messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -24, -13, 2, 21, 15, 19, -24, 17],\n [0, -15, 21, 20, 13, -4, 1, 24, -11],\n [0, 0, 3, 13, 0, 9, 11, -6, 6],\n [0, 0, 0, 12, -25, 1, -17, 15, -21],\n [0, 0, 0, 0, 1, 3, -18, -25, -18],\n [0, 0, 0, 0, 0, -7, -9, -20, 25],\n [0, 0, 0, 0, 0, 0, -5, -11, ... | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-22, -21, -25, 13, -12, 5, 9, 7, 7],\n [-15, -23, 18, 18, -19, 2, 21, -16, -5],\n [-18, 22, 10, -24, 25, 13, 21, -3, 21],\n [-20, 20, 11, 10, 12, 24, 4, 24, -7],\n [7, -11, -8, 20, 7, 17, 17, 13, 0],\n [-25, 25, -3, -14, 21, -2, -20, -21, -4],\n [0, 21, -7, 15, 18... | 290 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-19, -15, -16, 0, -20, -11, 16, -12, 1],\n [0, 3, -15, -23, 25, -12, 3, -3, 5],\n [0, 0, 6, -13, -21, 19, -13, -18, -2],\n [0, 0, 0, 15, 17, 21, 23, 3, 15],\n [0, 0, 0, 0, -18, -17, -7... | 440 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -10, 19, -19, -13, -6, -12, 7, -5],\n [0, 8, 18, 19, 10, -24, -25, -14, -23],\n [0, 0, -5, -16, -24, -24, 11, -12, 19],\n [0, 0, 0, -10, 9, -4, 18, -13, -13],\n [0, 0, 0, 0, -7, -14, -6, -8, 11],\n [0, 0, 0, 0, 0, 11, -13, -17, -3],\n [0, 0, 0, 0, 0, 0... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 3, -2, -6, -16, 4, 19, -7, 12],\n [11, 19, -10, 14, -8, -20, -12, 9, -3],\n [13, -19, -13, -6, -16, 1, 0, -19, -5],\n [3, 20, -23, -24, 2, -25, -9, 20, 1],\n [4, 18, 7, 18, -24, -1... | 376 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 16, -23, 14, -6, 17, 10, 8, 15],\n [-21, 17, 11, -25, 6, 18, 4, 4, -3],\n [19, 17, 4, 3, -18, 20, -3, -24, -13],\n [10, -25, -15, -17, -16, 6, -8, -22, 23],\n [11, 17, 5, 11, 4, -21, -20, -25, -8],\n [-19, 2, 14, -22, 6, 18, -4, -6, 24],\n [-5, -15, 2... | 882 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 11, -17, 24, 16, -8, 6, -22, 19],\n [11, 25, 17, 20, -23, 10, -25, 1, 0],\n [-12, 1, -17, 18, 9, -14, 16, -25, -22],\n [17, -6, -12, -6, 1, 7, 23, 14, -20],\n [8, 2, -12, -10, -5, 1, 17, -10, 15],\n [-20, -18, 14, 8, 19, 22, 2, -6, -16],\n [8, 16, 17, 1... | 976 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[23, -6, 11, -2, -15, 14, 19, -7, -14],\n [8, -24, -19, -18, 24, -20, 5, 8, -15],\n [21, 13, 6, -5, -3, -6, -1, -18, 18],\n [-4, 20, 9, 12, 12, 11, -10, 15, -17],\n [-8, -24, 8, -17, 19, -8, -24, 9, -4],\n [1, -23, -6, 25, 3, 4, 12, 6, -8],\n [-17, 24, -15,... | 232 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[21, -10, 16, 21, -2, 6, 16, 14, 8],\n [-10, 13, -2, 4, -14, -3, -22, 18, 16],\n [16, -2, 11, 14, 20, -3, -5, 3, -6],\n [21, 4, 14, -1, 14, 13, -10, 0, 7],\n [-2, -14, 20, 14, -4, -20, ... | 673 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[25, -4, 6, -7, 1, 19, 22, -16, 5],\n [-4, -15, -9, 18, -14, -13, 7, 18, -5],\n [6, -9, -14, 6, -11, -12, 4, 0, 20],\n [-7, 18, 6, 14, 2, 18, 18, 4, 4],\n [1, -14, -11, 2, 9, 1, -4, 5, 9],\n [19, -13, -12, 18, 1, -18, -4, -16, -4],\n [22, 7, 4, 18, -4, -4,... | 974 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-15, 12, 4, -16, 6, 6, -22, -2, -22],\n [12, 22, -6, 18, -5, 16, 20, 12, 10],\n [4, -6, 24, -5, 6, -1, 12, -6, 4],\n [-16, 18, -5, -22, -17, -4, 7, 10, -12],\n [6, -5, 6, -17, -17, -1, -2, -6, -9],\n [6, 16, -1, -4, -1, 1, -10, 16, 4],\n [-22, 20, 12, 7, -... | 372 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-21, 24, 20, 1, 3, 4, 24, 8, 11],\n [-17, 3, 19, -19, 6, -10, -16, 4, 20],\n [-8, -4, 25, 12, -19, -13, -20, 24, 3],\n [-21, 20, -5, 8, -4, 0, 16, -3, -18],\n [-5, -20, -15, 25, 15, 6, 7, -25, 5],\n [-24, -14, 16, 20, -15, 25, -25, 19, -17],\n [-19, 2, -1... | 784 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -8, -10, -21, 25, -15, -19, -19, -13],\n [6, 19, 15, 9, 12, 6, 6, -5, -23],\n [-8, -19, -17, 23, -18, -24, 11, -6, 23],\n [-9, -18, 9, 24, -13, -8, -23, -4, -20],\n [21, -9, -7, -18, -4, 24, -6, 8, -7],\n [-25, 20, 10, 18, 1, -16, 6, -11, 16],\n [-23, 7, -24, 1... | 968 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, 16, 13, -7, 2, 24, -4, 14],\n [-1, 20, -11, -10, 16, -11, -2, -8, 8],\n [16, -11, 4, -4, -2, 0, -6, -10, -10],\n [13, -10, -4, -9, -10, 9, -7, 18, 1],\n [-7, 16, -2, -10, 6, -12... | 368 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-16, 7, 12, -6, 0, -20, -2, -2, -8],\n [7, -9, -12, -10, 6, 10, 4, -2, 2],\n [12, -12, 22, -2, -15, -9, 0, 8, 12],\n [-6, -10, -2, -19, 1, 13, 5, 23, 10],\n [0, 6, -15, 1, 18, -1, 6, 3, 17],\n [-20, 10, -9, 13, -1, -1, 0, 12, 17],\n [-2, 4, 0, 5, 6, 0, -2... | 562 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[20, -10, -4, -4, 4, 18, -2, -12, 18],\n [-10, -11, -12, -8, 18, 10, 10, -4, 6],\n [-4, -12, 19, 16, -2, 19, 17, 0, -10],\n [-4, -8, 16, -7, 2, 8, 2, 6, -1],\n [4, 18, -2, 2, 8, -6, -10, 2, -1],\n [18, 10, 19, 8, -6, 12, -9, -18, -8],\n [-2, 10, 17, 2, -10,... | 856 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[18, -21, -2, 4, -14, 0, 14, -4, -4],\n [-21, -3, -10, 12, -6, 0, -18, -20, -16],\n [-2, -10, -25, -6, -11, -10, -2, 11, 4],\n [4, 12, -6, 15, -6, -12, -6, 9, 18],\n [-14, -6, -11, -6, 3, -10, 10, 8, 20],\n [0, 0, -10, -12, -10, -6, -6, 10, 12],\n [14, -18,... | 166 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[21, -17, 0, -4, -7, -24, -23, 11, -16],\n [0, 1, -5, -18, 13, 19, -12, -6, 18],\n [0, 0, 21, 20, 6, 14, 14, 14, 22],\n [0, 0, 0, 2, -15, 8, -25, 9, 1],\n [0, 0, 0, 0, 2, -15, 6, 0, 13],\n [0, 0, 0, 0, 0, 18, 25, 5, -7],\n [0, 0, 0, 0, 0, 0, -2, -4, 9],\n ... | 576 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 18, -18, -4, -10, 9, -2, 0, -10],\n [18, 20, 1, -2, 6, -8, 7, 4, -7],\n [-18, 1, 18, 2, 1, 8, 7, -2, -12],\n [-4, -2, 2, -4, -4, 10, -11, 0, -3],\n [-10, 6, 1, -4, -1, 6, 2, -9, -4... | 391 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -12, 10, -20, -11, 5, -20, -2, 20],\n [-16, -6, -21, -13, 2, -22, 14, -24, 23],\n [6, 6, -23, 23, -21, 22, -17, 4, 19],\n [-22, 20, -21, 16, -1, -14, -21, 23, 5],\n [15, 13, -16, 23, 0, 11, -8, -2, -17],\n [-12, 15, -10, 11, 3, 3, -19, -13, 16],\n [19... | 529 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -11, 25, -14, -23, 25, -13, 0, -1],\n [-25, 15, 0, -17, 11, -16, 2, -24, 24],\n [-6, 5, -21, -13, -24, 8, 10, -5, -5],\n [5, -3, 7, -12, -17, -18, -3, 5, 8],\n [12, -24, 4, 19, 24, 19, 23, -2, -15],\n [22, -9, -2, 15, -14, 11, 23, -24, 17],\n [-15, -11, 20, -2... | 653 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 5, 4, 8, -1, 12, -9, -4, 7],\n [8, -3, -23, 8, 19, -5, 19, 17, 19],\n [2, -10, 21, 3, 10, 3, 21, -4, 21],\n [16, -8, -6, -10, -23, -10, -3, 23, 8],\n [-6, 6, -11, 14, -10, 24, 1, -15, -18],\n [21, -9, -2, 14, 23, -16, 17, -20, 5],\n [1, -6, 13, -4, -2... | 460 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-17, 6, 10, -9, 20, -6, 19, -12, -1],\n [6, -12, 3, 12, -6, -4, 0, -6, -2],\n [10, 3, 20, -20, 8, 2, -15, 0, -7],\n [-9, 12, -20, -3, -13, 12, -3, 2, 18],\n [20, -6, 8, -13, -9, 18, -4, 0, -15],\n [-6, -4, 2, 12, 18, -19, 20, -20, 2],\n [19, 0, -15, -3, -... | 672 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[16, -11, 25, 1, -19, 8, -22, 13, 8],\n [23, -6, -8, 13, -17, -5, 13, 19, 2],\n [16, -8, 22, -2, 20, 12, 20, 12, -4],\n [-13, 14, 17, 24, 9, -25, -18, -21, -7],\n [-9, -7, -12, 12, 5, -12, 0, 7, -4],\n [-16, -8, 24, 20, -8, 14, -24, -11, -3],\n [-24, -24, ... | 528 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -17, 2, -6, 24, 13, -16, 20, 10],\n [-19, 18, -1, 5, 8, 25, -25, -24, -18],\n [24, -12, 13, -24, 5, -17, 20, -12, 14],\n [-5, -7, 11, 18, -23, 19, -25, 19, 19],\n [9, 15, -2, -24, 10, 16, 11, -23, -8],\n [23, 15, -3, -3, -20, -5, 24, -14, 11],\n [2, -8, -20, -... | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 22, 17, 12, -14, -15, -12, -13, -18],\n [13, 15, -4, -5, -24, 21, -17, 6, 19],\n [20, -5, 2, -25, 8, 20, -6, 22, 12],\n [7, 18, 5, -6, 13, -19, -1, -25, 8],\n [-22, 15, -4, -4, -12... | 785 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[22, -3, 12, 20, 17, -16, -1, -8, -4],\n [-3, -11, -2, 12, -16, 20, -18, 2, -2],\n [12, -2, 23, -8, 2, 0, -6, -9, 4],\n [20, 12, -8, -21, -2, 7, -10, 18, -13],\n [17, -16, 2, -2, -25, 0, -6, -24, 4],\n [-16, 20, 0, 7, 0, -8, -13, 14, 14],\n [-1, -18, -6, -1... | 122 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -13, -12, 13, -23, -12, -24, 22, 1],\n [0, -16, 22, 16, 19, 25, 20, -4, -15],\n [0, 0, 19, 5, -7, 12, 18, -11, 23],\n [0, 0, 0, 25, -19, -7, 3, -3, -14],\n [0, 0, 0, 0, 4, 19, 1, -... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, -16, -12, -12, -6, 10, -3, -14, 18],\n [-16, -8, 22, 8, -1, -21, -10, 6, 12],\n [-12, 22, 6, -9, 6, -12, -8, 4, -4],\n [-12, 8, -9, 18, -4, -13, -6, -19, 2],\n [-6, -1, 6, -4, -3, 4, 4,... | 828 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 17, 7, -6, 18, 18, -22, -4, -5],\n [13, 8, -12, 16, -1, -15, -13, 18, -20],\n [2, -10, -17, -24, 15, -20, 8, 25, 16],\n [19, -24, 5, 7, 9, -7, -21, 22, 24],\n [-8, 14, 20, 4, -14, -10, 12, 21, -12],\n [8, 17, -6, 23, -20, 4, 19, 10, 23],\n [12, 2, 14, ... | 704 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -12, 0, -5, 8, -11, -16, 0],\n [0, -11, -3, -10, -16, 5, -5, 7, 18],\n [-12, -3, -7, 11, 14, -7, 22, -4, 12],\n [0, -10, 11, -20, -8, 4, -6, 18, 8],\n [-5, -16, 14, -8, 20, 8, 0, 15, 2... | 613 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 6, -10, -18, 2, 14, -2, -2, -19],\n [6, 22, 2, -6, 19, -2, -6, 0, 0],\n [-10, 2, 2, 18, -4, -10, -10, 14, 14],\n [-18, -6, 18, -19, 10, -6, -6, 0, -7],\n [2, 19, -4, 10, 8, 8, -2, 22, 2],... | 22 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -4, -12, -2, 20, -2, -1, 8, -2],\n [-4, 20, 8, 10, 3, -10, -10, 4, -14],\n [-12, 8, 12, 8, 4, -12, 4, -14, 3],\n [-2, 10, 8, 5, -12, 3, 4, 13, 0],\n [20, 3, 4, -12, 14, 12, 6, -12, -10],\n [-2, -10, -12, 3, 12, -15, -8, -14, 0],\n [-1, -10, 4, 4, 6, -8... | 81 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -15, -12, -12, -12, 2, -15, 4, -6],\n [-15, 7, 8, -8, -8, -2, 15, -18, 8],\n [-12, 8, 19, 10, 0, -8, -20, -4, 16],\n [-12, -8, 10, 9, 2, 14, -3, -7, 13],\n [-12, -8, 0, 2, -25, 0, 3... | 718 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 2, 12, 24, -8, 16, 4, -4, 0],\n [2, 9, -12, 5, 18, -10, 7, 8, 11],\n [12, -12, 9, -6, -10, -3, -2, 7, -6],\n [24, 5, -6, 1, -12, -10, 15, -8, 1],\n [-8, 18, -10, -12, 16, 8, 10, -12, -8]... | 440 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[19, -4, -14, -14, 0, -9, 9, 6, -4],\n [-4, 9, -4, -5, 16, -22, -14, 4, 2],\n [-14, -4, -6, 20, 6, -16, 2, -6, -2],\n [-14, -5, 20, -9, 6, 14, 0, 6, 24],\n [0, 16, 6, 6, -7, -6, -2, -10... | 176 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 20, 24, -11, -25, -7, 16, -20, -16],\n [1, 6, -5, 10, 10, -22, 4, -14, 6],\n [-8, -12, 20, 8, -24, -22, -17, -16, -11],\n [25, 4, -22, -7, 25, -15, -11, 25, -8],\n [24, 19, 21, 3, -2, -7, -15, 7, -5],\n [-17, -25, 6, 22, 0, -14, -4, 24, -15],\n [9, -1, -4, 14, ... | 334 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -2, 8, 14, 6, 20, 22, -7, -8],\n [-2, 1, 0, -9, 2, 14, -22, -12, -8],\n [-13, -13, -19, 5, -3, -3, 13, 3, 23],\n [18, -12, -3, 11, 10, -3, 21, -4, 18],\n [-11, -2, 13, -3, 2, 11, 8, -3, -11],\n [3, -24, -23, -24, -9, -6, 6, -20, 13],\n [-17, 20, -22, 8, -21, -4... | 936 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 4, 5, 16, 22, -6, -20, -17, 15],\n [-24, 24, -1, 4, 6, -9, 6, -22, 23],\n [-9, 23, -20, -17, -14, -2, 22, -4, 10],\n [-7, 25, 2, 0, 4, 3, -11, -5, 3],\n [2, 12, 22, -6, -24, 8, -21... | 898 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-19, -24, -12, 2, 7, -21, 15, 20, -1],\n [11, -18, 7, -3, -24, 15, 6, -12, 9],\n [14, -17, 1, 17, -21, -11, 20, 18, -25],\n [-15, -5, -16, 13, 5, 3, -6, 14, -10],\n [7, 7, -6, -4, 6, -14, 19, -16, -16],\n [-18, -9, -24, -18, -22, -7, -5, -8, -23],\n [-7, -24, 23, ... | 798 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 15, 6, -10, -14, 17, 11, -2, 5],\n [15, 12, -11, 8, -14, 8, -14, 2, -4],\n [6, -11, -24, 20, -10, 0, 2, 17, 24],\n [-10, 8, 20, -22, -4, 2, -4, 0, -15],\n [-14, -14, -10, -4, -14, ... | 713 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 9, 9, -2, -17, -9, -15, 20, -2],\n [0, -25, -18, 10, -3, 11, -25, 16, -24],\n [0, 0, -4, -24, 0, -7, -7, -11, 1],\n [0, 0, 0, 18, -9, -9, 7, -11, -11],\n [0, 0, 0, 0, -15, -11, 4, 19, -9],\n [0, 0, 0, 0, 0, -17, -21, -22, 10],\n [0, 0, 0, 0, 0, 0, -14,... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 1, 18, 12, 10, -8, 0, -1, 8],\n [1, 25, -8, 4, -24, 8, 3, -21, 4],\n [18, -8, -19, -10, -16, 3, 14, 9, -2],\n [12, 4, -10, -11, -10, -22, -5, 0, -9],\n [10, -24, -16, -10, 25, -10, 14, 0, 14],\n [-8, 8, 3, -22, -10, 24, -8, 3, 10],\n [0, 3, 14, -5, 14,... | 904 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 22, 5, 22, 20, 2, 6, -2, -16],\n [-9, -18, 8, 10, -13, -5, 25, 6, 2],\n [-13, 23, 21, -18, 10, -13, -22, 15, -2],\n [-5, 15, -15, -7, 8, -22, -9, -10, 10],\n [-1, 13, -15, -2, -2, 1, -5... | 832 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-23, 10, 5, -19, 23, -13, -20, -10, -17],\n [22, 1, 11, -4, 13, 6, 9, -25, -2],\n [-18, -14, 1, 24, 12, -7, 6, 20, 0],\n [-1, -2, 8, -18, 22, 0, -19, 20, 15],\n [24, -8, -22, -9, 6, 10, 9, 11, -12],\n [-1, 12, 8, 12, -16, 24, -6, 22, -19],\n [-15, 0, -23, 2, -17, ... | 792 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-21, -1, -7, 3, -19, -19, -16, -10, -5],\n [-21, 0, -10, 8, 19, 18, 11, -22, 15],\n [-6, -24, 24, -23, 11, -24, -7, 15, -1],\n [22, 15, 6, -3, -19, 13, -9, 25, -12],\n [0, -1, -6, 5, 2... | 308 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-24, -5, 25, 21, 14, -11, 19, 3, 16],\n [0, 4, -16, 21, -8, -24, 24, 14, 16],\n [0, 0, 13, 3, -24, 21, -12, -7, 7],\n [0, 0, 0, -10, 20, 25, -17, -8, 16],\n [0, 0, 0, 0, 9, -9, -13, -22, -23],\n [0, 0, 0, 0, 0, -22, 16, 21, 13],\n [0, 0, 0, 0, 0, 0, 3, -1... | 720 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[25, -5, -14, -11, -5, 22, -12, -24, -3],\n [0, 6, -16, 5, 3, 3, 16, -15, -10],\n [0, 0, 10, 8, 16, 19, 19, -20, 15],\n [0, 0, 0, -22, -17, -4, 25, -7, 24],\n [0, 0, 0, 0, -16, -5, 3, -5, 0],\n [0, 0, 0, 0, 0, 9, 19, 10, 4],\n [0, 0, 0, 0, 0, 0, -2, 18, -12... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-22, 16, 24, -9, -5, 14, -19, 17, -20],\n [-7, 22, -8, 9, 4, 14, 6, 2, 21],\n [7, 13, -20, -14, 12, 15, 15, -16, 18],\n [-3, 19, -10, -2, 0, -7, 21, 6, 9],\n [5, -9, 10, 12, -6, 7, -9, 10, -12],\n [-13, -2, -21, 2, -5, -1, 7, -19, -19],\n [-15, 9, -3, 10, -3, -6, ... | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-17, -8, 23, -9, 8, -8, -1, -8, 7],\n [12, 6, 1, 2, -5, 14, 13, 17, -8],\n [-6, 17, 6, 9, -12, 11, -10, -2, 20],\n [-15, 17, -22, -15, 3, -12, -20, 5, -25],\n [23, -7, -10, -7, 11, -13, -17, -3, 7],\n [-6, 14, -4, -20, -16, 22, -15, 22, -17],\n [25, 6, 6, -13, -25... | 466 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[21, 0, -4, -1, 15, -20, 13, -13, 16],\n [17, 5, 22, -7, -16, -7, 18, -25, -2],\n [-19, -25, 13, 8, 21, -13, 22, 2, 11],\n [-13, -19, -17, 3, 18, -24, 21, -8, 11],\n [7, -15, -24, 0, 9, 14, 1... | 672 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 20, -25, 7, 17, 2, 24, 0, -15],\n [8, -3, -18, 20, -18, 4, 10, 23, 12],\n [23, 4, 0, 10, -6, 7, 22, -14, -3],\n [-3, 6, 6, -23, -24, -13, 24, 15, 15],\n [12, -2, 3, 9, -17, 14, -21, 7, -23],\n [22, -5, -12, -23, -18, 3, 19, 12, 11],\n [11, -15, -9, 1, -... | 536 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, -11, 20, 19, 5, 25, -17, -5],\n [0, 8, 22, 5, 10, 13, -3, -13, -20],\n [0, 0, -4, -14, 23, 4, -24, -2, 11],\n [0, 0, 0, 19, -24, 8, -22, 13, -14],\n [0, 0, 0, 0, 6, -11, -10, -16, -8],\n [0, 0, 0, 0, 0, -18, 13, -9, 11],\n [0, 0, 0, 0, 0, 0, -17, -... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -13, 0, -8, 12, -3, -6, 7, 1],\n [-13, -6, 1, 0, -8, -19, -11, 10, 14],\n [0, 1, -7, -6, 23, -16, 0, -13, 0],\n [-8, 0, -6, 20, -18, -2, 3, 10, -18],\n [12, -8, 23, -18, 0, 20, 6, -8, -22... | 189 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -3, 15, -13, 19, 20, 2, 10, -23],\n [3, 18, -5, 16, 10, 20, -12, 13, 25],\n [-5, 18, -17, -8, 21, 7, 16, 5, 10],\n [-3, -25, 17, 2, -21, 8, -6, -19, 13],\n [17, 16, -16, 14, 18, 7, 0, -13, 21],\n [8, -12, -22, 11, -25, 25, 8, -23, 4],\n [-14, -23, 17, -... | 844 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -23, -18, 7, 16, -5, -21, -9, -19],\n [0, 5, 3, 4, 19, -16, 17, 22, 12],\n [0, 0, 3, 0, -7, 21, 11, -4, 14],\n [0, 0, 0, -15, -4, -25, -18, 12, -5],\n [0, 0, 0, 0, 16, 21, 23, -4, 14],\n [0, 0, 0, 0, 0, 18, -1, -6, 6],\n [0, 0, 0, 0, 0, 0, 8, -18, -17]... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -9, -17, -19, -17, -15, 23, -23, -9],\n [18, -11, -13, -20, -15, 12, -14, 9, -15],\n [-13, -13, 24, -12, 21, 24, -17, 9, 16],\n [-7, 8, 8, 8, -2, -5, -1, 10, 6],\n [5, -15, 10, -4, 25, 6, -23, 4, -20],\n [9, 22, -21, 16, 3, 18, 25, 1, -12],\n [23, 7, ... | 304 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[19, -3, 3, -9, -23, -3, 19, -5, 6],\n [0, -20, -3, -10, 24, 2, -7, 20, -23],\n [0, 0, 15, 0, -11, -24, 9, 25, -3],\n [0, 0, 0, -25, -19, 10, 2, 18, 10],\n [0, 0, 0, 0, 22, -25, -14, 9,... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 3, 4, 2, -16, -8, -2, 14, 0],\n [0, 25, 13, -6, 25, 8, 7, -18, 6],\n [0, 0, -10, -13, 24, -14, 16, 21, -1],\n [0, 0, 0, -24, -19, 3, -17, 6, -9],\n [0, 0, 0, 0, -1, 24, 8, 12, -24]... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, 10, 10, 16, 6, -3, -8, 16, 6],\n [10, 20, 12, -6, 9, -10, 14, -8, -6],\n [10, 12, -10, 2, -12, -8, -6, -22, 10],\n [16, -6, 2, -14, 1, -13, -14, -8, 8],\n [6, 9, -12, 1, 12, -10, -15, -16, -4],\n [-3, -10, -8, -13, -10, -14, 7, -6, -2],\n [-8, 14, -6,... | 648 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 4, 3, -11, -18, -16, -6, -23, 21],\n [2, -18, 2, 5, 0, 6, -2, 18, 6],\n [2, 10, -4, 5, 4, 1, -13, -13, -21],\n [15, -19, -23, 11, 6, 15, -17, -9, 12],\n [-24, -23, -18, 4, -4, 16, -11, 7, 23],\n [-24, 10, -19, -1, -9, -2, -12, -11, -3],\n [-6, 24, 15,... | 290 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-18, -5, 20, 6, -10, 14, -13, -8, -12],\n [-5, -20, -8, -6, 16, -14, -12, -18, 18],\n [20, -8, 6, -10, 11, 6, 2, -4, 4],\n [6, -6, -10, -14, 1, 0, -6, 8, 2],\n [-10, 16, 11, 1, -24, 11... | 864 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 5, -21, 25, -23, 24, 10, -5, 17],\n [0, -10, -16, -21, 4, -14, 19, 17, 9],\n [0, 0, -24, 21, 8, -2, -12, 17, 24],\n [0, 0, 0, -13, 6, 16, 9, -23, -16],\n [0, 0, 0, 0, -16, -8, -8, 10, -4],\n [0, 0, 0, 0, 0, -14, 11, -11, -19],\n [0, 0, 0, 0, 0, 0, 21, ... | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -3, 10, -6, -17, -11, 22, 13, -14],\n [5, -2, -22, 21, -9, -13, 1, 5, 1],\n [12, -24, 9, 14, 21, 23, 15, 21, 5],\n [6, 22, 22, -16, -10, 6, -1, -25, 4],\n [-14, 17, -23, -3, 20, -10, 7, ... | 44 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 13, -22, -24, -11, 17, 18, -11, 25],\n [0, 7, -17, 11, 14, -14, 17, 18, 8],\n [0, 0, -24, 9, 11, -14, -21, 14, -9],\n [0, 0, 0, 19, 2, 12, 5, -14, -19],\n [0, 0, 0, 0, -11, -21, -9, 1, -10],\n [0, 0, 0, 0, 0, 16, -14, 23, -22],\n [0, 0, 0, 0, 0, 0, 5, -18, -17... | 880 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[25, -3, -25, 8, 3, -22, 15, -14, 12],\n [15, 21, 21, -7, 5, 23, 22, 17, 12],\n [12, 11, -21, 9, -16, 9, -5, -12, 7],\n [16, 20, -9, 12, 13, 2, -13, -10, -23],\n [-12, 5, 1, 9, -15, -17, -13, -24, -25],\n [-9, -8, 0, 22, 8, -17, -5, -21, -4],\n [13, 3, 19,... | 844 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-13, 5, -23, -12, 25, -19, 7, -18, -21],\n [0, 2, -5, -23, -20, 7, 19, -1, -12],\n [0, 0, -14, -13, 7, 15, -1, 4, 19],\n [0, 0, 0, -2, 17, 8, 19, 24, 14],\n [0, 0, 0, 0, -15, -24, 22, 14, 13],\n [0, 0, 0, 0, 0, 9, -4, -12, 21],\n [0, 0, 0, 0, 0, 0, -20, -... | 400 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, 10, -16, 7, 6, 24, 13, -25, 6],\n [0, -2, -10, -24, 22, -14, 19, 13, 14],\n [0, 0, -10, -7, 1, -14, 7, 13, -4],\n [0, 0, 0, 22, 1, -24, -13, 13, -12],\n [0, 0, 0, 0, 15, 0, -19, -13, -2],\n [0, 0, 0, 0, 0, 3, -13, -3, -12],\n [0, 0, 0, 0, 0, 0, -7, -... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[22, 15, 21, -5, 17, -22, 15, -19, 14],\n [20, -2, -5, -5, 13, -17, -3, 1, 4],\n [19, 16, 3, 9, 18, -25, 0, -5, -18],\n [-22, -8, 13, -21, -2, -5, -3, -23, 7],\n [11, 14, 20, 19, -5, 5, 18, 13, 20],\n [0, -20, 19, 22, 1, 18, -24, -6, -20],\n [-17, 7, 20, 14... | 558 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, 0, 18, -2, 20, -14, 0, 16],\n [12, 0, -2, 14, -17, -2, 18, 0, 11],\n [0, -2, -24, -6, 10, 12, 14, -14, -14],\n [18, 14, -6, -22, -2, 6, -16, -8, 12],\n [-2, -17, 10, -2, 15, -21, -5, ... | 696 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -24, 12, 23, -8, 19, 13, -25, 14],\n [0, -1, -4, -18, -2, 16, 19, 3, -5],\n [0, 0, -22, -23, -16, 13, 5, -21, 1],\n [0, 0, 0, -9, 18, 11, 23, -13, 18],\n [0, 0, 0, 0, -9, -11, -1, -16, -4],\n [0, 0, 0, 0, 0, 9, 25, -1, -4],\n [0, 0, 0, 0, 0, 0, 12, 25,... | 920 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -4, -18, -4, -6, 18, 6, 15, 1],\n [-4, 14, -9, 6, -19, -4, 12, -7, -2],\n [-18, -9, 20, -3, 10, 0, -5, 11, -2],\n [-4, 6, -3, 23, 0, 18, 4, -14, -8],\n [-6, -19, 10, 0, 2, 11, -12, 10, 9],\n [18, -4, 0, 18, 11, -22, -19, 4, -20],\n [6, 12, -5, 4, -12, -19, 12,... | 847 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-18, -1, -16, -6, -9, 13, -19, 20, -15],\n [0, -14, -5, 24, 10, 16, -15, -12, -16],\n [0, 0, -22, 21, -23, 0, 13, 10, -21],\n [0, 0, 0, -2, 12, 6, 0, 1, -3],\n [0, 0, 0, 0, 9, 10, 16, -7, -2... | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 4, -8, -2, -18, -15, 5, -18, -6],\n [4, -1, 1, 10, -7, -10, -6, 4, -10],\n [-8, 1, -17, -16, 2, -14, 6, 1, 13],\n [-2, 10, -16, 14, -9, 7, -13, 20, 12],\n [-18, -7, 2, -9, -23, 2, 0, -8,... | 831 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -18, 10, -22, -6, 13, 9, 6, -6],\n [-18, 12, -10, -15, 6, 22, -10, -4, -11],\n [10, -10, 3, -6, 13, 1, -21, 12, 10],\n [-22, -15, -6, 16, -3, 2, -2, -4, -12],\n [-6, 6, 13, -3, -19... | 450 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 19, -17, -14, -3, 15, 9, -8, 20],\n [0, 4, 4, 10, 9, 7, 16, 6, 2],\n [0, 0, -11, 16, 18, -2, 6, 25, -24],\n [0, 0, 0, 15, 21, 11, -6, -15, 3],\n [0, 0, 0, 0, -9, 13, -11, 22, -2],\n [0,... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-22, -22, -5, -2, -25, 7, -1, 7, 12],\n [0, -5, -5, -3, -7, 6, -15, -10, 5],\n [0, 0, -4, 15, 11, -11, 12, 6, -8],\n [0, 0, 0, -21, -16, 3, -8, -2, 2],\n [0, 0, 0, 0, 21, -17, -7, -16, 7],\n [0, 0, 0, 0, 0, -23, -6, 9, 11],\n [0, 0, 0, 0, 0, 0, 11, -8, -3],\n [0, ... | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 7, 13, -4, 2, -23, -15, 8, -21],\n [1, -12, -14, -17, 16, 5, -13, 16, -21],\n [-17, 22, 24, -21, -8, 5, -4, -23, 12],\n [12, -7, -13, 21, 12, -10, -8, 4, 12],\n [13, -9, -21, 18, 2, 0, 9... | 621 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-21, -8, -18, -21, 10, -6, 0, -16, 6],\n [-8, -12, 0, -14, 2, 8, -2, -19, 7],\n [-18, 0, 9, 8, 1, -5, -4, -18, -8],\n [-21, -14, 8, 9, -2, -6, -9, 11, 2],\n [10, 2, 1, -2, -16, 12, 0, -19, -9],\n [-6, 8, -5, -6, 12, -17, 0, 0, 12],\n [0, -2, -4, -9, 0, 0,... | 579 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[16, -15, 9, -1, -5, -4, 8, 2, 22],\n [-15, 23, 3, 10, -19, 18, -6, 7, -22],\n [9, 3, 19, 14, -5, 10, -10, -4, 0],\n [-1, 10, 14, 24, 0, 4, -8, -12, -8],\n [-5, -19, -5, 0, 22, 8, 6, -2... | 962 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, 11, -13, -6, 20, 25, 17, -10, -15],\n [0, -25, 7, -18, 14, 15, -19, 15, -19],\n [0, 0, -6, -1, -5, 21, -3, -16, 15],\n [0, 0, 0, 15, 4, 7, -18, 23, 14],\n [0, 0, 0, 0, 4, -21, 19, -18, 5],\n [0, 0, 0, 0, 0, 16, -8, 25, -15],\n [0, 0, 0, 0, 0, 0, -22, -... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -8, -6, -7, -14, 24, -3, -19, -14],\n [0, -2, 20, 17, 5, 15, -24, -22, 1],\n [0, 0, -6, -14, 17, 14, -4, -3, -14],\n [0, 0, 0, -20, 0, 6, 4, 13, 20],\n [0, 0, 0, 0, 9, -15, 11, -17, 24],\n [0, 0, 0, 0, 0, 4, -22, -3, 11],\n [0, 0, 0, 0, 0, 0, 2, 15, 6],... | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -10, -21, -21, -10, -6, -19, 8, 4],\n [0, 16, -3, 19, 15, -7, -20, -9, -6],\n [0, 0, 23, 13, -5, -8, 13, 14, -9],\n [0, 0, 0, 9, 22, 3, -2, -14, 17],\n [0, 0, 0, 0, -22, -3, 1, -11,... | 904 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -1, -15, 4, -22, 6, 0, -2, -19],\n [-12, -20, -9, 10, -14, -14, -15, -4, 20],\n [20, -19, -2, 11, -8, 0, 22, 3, 15],\n [-20, 7, 5, 22, -17, 15, 16, 7, 25],\n [18, -25, 4, 8, 25, -25, 13,... | 255 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-22, 22, 14, -23, 7, -15, -11, 0, -7],\n [0, -3, -6, 22, 24, -11, 7, 11, -23],\n [0, 0, -18, 11, 5, -6, -10, 4, 8],\n [0, 0, 0, -1, 11, -6, -7, 6, 23],\n [0, 0, 0, 0, 6, -21, 1, 2, -17],\n [0, 0, 0, 0, 0, -3, 4, 13, -8],\n [0, 0, 0, 0, 0, 0, 1, -4, 4],\n [... | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -14, -22, -16, -10, 11, 20, 19, 8],\n [-17, 14, -17, 17, -18, 12, -24, 1, -6],\n [-20, 17, 9, -15, 6, -15, -1, -24, -13],\n [20, 11, -1, 11, 3, -10, 5, -23, 14],\n [-14, 21, -9, -9, -14, 9, 7, 23, 1],\n [7, 22, 23, -11, -14, 4, 11, 1, -5],\n [-23, -13, -4, -18... | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -16, -25, 8, 17, 9, -15, -14, 1],\n [3, 25, 25, -25, 8, -6, 20, 5, -25],\n [-10, -22, -4, 10, -17, 17, 24, -17, -21],\n [-10, -6, 3, -25, -9, 9, 24, -14, -15],\n [24, 10, -2, 23, 16, -13... | 700 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 21, -17, -9, 20, 7, 20, 17],\n [14, -10, -10, -23, 20, 4, -22, 0, 24],\n [-10, -7, -25, 20, 13, -25, -9, 7, -3],\n [23, 7, 6, -24, -1, 1, 24, 17, -6],\n [16, -11, 12, 24, -4, 5, -18, 2... | 160 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[17, 11, -4, -2, -2, 4, 17, -17, 8],\n [11, 18, 14, 5, 6, 7, 4, -12, -18],\n [-4, 14, -12, 9, 4, 0, 8, 2, 8],\n [-2, 5, 9, 22, -2, -4, -3, 14, -2],\n [-2, 6, 4, -2, 20, 10, -8, 4, 6],\n [4, 7, 0, -4, 10, 5, -10, 7, -16],\n [17, 4, 8, -3, -8, -10, 25, 10, 4],\n [-17... | 516 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 8, -9, -10, 17, -12, -10, 21, -21],\n [0, 11, 24, 12, 0, -7, -16, -22, 12],\n [0, 0, 14, 16, -9, -23, 14, -16, 19],\n [0, 0, 0, -10, -20, 1, -25, 7, 17],\n [0, 0, 0, 0, -11, -2, -2, 16, -20],\n [0, 0, 0, 0, 0, -22, -14, -13, 20],\n [0, 0, 0, 0, 0, 0, -6... | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 18, 13, -24, 13, -1, 25, -23, 17],\n [0, 14, 5, -6, 6, 23, 19, 8, 0],\n [0, 0, 16, 16, 12, -14, -10, -20, -22],\n [0, 0, 0, -2, -10, -7, 2, 14, -6],\n [0, 0, 0, 0, 9, -24, 23, 9, -16],\n [0, 0, 0, 0, 0, 20, 7, 22, -24],\n [0, 0, 0, 0, 0, 0, -23, -16, 4]... | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 14, -16, 12, 0, -4, 21, -15, 10],\n [14, 14, -4, 10, -18, 8, -8, 8, 14],\n [-16, -4, -16, -14, 4, -18, -20, -1, -18],\n [12, 10, -14, 21, -12, -18, -3, -2, 0],\n [0, -18, 4, -12, -2, -4, ... | 296 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-21, -16, 15, -18, -4, -19, 25, -4, -15],\n [0, 25, -11, -20, 12, 10, 13, 11, 11],\n [0, 0, -3, -13, -22, 23, 18, -2, -11],\n [0, 0, 0, -10, -8, 15, -5, 13, 24],\n [0, 0, 0, 0, 24, 24,... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 12, -2, 0, -20, -13, -18, -2, -5],\n [12, -9, -4, -7, 1, 10, 13, -8, -5],\n [-2, -4, 16, 0, -8, 6, -4, 8, 0],\n [0, -7, 0, -12, -17, -10, -14, -16, 7],\n [-20, 1, -8, -17, -19, 12, -6, 13, 8],\n [-13, 10, 6, -10, 12, 4, 2, -18, -6],\n [-18, 13, -4, -14, -6, 2, ... | 788 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -8, 24, 10, -8, 8, 21, 12, -11],\n [-12, -3, -6, 21, -13, 1, -25, -20, -4],\n [-11, -25, 9, -3, -20, 18, 21, 5, -25],\n [-9, -9, -18, 12, -22, 24, 4, -7, -20],\n [11, -3, -22, 4, 22, -8, 11, -8, -5],\n [8, 10, -4, 3, -21, 8, 23, -9, -19],\n [-17, 10, 24, -24,... | 163 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, -4, -4, -8, 4, -14, 11, 22],\n [-4, -13, 22, 0, 2, -4, 2, 12, 8],\n [-4, 22, -19, -16, 0, -12, -9, 16, 20],\n [-4, 0, -16, -1, -16, -9, 4, 8, 16],\n [-8, 2, 0, -16, -24, -10, 16, 14, ... | 956 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -16, 18, -1, 15, 6, 0, -12, -14],\n [-16, 16, -2, -2, 4, -4, -8, 2, -6],\n [18, -2, -4, 8, 8, 8, 4, 18, 18],\n [-1, -2, 8, 4, 6, 8, 0, -3, 16],\n [15, 4, 8, 6, 16, 14, -8, -8, 9],\n [6, -4, 8, 8, 14, -7, 18, -2, 4],\n [0, -8, 4, 0, -8, 18, 19, 11, 7],\... | 4 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -18, 2, -10, 0, -6, -8, 8, -9],\n [-18, -21, 9, 2, -14, 18, -10, 1, -18],\n [2, 9, -1, 1, -8, 13, -4, 6, 2],\n [-10, 2, 1, -8, -16, -15, 10, 2, 8],\n [0, -14, -8, -16, -4, 6, -18, 5, -2],\n [-6, 18, 13, -15, 6, -21, 8, -1, 13],\n [-8, -10, -4, 10, -18, ... | 709 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 3, -18, -4, -15, -2, -4, -2, -6],\n [3, -11, -11, 16, -4, 20, -17, -12, 11],\n [-18, -11, -5, -2, 12, 8, -12, 11, -12],\n [-4, 16, -2, 19, 18, -18, 10, 8, 4],\n [-15, -4, 12, 18, -14, 0, 3, -8, 4],\n [-2, 20, 8, -18, 0, -12, -10, -4, -5],\n [-4, -17, -12, 10,... | 841 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[21, -3, -14, -10, 19, -1, 20, -21, -11],\n [11, 9, -6, -19, 10, -13, 15, 25, 6],\n [18, -20, -19, 9, 11, -4, 19, -12, -21],\n [-2, -10, 15, -22, 22, 21, 23, -7, 15],\n [13, 10, -14, 21, -4, 4, 13, -15, 10],\n [-2, -9, -9, -15, -10, -18, 3, 21, 0],\n [-3, -... | 877 | MATH |
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