messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 25, 19, -1, -23, -12, -11, 1, 24],\n [0, 7, 19, 15, -17, -13, -5, 17, -12],\n [-23, -12, 7, -25, -18, 20, -11, -6, -3],\n [-25, 4, 13, 6, 8, -11, 20, -7, -20],\n [-13, -22, -20, 2... | 890 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-24, 0, -10, 1, -1, 16, 8, 0, 6],\n [0, -13, 0, -15, 2, 19, 12, 23, -2],\n [-10, 0, -4, 4, -16, 2, 0, -8, -16],\n [1, -15, 4, 15, 6, -20, -8, 8, -3],\n [-1, 2, -16, 6, -20, -6, -2, -4, -2],\n [16, 19, 2, -20, -6, -18, 1, -18, -3],\n [8, 12, 0, -8, -2, 1, 3, 8, 5],... | 628 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -4, 10, 15, -4, -2, 2, 12, -18],\n [-4, 13, -13, 11, -2, -6, 8, 10, 16],\n [10, -13, 3, -3, 15, 10, -10, 9, -12],\n [15, 11, -3, 11, -16, -14, 20, 19, 14],\n [-4, -2, 15, -16, -7, -18, -4, 21, 8],\n [-2, -6, 10, -14, -18, -18, 0, 6, 20],\n [2, 8, -10, 20, -4, ... | 630 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[17, -22, -16, -8, 10, 24, -17, 11, 24],\n [0, 7, 8, 2, 20, -15, -2, 17, -11],\n [0, 0, 9, -5, -1, -21, 25, -12, -5],\n [0, 0, 0, 13, -17, 2, 13, 0, -18],\n [0, 0, 0, 0, 9, 21, 25, -2, -20],\... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, -14, 4, 6, 4, -3, 4, -11, -6],\n [-14, 20, -2, 0, -1, -2, 12, 3, 6],\n [4, -2, 0, -8, -8, -14, -2, 18, -10],\n [6, 0, -8, 11, -17, -4, 8, -6, 3],\n [4, -1, -8, -17, -18, 16, -6, 0, 6],\n [-3, -2, -14, -4, 16, -17, -14, -4, -11],\n [4, 12, -2, 8, -6, -14, 25, 8,... | 172 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 23, -20, -25, 10, 23, -6, -15, -16],\n [0, -4, 22, -10, 14, -21, -13, 13, -17],\n [0, 0, -17, 2, 25, 18, 9, 19, -2],\n [0, 0, 0, -21, 5, 14, -23, 21, 10],\n [0, 0, 0, 0, -1, 7, -23, 8, 21],\n [0, 0, 0, 0, 0, -12, 9, 21, 25],\n [0, 0, 0, 0, 0, 0, -8, 2... | 296 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -24, 23, -25, 25, 11, 17, -22, 11],\n [-21, -20, -25, 8, -17, 9, -21, -14, 21],\n [1, 18, 24, 22, 9, 7, 24, -7, -16],\n [22, -24, -13, 11, 3, 8, -16, -21, 5],\n [3, 23, 6, 13, -21, 16, 8... | 403 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -14, -20, 4, -12, 10, -6, 16, 5],\n [-14, 16, 10, -20, -10, -8, 2, -2, -6],\n [-20, 10, 7, -2, -3, -2, 12, 4, -24],\n [4, -20, -2, -18, 0, -6, -2, 6, 3],\n [-12, -10, -3, 0, -10, -18, -5, 22, -1],\n [10, -8, -2, -6, -18, -14, -16, 16, 0],\n [-6, 2, 12, -2, -5, ... | 640 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-21, -14, 2, 1, 24, -1, -23, -18, 17],\n [0, 14, -13, 14, 19, -17, -22, 24, -16],\n [0, 0, -16, -13, -16, -17, 2, 23, 2],\n [0, 0, 0, 12, 19, 1, 23, -17, -20],\n [0, 0, 0, 0, 3, 6, 25, -1, 11],\n [0, 0, 0, 0, 0, 25, -15, 15, 17],\n [0, 0, 0, 0, 0, 0, 5, 18, 0],\n ... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -5, 6, -15, 18, -11, 19, -16, 1],\n [0, -19, 9, 19, 1, 0, 25, 14, -6],\n [0, 0, 1, -20, -23, 15, -12, 21, -14],\n [0, 0, 0, 23, -11, -10, -7, -22, -17],\n [0, 0, 0, 0, 16, -2, 2, 0, -6],\n [0, 0, 0, 0, 0, 15, -21, 8, 17],\n [0, 0, 0, 0, 0, 0, 1, 17, 16... | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, -19, 6, -3, -4, -14, -13, -14, -16],\n [0, -7, 15, 7, 10, 6, 1, -17, -18],\n [0, 0, 3, 17, -4, -1, -21, 19, -16],\n [0, 0, 0, 4, 23, 19, -15, -20, -9],\n [0, 0, 0, 0, -2, -6, 11, 24, -4],\n [0, 0, 0, 0, 0, -23, -3, -10, 15],\n [0, 0, 0, 0, 0, 0, -18, 5, 21],\n... | 568 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 8, -14, -8, -20, -4, -6, -20, 11],\n [8, -14, 13, 20, -3, 4, 8, 13, -18],\n [-14, 13, -1, 16, -10, 9, -8, 2, -4],\n [-8, 20, 16, 24, 10, 10, 6, 12, -4],\n [-20, -3, -10, 10, 23, -20, -7, -20, 14],\n [-4, 4, 9, 10, -20, -20, -15, 15, -24],\n [-6, 8, -8, 6, -7, ... | 256 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 21, 0, 14, 13, 3, 8, 2, -11],\n [-7, -16, 11, 1, 23, -21, 15, -21, -15],\n [1, -4, 24, 23, 21, 1, 6, 9, 7],\n [8, -7, 17, -7, 11, -16, 1, -20, 14],\n [16, -2, -11, 4, 25, 20, 0, -22, 3],\n [-21, -7, 2, -17, -14, -14, 7, -6, 7],\n [-18, -21, 16, -15, 10,... | 397 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -6, -3, 8, -2, -4, 11, 0, 10],\n [-6, -6, 9, 14, -5, -10, 13, -5, 0],\n [-3, 9, -15, -12, -14, 6, 7, -12, 9],\n [8, 14, -12, -20, -2, 12, 10, -15, 0],\n [-2, -5, -14, -2, 5, -8, 13, 4, 16... | 461 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 8, 9, -24, 13, 23, -15, 20, -9],\n [25, 17, -9, 14, 25, 2, 20, 1, 24],\n [14, -2, -10, 23, -9, 25, 13, -22, 1],\n [21, -1, -18, -12, -15, 7, 2, 19, -7],\n [2, -17, -5, -17, 7, 8, -22, -24, 18],\n [4, -13, -18, -12, 11, 22, 16, -3, -14],\n [-20, 21, 19,... | 427 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 10, -25, -16, 16, -5, 6, -11, -12],\n [0, -15, -9, 5, 23, 20, 11, 10, 21],\n [0, 0, -7, -14, 3, 22, -4, -4, -3],\n [0, 0, 0, 6, 9, -18, 6, -18, 8],\n [0, 0, 0, 0, -25, -4, -5, -11, -1],\n [0, 0, 0, 0, 0, 3, -5, 24, -13],\n [0, 0, 0, 0, 0, 0, 3, -24, -14],\n [0,... | 750 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -17, 3, -21, -12, 15, -12, -4, 20],\n [0, -19, 8, -16, 13, 14, 21, -21, 9],\n [0, 0, -3, -23, -7, -18, -1, 16, -7],\n [0, 0, 0, -12, -21, 22, -6, 17, -19],\n [0, 0, 0, 0, 11, -16, 21, -25, 21],\n [0, 0, 0, 0, 0, -22, 14, 18, 21],\n [0, 0, 0, 0, 0, 0, 16, 8, 8],... | 280 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -12, -2, 0, 0, 14, -3, 16, -14],\n [0, -8, 8, -20, 18, 23, 8, 13, -18],\n [0, 0, -16, 19, -5, -16, 14, 4, 16],\n [0, 0, 0, -19, -25, -2, -18, 12, 16],\n [0, 0, 0, 0, -3, -22, 24, 21, -11],\n [0, 0, 0, 0, 0, 24, 12, 13, 2],\n [0, 0, 0, 0, 0, 0, -25, 25, -10],\n ... | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -5, -21, 2, 2, 12, 3, 15, 0],\n [-9, 3, 20, 4, -21, 17, 14, -6, -18],\n [16, -9, -4, 5, -7, 19, 15, -18, 17],\n [19, 1, -7, 7, 20, 16, -10, -18, 15],\n [-8, 16, -18, -12, 24, -24, -3, -16, 11],\n [8, -9, 6, -22, -12, 14, -22, -10, -22],\n [21, -10, -16... | 831 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -1, 18, 8, -10, 7, -16, 15, -12],\n [-1, 13, 8, 10, 4, -1, 6, -10, 8],\n [18, 8, 10, -8, -1, 4, 6, 2, -10],\n [8, 10, -8, -14, 14, -22, -2, 15, -6],\n [-10, 4, -1, 14, 6, 5, -2, 2, -12],... | 148 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 22, 16, 11, -5, -12, -17, -7, -16],\n [0, 6, -9, 24, 4, -22, 20, 5, -19],\n [0, 0, 6, 5, 22, 21, -8, -1, 24],\n [0, 0, 0, 15, -4, -19, 1, 23, 0],\n [0, 0, 0, 0, -17, -23, -12, 16, -12],\n... | 840 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-15, 13, 23, -16, 22, -10, 8, -3, -12],\n [0, 2, -25, -7, 12, 13, 25, 8, -1],\n [0, 0, -10, 0, -2, 6, 7, -8, -22],\n [0, 0, 0, 15, 14, -15, -13, 22, -6],\n [0, 0, 0, 0, 1, -7, -16, 18, -11],\n [0, 0, 0, 0, 0, -11, 12, 8, 3],\n [0, 0, 0, 0, 0, 0, 19, -2, 19... | 500 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-22, 2, 7, -15, -11, 10, 6, 5, 10],\n [2, -3, 6, 10, -1, -18, -2, 6, 6],\n [7, 6, -1, 8, 10, 10, 10, 15, -3],\n [-15, 10, 8, -20, -1, -7, 6, 12, -8],\n [-11, -1, 10, -1, 25, -2, 2, -10... | 383 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 14, 19, -24, 15, 7, -6, -13, -16],\n [0, 13, 15, 25, 17, 19, 13, 25, -9],\n [0, 0, 9, 13, 24, -10, 23, 24, 10],\n [0, 0, 0, 19, -3, 11, -8, -25, -8],\n [0, 0, 0, 0, -10, 0, 12, -25, 3],\n [0, 0, 0, 0, 0, -1, -24, -13, 1],\n [0, 0, 0, 0, 0, 0, 24, 15, -16],\n [... | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-25, 6, -23, 21, -23, 15, -18, 23, -20],\n [3, -10, 7, 19, 22, 19, 23, -18, -3],\n [11, 2, -12, -4, -2, 5, -10, 19, -10],\n [-15, 20, -21, 7, -2, -19, -25, -3, 5],\n [-17, 5, -7, -4, -... | 70 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -19, 21, -8, -2, 9, 4, 11, -23],\n [0, -12, -19, -25, -18, 4, -24, -22, -11],\n [0, 0, 13, -3, 19, -12, 3, 5, -17],\n [0, 0, 0, 21, 4, 12, 22, -11, 25],\n [0, 0, 0, 0, 3, -15, 25, 1, 0],\n [0, 0, 0, 0, 0, 21, 17, -15, 18],\n [0, 0, 0, 0, 0, 0, -18, 5, 8],\n [0,... | 312 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -14, 7, 21, 23, -5, 3, 4, 21],\n [0, 15, -12, -4, 2, 7, -2, -22, -2],\n [0, 0, -23, -15, 9, -16, 17, 20, -22],\n [0, 0, 0, 13, 0, 13, -8, 11, -13],\n [0, 0, 0, 0, -23, 19, -25, 16,... | 825 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 22, -16, 1, 20, 16, 3, -8, 21],\n [0, 4, -20, 21, -25, -12, -6, -25, 20],\n [0, 0, -19, 10, -8, 16, 10, 12, 3],\n [0, 0, 0, -15, -25, -6, -15, -24, 15],\n [0, 0, 0, 0, -22, -24, 9, -13, ... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 5, -23, 11, -25, 20, 16, -15, 23],\n [0, 5, 13, -17, 1, 11, -9, 8, -20],\n [0, 0, 18, 7, 0, 20, -16, 15, -16],\n [0, 0, 0, -25, 15, -12, 11, 3, 5],\n [0, 0, 0, 0, -4, -11, -3, -12, 25],\... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -17, 4, 14, 3, 17, 16, -6, 6],\n [-17, -24, 10, 4, -2, 1, 3, 6, -6],\n [4, 10, 1, -6, -15, -12, -4, 6, -24],\n [14, 4, -6, 4, 3, -12, -16, 9, -4],\n [3, -2, -15, 3, 19, 2, -14, -18, -7],\n [17, 1, -12, -12, 2, -5, -16, -2, -1],\n [16, 3, -4, -16, -14, -... | 881 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[17, -6, 0, -8, 3, -25, 4, -22, -8],\n [4, 12, 3, 11, -7, -6, -13, 17, -6],\n [-9, 2, -13, 18, -22, 2, 15, -21, -19],\n [-9, 9, 20, 0, -5, -16, -19, 17, 12],\n [9, 20, 13, -13, 17, -21, -18, 23, 13],\n [-19, -19, -14, 18, 9, 12, -9, -19, -9],\n [-5, -21, 0... | 232 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -6, 18, 6, -6, -12, -6, 0, -4],\n [-6, 10, -4, -3, 8, 14, 14, 3, -15],\n [18, -4, 23, 2, 20, 0, -6, 4, -10],\n [6, -3, 2, 6, 4, -20, -12, 2, 9],\n [-6, 8, 20, 4, -1, 2, -4, 6, 24],\... | 345 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 3, 2, 18, -2, 3, -19, 5, 12],\n [-3, 20, 20, -2, -12, 5, -2, -8, 20],\n [11, -22, -1, 18, 12, -19, -6, -16, 6],\n [16, -15, 10, 7, 24, 8, 22, 19, 12],\n [-22, -16, 5, -7, 14, -17, 8, 14, 22],\n [16, 15, -20, -13, 17, 8, 21, 25, 8],\n [8, 5, 12, -24, -24, -4, -... | 476 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 19, -12, -5, -16, -1, -5, -15, -10],\n [19, -2, 1, -2, 2, 2, 6, -10, -4],\n [-12, 1, -4, -16, 12, -16, 14, 5, -3],\n [-5, -2, -16, 10, -20, -6, -4, -8, -1],\n [-16, 2, 12, -20, 17, 11, 4, 0, 0],\n [-1, 2, -16, -6, 11, 6, 8, -16, 1],\n [-5, 6, 14, -4, ... | 46 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -24, 12, -9, -23, -25, -4, -8, 8],\n [-3, 1, -21, -21, -25, -4, -22, -5, 18],\n [8, 11, -18, 3, -22, 3, -5, 16, -13],\n [-25, 16, -6, 21, -9, -24, 25, 4, -19],\n [-21, -20, 21, -9, ... | 318 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 1, -11, 4, 14, -9, -16, 1, -25],\n [23, -14, -19, 22, 19, -19, 1, -12, -10],\n [1, 17, 7, -10, -19, -10, 22, -11, 13],\n [2, -15, -11, 11, -17, -24, -4, -11, 18],\n [9, -11, -11, -4, 9, 9, 23, -3, -6],\n [-14, -1, 6, -19, -8, -9, -15, -23, 5],\n [-16,... | 219 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, 4, -2, -10, 2, 9, -5, 7, 4],\n [4, 24, 2, 17, 4, 22, -12, -10, -4],\n [-2, 2, 11, -6, 8, 7, 13, -5, -17],\n [-10, 17, -6, -12, 4, 20, 8, -4, 5],\n [2, 4, 8, 4, -15, -16, -2, 21, -20],\n [9, 22, 7, 20, -16, 7, -5, 8, 20],\n [-5, -12, 13, 8, -2, -5, -5... | 151 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -22, 20, 16, 17, -11, 9, -16, 13],\n [0, -22, -21, -23, 18, -15, 24, 24, 15],\n [0, 0, 22, -25, 4, -17, -16, 18, 6],\n [0, 0, 0, -15, 4, 18, 9, -24, 25],\n [0, 0, 0, 0, 5, 20, -17, -20, -21],\n [0, 0, 0, 0, 0, 13, -5, -12, 7],\n [0, 0, 0, 0, 0, 0, -10, -23, -... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -2, -17, 18, 24, -13, 15, 8, 8],\n [-17, 22, -21, -25, 9, -5, -6, 17, -14],\n [9, -11, -18, -12, 1, 2, 4, 5, -8],\n [0, -22, -16, -16, 19, -8, 13, 14, 16],\n [16, -14, -19, 12, 5, 8, 8, 3, 22],\n [-10, 20, 0, -6, -12, 4, -13, 24, -11],\n [-1, -8, -20, 5, -3, ... | 741 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-16, -5, -8, 8, 1, -6, -7, 12, -14],\n [-5, -11, 4, -6, 4, 2, -3, 0, -6],\n [-8, 4, -20, -1, -5, -2, -9, -8, 3],\n [8, -6, -1, 19, -8, 4, -9, -15, -11],\n [1, 4, -5, -8, -6, 10, 10, 13, -6],\n [-6, 2, -2, 4, 10, 6, -2, 14, -4],\n [-7, -3, -9, -9, 10, -2, -6, -6, 0... | 240 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-24, 17, -23, 23, 3, 14, 2, -23, -3],\n [0, -20, 18, 19, -19, 24, 15, -5, -16],\n [0, 0, -10, -11, -23, -19, 17, 6, -1],\n [0, 0, 0, 16, -15, -20, 16, 10, -20],\n [0, 0, 0, 0, -23, -15, -19, -1, -16],\n [0, 0, 0, 0, 0, 21, -20, 23, -12],\n [0, 0, 0, 0, 0, 0, -22, ... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 5, -20, 4, 6, 0, 0, 14, -7],\n [-9, -25, 21, 3, 0, -11, 14, 8, 8],\n [-3, -20, 7, -13, 17, 3, -3, 11, 4],\n [10, 24, 0, 16, -25, -1, 19, 1, 20],\n [9, 1, -23, 22, -8, -5, -11, 16, 7],\n [-24, -5, 22, -20, 3, 1, 0, -13, 22],\n [-6, -22, -24, 25, 22, 25, ... | 392 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 6, 0, -18, 0, -25, 9, 6, -23],\n [12, -6, 4, 7, -25, 23, 17, 4, -5],\n [-23, -8, 5, -11, 8, 10, -13, 3, 7],\n [25, 25, -3, -20, 6, -12, 12, 14, 7],\n [-20, 25, 10, 9, -22, -4, 12,... | 412 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 3, 25, -10, 9, -15, -3, -18, -24],\n [25, -11, -22, -4, -14, -13, -1, 25, -12],\n [-21, -8, -19, -6, -4, 10, -12, 6, 6],\n [13, -9, 11, 23, -13, 14, -13, -6, 23],\n [25, 11, 21, -8, -21, -20, -5, -24, -14],\n [7, 14, 9, -3, 7, -12, -14, 5, 8],\n [12, 2... | 47 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -21, -18, -3, -19, 12, -10, 2, -12],\n [0, -1, 21, -25, -8, 6, 25, 10, -24],\n [0, 0, -19, 15, -22, -3, -1, -10, -20],\n [0, 0, 0, 25, 2, 17, -17, 8, 14],\n [0, 0, 0, 0, 5, 12, -20, 20, 8],\n [0, 0, 0, 0, 0, -14, 21, -15, -19],\n [0, 0, 0, 0, 0, 0, -10, -11, -... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 25, 6, -12, 17, -13, 5, 0, -5],\n [17, 7, 8, 24, -8, 2, -9, -1, -19],\n [3, 8, -4, 7, -16, 6, -22, 23, -6],\n [9, 20, 9, 4, 25, -7, 7, 24, -2],\n [17, 0, 17, -4, 17, 0, 0, -10, 18],\n [-6, -5, -3, -14, -15, 11, 23, 11, -7],\n [12, 3, 8, -1, -18, 5, 17,... | 592 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, -13, -5, 16, -9, -3, -7, 4, 16],\n [19, 13, -21, -15, 7, -1, -19, 15, -15],\n [20, -8, -9, -1, -23, -7, 3, -21, -13],\n [-21, -3, -3, 2, -23, -14, 1, 21, 22],\n [-20, -22, -8, -11, -16, 18, -19, -19, 9],\n [16, 1, -24, 25, 4, 1, 9, -23, -4],\n [0, -21, 22, -7... | 531 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-25, 12, -25, 2, 1, -20, -20, -15, 20],\n [0, 22, -24, 5, -4, 4, -22, -18, 20],\n [0, 0, 20, 0, 14, 4, -7, -1, 22],\n [0, 0, 0, 24, -18, 12, 7, -22, -3],\n [0, 0, 0, 0, 3, -4, 1, -12, 10],\n... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[21, -6, 12, -16, -10, 1, -10, 2, 6],\n [-6, 11, -14, -12, 2, -8, -12, -18, 10],\n [12, -14, -18, 6, 17, -10, -10, -12, 10],\n [-16, -12, 6, -10, 7, -14, 8, 2, 20],\n [-10, 2, 17, 7, 16, 16, 0, -12, -6],\n [1, -8, -10, -14, 16, 9, -13, -10, -3],\n [-10, -12, -10, 8... | 376 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -14, -4, 5, 14, -2, -23, 3, -11],\n [0, 4, -15, 3, 3, 10, 1, -14, 5],\n [0, 0, 9, 0, -15, -25, -18, 11, 6],\n [0, 0, 0, -19, 14, 5, 5, -7, 14],\n [0, 0, 0, 0, -13, -14, -24, -7, -14],\n [0, 0, 0, 0, 0, -1, 2, -18, 9],\n [0, 0, 0, 0, 0, 0, -25, -8, -15],\n [0, 0... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-20, 17, -5, 9, 22, 2, 21, -13, 17],\n [0, 25, -14, 2, -23, 9, -13, 7, 4],\n [0, 0, -7, 12, 3, 15, -1, 20, 12],\n [0, 0, 0, -18, 14, 5, 15, -8, 6],\n [0, 0, 0, 0, -18, 13, -21, -7, 18],\n [0, 0, 0, 0, 0, -20, 7, 20, 10],\n [0, 0, 0, 0, 0, 0, 18, -3, -3],\n... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 7, 15, -14, -17, -10, -17, -10, 14],\n [0, 8, 20, -18, -23, 13, -11, -6, 4],\n [0, 0, -1, -20, 2, -12, -5, 13, -10],\n [0, 0, 0, -19, 2, 19, -22, 18, -24],\n [0, 0, 0, 0, -5, -5, -20, -5, -16],\n [0, 0, 0, 0, 0, 2, -1, -20, -22],\n [0, 0, 0, 0, 0, 0, 18, -4, 6... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-24, -8, 15, -22, 1, 1, 16, -15, 11],\n [8, 6, 18, 13, 8, 3, -3, -6, 1],\n [4, -25, -17, 24, 6, -15, -16, -18, -3],\n [1, -24, -12, -23, -2, 15, 11, 11, 4],\n [-1, -16, 21, 17, -12, 13... | 887 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[20, -10, 16, -20, 4, -14, -12, 4, 16],\n [-10, 17, 0, -7, 4, 12, -12, 24, 5],\n [16, 0, -1, -20, -8, 6, 14, 4, 0],\n [-20, -7, -20, 15, 0, 0, 6, 6, 3],\n [4, 4, -8, 0, -20, -4, -14, 5, -6],\... | 576 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 7, -22, 10, -17, -1, -15, 11, 9],\n [0, 9, 19, 12, 10, 13, -3, 8, 3],\n [0, 0, -2, 22, -11, -25, 23, -6, -1],\n [0, 0, 0, 2, -16, -4, 21, -19, -20],\n [0, 0, 0, 0, -14, -16, -11, -19, 9],\n [0, 0, 0, 0, 0, -1, 25, -24, 5],\n [0, 0, 0, 0, 0, 0, -15, -1... | 120 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-21, 14, 0, 4, 2, -19, -4, -4, -6],\n [14, -16, -4, 8, -17, -5, 8, 6, -1],\n [0, -4, -18, 5, 6, -4, -6, 6, -9],\n [4, 8, 5, 0, 9, -4, 4, 0, 0],\n [2, -17, 6, 9, -19, -10, 15, 10, -12],\n [-19, -5, -4, -4, -10, -9, 0, -1, 18],\n [-4, 8, -6, 4, 15, 0, -11, ... | 765 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 17, -16, -9, 16, -24, -7, 20, 4],\n [-21, 15, 5, -25, -21, 8, 17, -4, 20],\n [-22, 21, -14, -23, -7, -13, -13, 15, 6],\n [18, -18, 16, -24, -7, -25, -9, -20, -14],\n [-4, 19, 8, -19, -24... | 914 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, 0, -5, 19, -18, -11, 19, 2, -8],\n [0, -1, -24, -12, -25, -7, 10, -5, 3],\n [0, 0, -1, -18, 6, 15, -6, 1, 22],\n [0, 0, 0, -23, -24, 24, -21, 21, 12],\n [0, 0, 0, 0, -9, -13, -9, 3, -15],\n [0, 0, 0, 0, 0, -15, 20, -11, -23],\n [0, 0, 0, 0, 0, 0, -8, -... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[16, -5, 21, -13, 21, 16, -2, -19, -8],\n [0, -5, 3, -16, -14, -12, 17, -10, -1],\n [0, 0, -7, -2, 5, 7, 8, 15, 5],\n [0, 0, 0, -1, -15, 4, 15, 10, -2],\n [0, 0, 0, 0, -25, -8, 5, -18, -19],\n [0, 0, 0, 0, 0, -17, -20, 3, -11],\n [0, 0, 0, 0, 0, 0, 15, 14, 10],\n [... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 16, -21, 1, 25, -20, 22, -3, -20],\n [0, 2, 12, 9, 6, -24, -20, -5, 15],\n [0, 0, -7, -24, -14, -11, 6, 2, -17],\n [0, 0, 0, -1, 15, -16, -23, 12, 25],\n [0, 0, 0, 0, -16, -22, -17, -12, 10],\n [0, 0, 0, 0, 0, 23, -22, 16, 25],\n [0, 0, 0, 0, 0, 0, 24,... | 552 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -15, 25, 17, 4, -23, -5, -9, -8],\n [-17, 15, 5, -15, 19, -16, -6, -10, 17],\n [-17, -9, -19, -1, -7, -1, 20, -2, -18],\n [24, 1, 4, -18, 7, -10, -17, -2, 11],\n [-24, -2, -13, 21,... | 517 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[17, 14, 6, 13, 14, 12, 21, 10, 0],\n [-12, 15, 18, -14, 14, 1, 14, -6, 9],\n [4, -24, 5, 25, 15, 10, 3, 23, -14],\n [15, -4, -9, -11, 9, 25, 7, -1, -23],\n [14, 16, -9, -14, 5, -19, -25, 23,... | 979 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-17, 0, 0, 4, 14, -4, 14, 14, 8],\n [0, -15, -10, 12, -8, 6, -8, 6, 6],\n [0, -10, 16, 4, -2, -5, 0, -20, -2],\n [4, 12, 4, 8, 11, 11, -3, -6, 0],\n [14, -8, -2, 11, 13, -4, -2, 8, -5],\n [-4, 6, -5, 11, -4, -5, 0, 10, 0],\n [14, -8, 0, -3, -2, 0, 6, 8, 22... | 904 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[18, -7, -19, -3, 8, 21, -17, 3, 10],\n [16, -23, 8, 16, 12, 2, -9, -20, -18],\n [11, 4, -15, -21, -20, 24, -9, -12, 7],\n [-13, 23, -1, 14, 8, -9, 24, 25, -8],\n [15, 5, 18, -1, -24, -1, -6,... | 996 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -24, 3, 7, -19, 8, -20, -21, -24],\n [-10, 9, -25, 25, 16, -14, 21, 19, 11],\n [-22, -11, 4, 3, -3, -5, 8, 15, -21],\n [-14, 15, -20, -11, -19, 10, 4, -10, 2],\n [-22, 19, -17, 11, 6, 5, 13, 24, 15],\n [0, 7, 7, -4, 10, -22, -12, 19, -25],\n [-17, -12... | 506 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[17, 14, -11, -23, -3, -19, -22, -21, 6],\n [-14, -2, 22, -7, -1, -5, 24, 23, 14],\n [-14, 12, -25, -9, -25, 10, -14, 6, 20],\n [-6, -4, 25, 2, -3, -11, 17, 14, -13],\n [13, -16, -13, 1, -19, 15, -16, 13, 19],\n [-8, 3, 13, 8, -16, 25, -17, -18, 0],\n [-24,... | 550 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, 14, -12, 8, 0, 8, 4, -2, -4],\n [14, -18, 14, -13, -12, -6, 10, -6, -5],\n [-12, 14, 19, -15, 8, 2, 15, -14, 8],\n [8, -13, -15, 15, -17, 2, -8, -6, 7],\n [0, -12, 8, -17, 16, 6, -2, 8, -8],\n [8, -6, 2, 2, 6, 15, 10, 18, 0],\n [4, 10, 15, -8, -2, 10, 23, -10... | 504 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-16, -21, -19, 0, 21, 5, -2, 10, -9],\n [0, -25, -12, -14, -10, 16, 3, 6, 6],\n [0, 0, -18, -6, -2, -16, -7, 23, -2],\n [0, 0, 0, 23, 24, -6, 3, 9, -22],\n [0, 0, 0, 0, 15, 15, -6, -7, -22],\n [0, 0, 0, 0, 0, 14, -5, -23, 10],\n [0, 0, 0, 0, 0, 0, 2, 9, -... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[17, 10, 9, 9, -20, 18, 6, 16, 16],\n [10, 23, 6, 4, -12, -10, 10, 13, -13],\n [9, 6, -13, -12, 20, 2, 0, -11, -16],\n [9, 4, -12, 4, 6, 2, 6, -2, -10],\n [-20, -12, 20, 6, -18, 16, -10, -4, 2],\n [18, -10, 2, 2, 16, 5, 0, -8, -6],\n [6, 10, 0, 6, -10, 0, ... | 784 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -15, 20, 23, 2, 24, 16, 14, -8],\n [0, 16, 1, -10, -4, -25, -2, -20, -9],\n [0, 0, 1, 20, -3, 3, -4, -13, -20],\n [0, 0, 0, 4, 7, -17, 20, -19, -5],\n [0, 0, 0, 0, -8, -4, -18, -3, ... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 12, -18, 1, -4, 9, 10, 10, -4],\n [12, 4, 8, 12, 15, 14, 2, 4, 16],\n [-18, 8, 9, -8, -1, 14, 3, -6, -4],\n [1, 12, -8, 5, 14, -1, 4, 0, 2],\n [-4, 15, -1, 14, 25, -16, -12, 4, 8],\n [9,... | 696 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[24, 13, -2, 2, 10, -15, 2, 1, -1],\n [13, -6, 5, -11, 2, 18, 9, 16, -9],\n [-2, 5, -24, -20, -1, 1, -2, 8, 7],\n [2, -11, -20, 4, 2, -1, -17, -8, -10],\n [10, 2, -1, 2, -21, 3, 4, 0, 4],\n [-15, 18, 1, -1, 3, 21, 1, -13, 0],\n [2, 9, -2, -17, 4, 1, -10, 0... | 704 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -9, -21, -16, -3, 3, 5, 10, 0],\n [-9, -13, 6, -10, 5, 2, 11, 6, 10],\n [-21, 6, -24, 10, 16, 20, -3, -6, -12],\n [-16, -10, 10, 15, 6, 0, -2, 17, 18],\n [-3, 5, 16, 6, 7, -10, 0, -20, -7],\n [3, 2, 20, 0, -10, 1, 15, 2, 12],\n [5, 11, -3, -2, 0, 15, -20, 2, 6... | 32 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, -18, 15, -24, 11, 18, -18, -19],\n [-15, 23, 21, -11, 7, 13, 20, -7, -13],\n [-13, -12, -25, 11, 7, 9, -21, -16, -9],\n [-12, 8, 11, 23, 8, -7, 18, -16, -10],\n [-4, 11, -22, -3, -14, 11, -8, 5, -24],\n [11, 24, -9, -18, -4, 9, 17, -17, 17],\n [6, 3, -8, -1... | 371 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-19, -3, 2, -10, 3, 18, 0, -25, 1],\n [21, -7, 21, -24, 20, -14, -5, -6, 1],\n [-3, 5, 3, 14, -23, -20, 3, 5, 16],\n [2, 0, -16, 25, 20, 4, -3, 23, -12],\n [17, 22, 22, -14, 10, 11, 25, -2, -21],\n [10, 18, 21, 22, 20, -13, 8, 1, 13],\n [22, 20, -10, 22, 6... | 616 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[24, 6, -5, -16, 22, 8, 8, -12, -12],\n [6, -17, 6, 0, 2, -2, 0, -6, 15],\n [-5, 6, -1, -14, 9, 10, 0, -6, 6],\n [-16, 0, -14, 7, 8, -11, -12, -8, 4],\n [22, 2, 9, 8, 17, 0, -20, 9, -18... | 540 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[19, -6, 0, -2, 15, 10, 2, 0, 2],\n [-6, -19, 14, -19, 9, -6, -8, 16, 2],\n [0, 14, 4, -4, -19, 4, 4, -2, 0],\n [-2, -19, -4, -3, 20, 2, 0, -12, -6],\n [15, 9, -19, 20, 10, -7, -13, -14, -18]... | 572 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -15, 24, 4, 12, 12, 9, -10, -5],\n [0, 18, 21, -10, 19, 2, 15, 4, -2],\n [0, 0, 24, 24, -3, 2, -19, -12, 22],\n [0, 0, 0, 12, -2, 18, 13, -18, -4],\n [0, 0, 0, 0, -3, -15, -13, -13, -18],\n [0, 0, 0, 0, 0, -17, 16, 14, -7],\n [0, 0, 0, 0, 0, 0, 6, 7, 11],\n [... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -15, 17, 9, -6, 16, 22, 7, -14],\n [0, -8, 5, -22, -11, -19, 17, -8, 11],\n [0, 0, -1, -10, -11, -20, -18, 20, -9],\n [0, 0, 0, 5, -22, 17, -7, -11, 22],\n [0, 0, 0, 0, -11, 24, 9, -15, -20],\n [0, 0, 0, 0, 0, -4, -17, -14, 12],\n [0, 0, 0, 0, 0, 0, -21, -11, 1... | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -19, -22, -19, -9, 17, 14, -17, 7],\n [9, -4, -16, -4, 0, 1, 12, 14, 7],\n [1, -9, -19, 22, 13, -23, 5, 1, -21],\n [-17, -7, 0, 6, -14, 24, 25, -20, -16],\n [3, -25, -7, 3, 4, 20, 15, 14, -25],\n [-14, 16, 21, 13, 2, -15, 7, 16, 4],\n [1, 6, 5, -9, -17... | 968 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -14, -2, 12, 9, -2, 2, -14, -1],\n [-14, -16, -2, 16, 0, -6, -6, -9, 2],\n [-2, -2, -13, 2, 10, -3, 0, -9, -6],\n [12, 16, 2, 0, 8, 8, 6, 2, -2],\n [9, 0, 10, 8, -13, 10, 19, 4, -2]... | 88 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, 0, 14, -9, 8, 2, -23, -9, 19],\n [21, 4, -7, 8, 21, -3, 2, -8, -9],\n [-8, 16, 2, 23, 24, -5, 15, -17, -5],\n [14, -22, 7, -13, -1, 7, 25, 10, -3],\n [-16, 22, 19, 3, 10, -3, 14, -13, -10],\n [17, 18, -3, 21, 24, -15, 13, -25, -8],\n [-16, -23, 12, -4,... | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-16, 8, 18, 11, 15, 13, 20, -15, -7],\n [13, 25, -24, -14, 6, -24, -15, -25, -23],\n [16, 14, 21, -8, -5, -12, -21, -12, 3],\n [-14, -3, -5, 12, 14, 13, -25, 0, -1],\n [24, 7, 3, 15, 1... | 169 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -3, -16, 14, -8, 1, -25, -11, -18],\n [0, -4, 4, -11, 1, -19, 20, 7, 2],\n [0, 0, 20, -15, 13, -8, 15, -13, 25],\n [0, 0, 0, 21, 12, 12, -13, 12, 19],\n [0, 0, 0, 0, -17, -5, 15, -19, 6],\n [0, 0, 0, 0, 0, -16, 19, 3, 16],\n [0, 0, 0, 0, 0, 0, 19, -5, ... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[23, 19, -21, 12, -21, 5, 0, 9, 8],\n [-14, -1, -8, 6, -10, 24, -1, 4, -4],\n [-3, -11, -3, -1, 7, 9, -17, -21, 25],\n [-25, -1, -10, 22, -20, 1, 3, 10, 1],\n [21, -22, 11, -7, -2, -23, 12, -... | 386 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -8, 19, 2, 20, 6, 18, -20, -2],\n [-8, 5, 2, 10, -8, 2, 0, 0, 10],\n [19, 2, 11, -10, -4, -16, -3, -22, 8],\n [2, 10, -10, 17, -15, -14, -7, 0, 3],\n [20, -8, -4, -15, 22, 6, 19, -... | 603 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 20, 25, -11, -6, 5, -12, 12, -1],\n [16, -4, 9, 18, 19, 20, -21, 17, 3],\n [8, 2, -22, 15, 0, 2, -22, -2, -12],\n [0, 14, -16, -14, 24, -12, -7, 13, -3],\n [-1, 3, 23, 10, -11, -7, -21, -14, 11],\n [16, -18, 22, 0, 25, 11, -5, -23, -2],\n [10, -9, -22... | 974 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-21, 10, 10, -5, -17, 18, -8, -23, -22],\n [5, -7, -23, -19, -5, -20, -19, -25, 10],\n [9, 5, -6, 18, 15, -7, 24, 0, 22],\n [-15, -8, -11, -13, 23, 14, -12, 14, -12],\n [-18, -16, 4, -15, -1... | 24 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -13, -15, -18, -5, 14, -12, 24, -10],\n [0, 17, -7, -9, -2, -24, 11, 15, 16],\n [0, 0, 2, -14, -14, -19, 21, -3, 18],\n [0, 0, 0, 3, 9, 15, -19, 21, -12],\n [0, 0, 0, 0, 1, -25, -1... | 752 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 12, -14, 13, 14, -3, -25, -22, 18],\n [0, -24, -17, -13, 3, 22, -15, -24, 0],\n [0, 0, -9, 20, -13, 3, 4, -19, 16],\n [0, 0, 0, -19, 8, 17, 21, 25, 23],\n [0, 0, 0, 0, 7, -7, 22, -1... | 880 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 14, -3, 10, 13, -19, -6, 20, -25],\n [19, 22, -7, 4, 11, 11, 25, 11, 7],\n [3, 4, 21, 25, 20, -19, 16, -20, 7],\n [-20, -24, -18, -6, -1, 10, -7, 13, -22],\n [3, 10, 13, 17, -16, 25, 22, -9, 16],\n [-7, 22, -17, 20, 3, -18, -22, -4, 10],\n [-16, -20, -18, 22, ... | 634 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-23, -13, -20, -18, 19, -10, -17, 23, 25],\n [-2, 22, 7, 10, 15, -22, 25, -10, 18],\n [-2, 9, -9, 15, -24, 15, 7, 23, 7],\n [4, 22, 11, 19, 7, -1, -25, 5, -15],\n [22, 6, -5, 21, 10, -14, 18, 5, -11],\n [-15, 21, 10, 4, -13, 25, 3, 23, 20],\n [-3, -3, 0, ... | 376 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, 2, -20, -21, -17, 20, -5, -12, 12],\n [-21, -4, -10, -16, -23, -19, 0, 7, 9],\n [-24, -20, 16, 4, -9, -25, 17, 16, -20],\n [9, -21, -17, 12, -23, 17, 21, 13, 3],\n [1, -15, -21, 0, 21, -8, 17, -5, 16],\n [10, 11, -7, 13, -18, -7, 23, -5, -8],\n [7, 2, -25, 24... | 353 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 19, 19, -12, -6, -6, -10, -15, 11],\n [8, 13, -25, -21, 12, 10, 18, -2, 21],\n [-25, 24, 24, -14, 20, -14, -23, 5, -23],\n [15, 14, 14, -15, -11, 16, -1, 10, 17],\n [1, -9, 19, 12,... | 664 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[16, -3, -18, -6, 19, 2, -12, 6, -25],\n [0, -6, 15, -10, 22, -10, 5, -12, -11],\n [0, 0, 16, 6, 4, -7, 19, -1, 16],\n [0, 0, 0, 6, -13, 17, 15, 13, 12],\n [0, 0, 0, 0, -9, -11, -5, 11, 24],\n [0, 0, 0, 0, 0, -13, -12, -19, 5],\n [0, 0, 0, 0, 0, 0, -19, -21, -23],\... | 176 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, 23, -11, -22, 6, 24, -2, 12],\n [10, 12, 17, -9, -21, 10, -2, 18, 12],\n [-1, -25, -3, 16, 2, -24, 15, -6, 9],\n [-6, -9, -15, 14, -16, 11, -8, 23, 19],\n [-18, -20, -1, 13, -10, 10, ... | 66 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -15, -7, 25, 2, -4, -1, -15, -18],\n [0, 2, -16, -22, -25, -8, 25, 10, 22],\n [0, 0, -17, -13, -12, 22, 14, -4, 24],\n [0, 0, 0, 4, 13, 18, -16, 18, -17],\n [0, 0, 0, 0, 24, 20, -18, -2... | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 20, -14, -12, 19, -9, 11, -23, 6],\n [-17, 5, 24, -22, -20, -9, 0, 15, 1],\n [10, -6, 0, 15, -2, 7, -8, 20, -17],\n [1, -6, -18, -17, -8, 21, -21, -16, 13],\n [20, 23, -24, -3, 2, -22, -... | 56 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 11, 12, -20, 0, -12, -3, -6, 16],\n [11, -23, 6, 8, 0, -10, 11, 4, -6],\n [12, 6, 20, 8, 16, 2, -18, 7, -6],\n [-20, 8, 8, 22, -5, 10, 5, -9, -1],\n [0, 0, 16, -5, -17, -6, 12, -9,... | 222 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 1, -13, -13, 24, 3, 4, 23, 17],\n [0, -21, -8, -6, -11, -23, 20, 15, 23],\n [0, 0, -7, 23, -3, 21, 1, -20, -5],\n [0, 0, 0, 9, 22, -20, 16, -2, 9],\n [0, 0, 0, 0, -8, -23, 17, -3, 24],\n [0, 0, 0, 0, 0, -1, 18, 1, 1],\n [0, 0, 0, 0, 0, 0, 23, -9, -17],\n [0, 0... | 800 | MATH |
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