [0, 0, 0, 9, 7, -23, -7, -17, ... | -112 | MATH |
[
{
"content": "Find the inverse of 1/450 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[[-16, -15, 14, 12, -15, 22, 4, -22, -24],\n [0, 13, -9, -3, 19, -16, -13, 16, 13],\n [0, 0, -10, -23, 10, -22, 10, -10, 15],\n... | 862 | MATH |
[
{
"content": "Find the value at position (3, 9) of the inverse of matrix 1/450 * A where A =\n[[-13, 10, 0, -6, -9, -1, 0, 3, -12],\n [10, -17, -4, 1, 6, -2, 2, 10, 10],\n [0, -4, -6, -2, 14, -12, 8, 4, -14],\n [-6, 1, -2, 16, -10, -19, 0, -4, -12],\n [-9, 6, 14, -10, 1, -8, 20, -2, -7],\n [-1, -2, -12, -19, -8... | -13 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 7, -3, -4, 7, 12, -8, 2, 8],\n [7, 6, -20, -11, 3, -10, -16, -4, 6],\n [-3, -20, 11, 10, 18, -6, -18, -22, -12],\n [-4, -11, 10, -16, -6, 2, 16, -16, 9],... | 168 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[1, -4, -5, -11, 21, 9, 2, 7, 4],\n [-4, -18, -19, -12, -18, -1, 7, -22, 18],\n [-5, -19, -20, 8, -18, -2, 7, -8, 12],\n [-11, -12, 8, 6, -10, -11, 2, 8, 2],\n [21, -18, -18, -10, -14, -18, 19, 0, 4],\n [9, -1... | 141 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (7, 3) rounded to the nearest integer?\n[[-12, 22, 14, -6, 22, 4, 18, 12, -10],\n [22, -14, -9, -2, -4, -3, -11, -4, -2],\n [14, -9, -6, 7, -12, -10, -7, -4, -14],\n [-6, -2, 7, 23, 10, -1, -10, 6, -3],\n [22, -4, -12, ... | -145 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[8, -16, -4, 2, -8, 22, -2, 9, 8],\n [-16, 20, 2, 12, 6, 4, 18, -8, 7],\n [-4, 2, -1, -4, 6, -13, -3, -11, 0],\n [2, 12, -4, -... | -83 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[23, -19, 14, 16, -2, 9, -13, 23, -13],\n [0, -7, 3, -4, 15, -5, -10, 4, -21],\n [0, 0, -20, -5, 16, 24, -15, -2, 2],\n [0, 0, 0, 14, 25, 21, -7, 24, -9],\n [0, 0, 0, 0, ... | 49 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -17, 0, 14, -4, -11, -12, 8, -2],\n [-17, 3, -1, 2, -15, 6, 4, 1, 14],\n [0, -1, -22, 8, -16, 8, 6, 10, -3],\n [14, 2, 8, 6, -7, -11, 0, 8, -8],\n [-4, -... | 333 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[-25, 6, -2, 22, 16, -17, 24, -25, 16],\n [0, -16, 18, 17, 15, 4, -21, -22, 19],\n [0, 0, -25, 23, -11, -2, -11, 24, -20],\n [0, 0, 0, 13, 15, 8, 13, 6, 3],\n [0, 0, 0, 0, -2, -11, -14, -6, -... | -1970 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[21, -8, 21, 17, -1, 1, 1, -14, -3],\n [0, 18, -19, -2, -19, 3, 2, -3, -16],\n [0, 0, 22, 8, -1, -24, 24, -21, -12],\n [0, 0, 0, 2, -17, -2... | 6572 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (8, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 13, 6, 3, -10, -25, -14, -7, -17],\n [22, -19, 4, -11, 18, -22, -20, 12, 21],\n [9, -24, -21, -18, 25, 4, 22, -... | -6 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[-23, -10, 9, -12, 23, 25, -19, 0, 17],\n [22, 5, -2, -7, 11, -25, -1, -16, -8],\n [16, -25, 3, -13, -22, -14, 22, -7, 0],\n [18, 12, -10, 18, -1, -16, 11, 2, 2],\n [-1, -1, 25, -14, -18, 10, 13, -2, -3],... | 1193 | MATH |
[
{
"content": "Find the inverse of 1/450 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[[-21, 10, 12, -14, 8, -10, 8, -17, 10],\n [10, 0, 16, -18, -12, -7, 5, -10, 6],\n [12, 16, -3, 6, -20, -4, 10, 3, 9],\n [-14, ... | -137 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -6, -16, -15, 13, -7, -7, 17, -20],\n [0, -25, -3, 14, 11, -16, -24, 10, -24],\n [0, 0, 16, -5, 4, -2, -24, 12, -4],\n [0, 0, 0, -2, 0, -24, 20, 19, 8],\n [0, 0... | 84716 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[14, 8, 6, 1, -6, 6, 3, -4, -11],\n [8, -14, -1, -6, 4, 8, 3, 4, 12],\n [6, -1, -25, -4, -11, -22, 4, -6, -13],\n [1, -6, -4, 0, 6, 4, -7, -16, -21],\n [-6, 4, -11, 6, 18... | 148 | MATH |
[
{
"content": "Find the value at position (3, 9) of the inverse of matrix 1/450 * A where A =\n[[-16, -23, -7, -24, -9, 3, -24, -10, 23],\n [-16, -22, 17, 0, 23, -2, -14, -5, 16],\n [-10, 10, 9, -17, -20, 18, -25, -12, -2],\n [-16, -8, 19, -17, 1, -7, 10, -23, 12],\n [-17, -16, -17, -9, 16, 12, 22, 23, 17],\n [-... | -24 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[15, 22, -6, 6, -8, -2, 3, -14, 5],\n [22, 19, -16, 0, -2, 2, 2, -22, 7],\n [-6, -16, 14, 2, -10, 18, -2, -2, 14],\n [6, 0, 2, 3, 14, 4, -8, 15, 0],\n [-8, -2, -10, 14, -3, 2, -6, -9, -4],\n [-2, 2, 18, 4, 2, ... | -249 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 18, -9, -23, 5, -5, 7, -25, -20],\n [25, -22, -4, -13, 18, 4, 14, 0, 13],\n [13, -19, -12, 0, -8, 25, -2, 25, -1],\n [24, 6, -20, -10, -23, -5, 6, -24, 21... | 13 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-19, -14, 19, 23, 15, -18, 2, -10, -23],\n [0, 6, -5, 19, -8, 22, 20, -15, 24],\n [0, 0, 25, -24, 15, -4, -17, -12, -11],\n [0, 0, 0, -1, 11, -20, 11, 7, -1],\n [0,... | 142435 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[6, 17, -3, -6, -7, 3, -18, 3, -8],\n [0, -14, -16, 21, 11, -9, 6, -22, 5],\n [0, 0, -8, -18, 6, -6, 23, 14, -13],\n [0, 0, 0,... | -22779 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[22, -12, 8, 0, -8, -6, -7, 2, -2],\n [-12, -20, -10, -12, 12, -4, -1, 21, -5],\n [8, -10, -15, -5, -8, 8, -17, 16, -6],\n [0, -12, -5, 22, -2, 2, 22, 11, -14],\n [-8, 12... | -533 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (5, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 9, 21, 1, 3, -21, -25, 17, 25],\n [-21, 3, -9, 25, 23, 11, -2, 1, -17],\n [12, -13, 0, -15, -2, 7, 23, -20, 9],\... | -11 | MATH |
[
{
"content": "Find the inverse of 1/450 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, -3, -7, 19, -23, 8, -1, 15, 5],\n [13, -12, 11, 21, -6, 6, 7, 5, -19],\n [-21, -22, -15, -7, 12, -6, 1, 3, -8],\n [11, 21, -1, -6, -20... | 4407 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, 0, 8, 16, 12, 4, 6, 18, -4],\n [0, -15, 6, 12, -10, -6, -10, -2, 4],\n [8, 6, -13, -18, 16, 12, -2, -5, -13],\n [16, 12, -18, 16, 4, 13, -3, -2, 18],\n [12, -10... | 1442 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-7, 17, -21, 4, -1, 4, -1, -17, 1],\n [-2, 14, 17, 12, -11, 12, 0, 4, -15],\n [3, -11, 18, -17, 16, 3, -11, -9, -10],\n [-4, 14, 23, 17, -15, 12, -1, 4, -24],\n [-25, 12, 11, -17, -21, 24, -2, 1, 4],\n [25, -... | 681 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[-15, -18, 9, 15, -10, -10, 16, -20, -6],\n [0, -18, -6, 6, 7, -20, 2, -18, -12],\n [0, 0, -4, 7, 17, -5, -20, 14, -19],\n [0, 0, 0, -18, -2, 1, 25, 2, -21],\n [0, 0, 0, 0, 21, 19, -13, 11, -24],\n [0, 0, 0, 0, 0, -1, 13, 2... | 2825 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-17, 20, 6, 3, -22, 8, 0, -5, 10],\n [20, -25, 18, -9, 10, -9, 0, -2, -20],\n [6, 18, 17, 10, 8, 6, 0,... | 591 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[20, -16, 6, 18, 11, -5, -4, -13, 0],\n [-16, -12, -13, 10, 6, -13, 9, 18, 0],\n [6, -13, 18, 2, 2, -17, 7, 7, 2],\n... | 0 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, -12, 0, -4, 8, 7, -13, 6, -18],\n [-4, 15, -6, -5, 8, 23, 4, -20, 9],\n [1, -6, 23, 12, 14, -12, -16, 16, -11],\n [14, 17, 22, -23, -11, 19, 5, -15, 20],\n [13, ... | 25928 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-18, 4, -4, -3, 14, 25, -13, 2, 4],\n [-21, -16, 13, -17, -12, 12, -16, 7, -15],\n [14, -20, -9, 10, -20, 21, -16, 23, 16],\n [-21, -7, -19, -2, 25, 16, -7, -15, -23],\n [4, 17, 12, -20, 21, 9, -4, -15, -18],... | 4 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-19, -1, 11, -10, 16, -2, -2, 4, -16],\n [-1, -20, 12, -6, -1, 4, -4, -19, 22],\n [11, 12, -19, -2, 4, 0, -16, -8, -3],\n [-10, -6, -2, -20, -11, -10, ... | 5 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-15, -6, -14, -2, 7, -4, -8, 16, 8],\n [-6, -22, 16, -16, -10, 20, 20, 10, 10],\n [-14, 16, -22, 4, 6, -4, 0, 11, 11],\n [-2, -16, 4, -23, 24, 2, 6, 3,... | 940 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -25, -18, 16, -11, 8, -7, 18, 4],\n [0, 18, 1, -6, -1, -17, 14, 8, -5],\n [0, 0, -22, 25, -18, -13, -5, 9, -21],\n [0, 0, 0, 16, -10, -22, 4, 20, 4]... | 2126 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -17, -21, -21, 15, 15, 8, -19, 0],\n [0, 8, 0, 6, -14, -20, -6, -7, -10],\n [0, 0, -8, -21, 24, -20, -12, 23, -8],\n [... | -55472 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[23, 17, -4, 2, -10, 18, -10, -10, 11],\n [17, -16, 5, 0, 1, -2, 4, -3, 12],\n [-4, 5, -1, 3, -6, -17, -7, -6, 0],\n [2, 0, 3, -25, 4, -4, 8, 3, -18],\n [-10, 1, -6, 4, 1, -10, 10, 10,... | 172 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-23, -1, 1, 7, -6, 13, -12, -2, 6],\n [-1, -17, -12, -9, 12, 0, 3, 8, -16],\n [1, -12, -15, 7, -6, 9, 2, 10, 8],\n ... | 6 | MATH |
[
{
"content": "Find the inverse of 1/450 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[[-15, -6, 22, 22, 22, 12, -11, 9, -17],\n [7, -15, -4, -20, 11, 24, -5, -14, -19],\n [-24, 13, 15, -2, 0, -1, -6, 14, 15],\n [... | -1560 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[21, 12, -13, 0, -12, 19, -2, 22, -25],\n [20, 19, 4, -16, -16, 2, -22, -12, -14],\n [12, 21, 11, -16, 15, 1, 16, -1... | 6 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -3, -17, 16, 21, -8, 25, 13, -7],\n [-21, -8, 7, 18, 12, -13, 23, -17, 0],\n [-25, -14, -2, -25, -22, ... | 62 | MATH |
[
{
"content": "Find the value at position (5, 2) of the inverse of matrix 1/450 * A where A =\n[[-23, 4, -10, 16, 6, -4, -3, 20, 8],\n [4, 15, -24, 17, -8, 14, -20, 4, 14],\n [-10, -24, 2, -9, -11, -7, -11, 6, 0],\n [16, 17, -9, -25, -12, -18, 7, 2, -4],\n [6, -8, -11, -12, 12, 8, 13, 18, -2],\n [-4, 14, -7, -18... | -9 | MATH |
[
{
"content": "Find the value at position (5, 3) of the inverse of matrix 1/450 * A where A =\n[[-20, 14, 2, -13, 3, 19, -6, -9, 9],\n [19, 13, 11, 17, -3, -8, 10, -6, -19],\n [10, 16, -25, 23, 11, 23, 9, 15, -23],\n [9, 3, -17, 11, 16, 21, -1, -14, 12],\n [-19, -19, -22, 19, 21, 5, 24, 24, 13],\n [-16, 22, -3, ... | -198 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 times the following and determine the value at position (2, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[22, 12, -20, 24, 8, -18, 20, -24, 0],\n [0, -2, 5, -10, 24, -5, 12, 0, -9],\n [0, 0, 16, -22, 24, 17, 22, -22, -7],... | -1463 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/450 * A where A =\n[[-23, 13, -2, -5, -20, 7, -18, 7, 22],\n [0, -24, 12, 14, 13, 13, -2, -5, 25],\n [0, 0, -15, -15, -23, -3, -25, -3, -4],\n [0, 0, 0, -9, 15, 24, -6, -17, -15],\n [0, 0, 0, 0, 18, 24, -18, 3, -18],\n [0, 0, 0, 0, 0, -1... | -30 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -15, -16, -14, -12, 4, 15, -13, 4],\n [0, -15, -25, 1, 21, 13, 17, 23, 11],\n [0, 0, 17, 0, -1, -9, -20, -11, -23],\n [0, 0, 0, 18, 25, -8, 22, 14, 6],\n... | -1123 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[15, -8, -17, -4, -16, 14, -3, 17, -13],\n [-2, -13, 22, 19, -1, 18, 21, 3, -10],\n [14, -20, -18, 8, -8, 17, 6, 23, -16],\n [8, -3, -7, -6, 8, 12, -9, 18, -21],\n [-24, 15, 8, -6, 20, 21, -24, 2, -8],\n [18, 13, 22, 25, 9,... | 68 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 20, 18, -22, 14, -9, 11, -23, -22],\n [0, -10, -15, 1, 0, 5, 8, -18, 13],\n [0, 0, 1, 19, 17, -23, 8, -10, -25],\n [0, 0, 0, 22, 6, 0, -20, 20, -15],\n [0, 0, 0,... | 175226 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-20, -16, 11, -14, 18, -9, 1, -24, -1],\n [0, 18, 2, 19, 11, 11, -9, -21, -7],\n [0, 0, 23, 17, 12, 19, 18, 4, 6],\n [0, 0, 0, 16, -15, 15, -13, 9, -9],\n [0, 0, 0, 0, 4, 0, -10, -15,... | -57 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value at position (5, 5) rounded to the nearest integer?\n[[-2, 16, -4, -16, -22, -18, 13, -11, -18],\n [0, 16, 13, 25, 9, 15, 22, -12, 6],\n [0, 0, 7, 22, 9, 1, -25, -20, -24],\n [0, 0, 0, 3, -10, 3, 5, -4, -16],\n [0, 0, 0, 0, 14, -18,... | 32 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/450 * A where A =\n[[17, -18, 4, -25, 8, -6, 10, 8, 8],\n [-13, -20, 10, -1, 1, 21, 5, -23, 2],\n [-22, -9, 12, 8, -6, -13, 21, -21, -2],\n [25, 12, -9, 5, 2, -25, -24, 7, 14],\n [3, -22, -8, -2, 6, -17, 21, -10... | -43 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -4, 0, -4, 4, 2, -17, -16, -18],\n [-4, -3, 7, 4, -5, 4, -4, -15, 2],\n [0, 7, 10, 4, 8, -4, 1, -8, 10],\n [-4, 4, 4, -22, 2, -2, 14, 14, 14],\n [4, -5, ... | -344 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-21, 5, 3, -11, -1, -13, 18, -2, -11],\n [-2, 0, -7, -2, -7, 16, -9, 22, -21],\n [-22, -4, -16, -5, -1, -20, 4, 3, -15],\n [-15, 22, 20, 1, -7, -4, 2, ... | -77 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[-24, -8, 5, -15, 1, -22, -4, 2, 10],\n [-8, 22, 8, -2, 5, 2, -2, -2, 0],\n [5, 8, 22, -4,... | -44 | MATH |
[
{
"content": "Find the value at position (3, 6) of the inverse of matrix 1/450 * A where A =\n[[24, 14, -5, -6, -9, 16, -22, 1, 15],\n [14, 8, -6, -17, 6, -11, -2, -16, -2],\n [-5, -6, -12, 0, 10, -12, -10, 8, 20],\n [-6, -17, 0, -3, -4, 8, -16, -4, -4],\n [-9, 6, 10, -4, 22, -2, -24, 4, -19],\n [16, -11, -12, ... | 3 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, 2, -20, 13, -7, -9, -20, -11, -4],\n [0, 8, -21, -3, -21, 18, -16, -22, -14],\n [0, 0, 4, 24, -2, -21, -13, 10, -17],\n [0, 0, 0, -2, 17, -22, 15, 0, 18],\n [0, 0, 0... | -68 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, -10, -10, 18, 15, -12, 18, 0, 1],\n [22, -9, 18, -22, -9, 7, 4, -5, -9],\n [-15, 25, 4, -8, -6, 8, 15, 2, -17],\n [18, 5, 19, -10, 5, 3, -13... | -302 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[18, 8, -8, 11, -15, -2, 0, 2, 6],\n [8, 19, 10, 16, -9, -2, 15, 10, -3],\n [-8, 10, -11, 12, 0, 6, 13, 11, 6],\n [11, 16, 12, -8, 16, 6, 4, -18, 10],\n [-15, -9, 0,... | 755 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, 6, -14, -15, -16, 9, 18, -22, 16],\n [-24, 18, 2, 17, 20, 21, -12, 18, 3],\n [-24, 8, 7, -6, 21, 4, 16, 0, -6],\n [-25, -25, -1, 7, -3, -15, 18, -11, -12],\n [-25, 7... | -78 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -19, 18, -6, -23, 10, 17, 18, 25],\n [-7, 4, -15, -13, 7, 12, 22, -24, 20],\n [-3, 24, 23, -6, 24, 25, 4, -11, -24],\n [4, -1, -22, -2... | 1314 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, 15, -17, 18, 4, -23, 8, 7, 1],\n [-17, -13, 4, -10, 25, 16, 0, -21, 20],\n [1, -11, 2, -23, 15, -25, -25, 25, -20],\n [-15, 24, 20, -10, 7, -2, 6, -16, -1],\n [-16,... | 28 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[18, -11, 1, -7, -11, 19, -19, 17, 14],\n [0, -2, -3, -15, -2, -21, 13, 22, 4],\n [0, 0, 3... | -9970 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[-5, 15, 25, 4, -1, -2, -15, 9, -22],\n [11, 10, -13, -17, 2, 20, -10, -20, 1],\n [-16, -3, -5, 0, 19, -23, 17, 9, -19],\n [1, 16, 7, -22, 0, -18, -6, -9, -21],\n [23, -17, -18, -19, 11, 10, -23, -18, -21],\n ... | 46 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, -9, -4, -8, -16, -2, -6, -14, -22],\n [16, -21, 0, 10, -10, -21, 0, -7, -20],\n [-2, 5, 5, -19, -16, 13, -4, -12, 2],\n [16, -4, 6, -15, -12, 5, 18, -22, 19],\... | 2641 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 1, -24, 2, -15, 20, -5, 16, 6],\n [0, -19, -4, -12, -13, -5, -4, 8, -16],\n [0, 0, -2, -23, 5, 17, 25, 15, -13],\n [0, 0, 0, 8, 15, -8, 10, 0, 7],... | 10297 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[14, 10, 0, 4, 9, 0, 4, 8, 8],\n [10, 2, -10, 4, -20, 6, 4, 10, -8],\n [0, -10, -11, 0, -2, 20, 10, 2, -10],\n [4, 4, 0, -1, -... | -43 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[23, -21, -21, -1, -2, 11, 5, 20, 8],\n [15, -12, 1, 21, -22, -3, 12, 20, -21],\n [1, 17, -12, -19, 20, 19, -8, 6, -24],\n [15, 17, -6, 3, 17, 0, 12, -2... | 391 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/450 * A where A =\n[[15, 22, -25, 23, 16, -6, -21, 14, 19],\n [-5, -21, -22, -18, -1, -19, 11, 16, 6],\n [-9, 2, -20, 16, 22, 16, 10, -24, 5],\n [-25, -23, -13, 5, 3, 18, 7, -16, 12],\n [-17, -25, 18, 11, 6, 7, -24, 20, -24]... | 777 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/450 * A where A =\n[[20, -11, -2, 22, -18, 2, 16, 20, -9],\n [9, 5, -22, 22, -12, -1, 20, 22, 14],\n [24, -19, 5, 9, 12, -6, -10, -4, 10],\n [-7, -24, -22, 8, -19, 21, 23, -12, 17],\n [6, -9, 11, -12, -9, 6, -24, 13, -22],\n [14, 4, 4, 7, 16, ... | 29 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (8, 5) of the inverse. Round your answer to the nearest integer:\n[[11, 0, -14, 6, -5, -4, 14, 0, -10],\n [0, -19, 7, -18, 18, 6, -12, 17, -4],\n [-14, 7, -18, -8, -2, -8, 10, 0, -18],\n [6, -18, -8, 9, 2, -2, -7, -20, ... | -31 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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[[1, -7, -23, -17, 13, -24, -17, -20, 12],\n [2, 22, 8, 3, 22, -23, -10, 18, 9],\n [-15, 17... | 43 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, 8, 16, -18, -8, 5, 4, 19, -14],\n [8, -3, 18, -5, 10, -9, 9, 4, 11],\n [16, 18, -23, 0, -6, 18, -13, 18, 4],\n [-18, -5, 0, 9, -6, -4, 0, 8, 8],\n [-8, 10, -6, -6, 4... | 184 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, 7, 4, 4, 19, 12, 18, 0, 10],\n [7, -20, -9, 8, 0, -17, 14, 18, -19],\n [4, -9, -10, -1, -18, -5, 4, 4, -4],\n [4, 8, -1, -24, 18, 0, -3, 0, 22],\n [19, 0, -18, 18, 13, 16, -4, 18, ... | 15 | MATH |
[
{
"content": "Find the value at position (9, 4) of the inverse of matrix 1/450 * A where A =\n[[10, -8, 5, 23, 9, 15, 2, 0, -20],\n [8, 2, 18, 21, -17, 3, 8, -14, -10],\n [-19, 5, 7, -19, -23, -6, -21, -23, 21],\n [12, -11, 9, -3, 7, -24, 10, -5, -12],\n [-12, 16, -15, -22, 21, 4, 10, -6, -10],\n [8, 19, -18, 1... | 17 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[19, 23, -21, 7, -4, 21, 16, -1, 17],\n [0, 3, 19, 4, 22, 25, 4, 18, 20],\n [0, 0, 2, -16, -22, 7, -9, -15, -19],\n [0, 0, 0, 15, -16, 0, -20, -... | 485 | MATH |
[
{
"content": "Find the value at position (8, 9) of the inverse of matrix 1/450 * A where A =\n[[-17, 2, 10, -3, 8, 10, 12, 6, -6],\n [2, -1, 0, 14, 3, -16, -16, -3, -3],\n [10, 0, 19, -15, -6, -10, 4, 0, -8],\n [-3, 14, -15, 25, 4, 4, 6, -22, -2],\n [8, 3, -6, 4, 4, 8, 14, 4, -4],\n [10, -16, -10, 4, 8, -25, -2... | -6 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[20, 16, -18, -11, -10, -18, 10, 6, -9],\n [0, -4, 6, -15, 19, -20, -4, -12, 2],\n [0, 0, 1, -25, -16, 7, -10, 13, -20],\n [0, 0, 0, 10, -3, -10, -25, 4... | 675 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/450 * A where A =\n[[1, 12, -2, -4, 6, 18, -7, -12, 4],\n [12, 22, -4, -10, -14, 4, 8, 24, -16],\n [-2, -4, -6, 14, 2, 0, -10, 4, -6],\n [-4, -10, 14, -9, 6, 9, 8, -4, 16],\n [6, -14, 2, 6, -2, -17, 13, -4, 1],\n [18, 4, 0, 9, -1... | 144 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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, -21, -24, 25, -12, 3, 15, -25, -13],\n [0, 6, 8, -12, 12, 12, 24, 25, 15],\n [0, 0, -20, 3, 11, -7, -2... | -117 | MATH |
[
{
"content": "Find the inverse of 1/450 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[-20, 17, 19, -8, -12, -6, -15, 11, 14],\n [-22, 18, -20, -3, -18, 4, 10, 16, -15],\n [21, -21, -23, -11, -24, -24, -18, 20, 4],\n [15, -21, 4, 18, -16,... | 1225 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/450 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, -7, 15, -3, -6, -20, 17, -2, 21],\n [-4, -20, -2, 16, -4, -8, -10, 10, -13],\n [11, -2, -7, 24, -6, 1, -9, -10, -25],\... | -6550 | MATH |
[
{
"content": "For the inverse of 1/450 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -20, 10, 8, 23, -18, 11, -16, -10],\n [0, -7, -19, -24, 19, -3, 5, -22, -10],\n [0, 0, -5, 2, 20, -14, -13, 14, -9],\n [0, 0, 0, -13, 8, 23, -20, -14, 3],\n [0, 0, 0,... | -311 | MATH |
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