messages listlengths 1 1 | ground_truth stringclasses 91 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, -4, -11, 2, 0, 4, -8, -8, 5],\n [17, 5, -16, 3, -17, 5, 11, -17, 2],\n [14, -7, 3, 6, 8, 9, -3, -4, -16],\n [18, -12, 2, -10, -1, -15, 6, -5, -10]... | 50 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, 16, 14, -14, 9, -12, -10, -11, -7],\n [15, 14, 4, 5, 18, 16, 3, 8, 16],\n [-18, 16, 18, -5, -16, -18, -14, 7, -5],\n [8, -10, -4, -4, 7, -6, 13, 13, -15],\n [11, 18, 4, -4, 10, 17, -6, 13, -12],\n [3, 9, -17, -13... | 61 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, 13, 14, -18, 0, -17, 7, 13, -13],\n [13, -15, -8, -2, 5, -14, 15, -13, 3],\n [-8, -3, 14, -10, -13, -3, 10, -16, 1],\n [17, 0, 7, -16, 0, 1, 13, -12, 14],\n [-1, -18, -8, 9, 6, 4, 12, 11, 16],\n [-12, -3, 7, -17, -18, -7, -14, 18... | 60 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-5, 2, 1, -11, -12, -16, -2, 14, -7],\n [3, 3, 11, -11, 8, 8, 15, 2, 11],\n [14, 9, 14, -14, 0, -15, 16, -2, 9],\n [11, 10, -13, 16, 18, 5, 10, 12, 16],\n [14, 2, 13, 4, 14, -16, -1, 6, 1... | 54 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, -13, -4, 18, 14, -11, -14, -15, -13],\n [13, 11, 16, -3, -6, 11, 0, -2, 0],\n [9, 7, 18, 7, 4, -10, -7, -18, -18],\n [15, 13, 6, -18, -3, -14, 3, 1... | 61 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[18, -7, -16, -18, 14, -9, 10, -6, -7],\n [12, -17, 16, 4, -2, 7, -11, 10, 7],\n [-9, 7, 15, -12, -15, -8, 10, 17, 6],\n [2, 17, -9, 18, -10, 5, 16, 16, 17],\n [-1... | 52 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-7, -10, -9, -2, -12, -6, -10, 8, -17],\n [-14, 10, 18, 0, -11, -18, 3, -2, -12],\n [6, -15, 17, -13, 12, 0, 8, -9, 7],\n [0, -16, -6, 9, 1, 9, -11, -18, -16],\n [-6, 9, 6, 14, -13, 13, 2... | 57 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -6, 9, 10, -6, 16, -13, -1, -14],\n [6, -17, -9, 11, -14, 14, -18, -1, 13],\n [-8, 2, 7, 6, 3, 8, -6, 14, 15],\n [16, -18, 2, -13, 9, -2, -14, 12, -14],\n [-16, 4, 18, 18, -9, -9, 0, -2, 2],\n [-5, -10, -18, -6, -15, -18, 13, 15, ... | 54 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-4, 11, -2, -14, 10, -15, -9, -2, -9],\n [-2, 1, 5, -14, 15, -13, -17, -6, -8],\n [4, -3, 12, -8, -3, -11, -15, -15, 6],\n [-16, 13, -16, 8, 10, 13, 0, 2, -14],\n [-1, 9, 3, 2, -13, -18, ... | 53 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 7, 6, -2, -6, 1, 6, -15, -9],\n [-16, -1, 17, 3, 15, -11, 0, 18, -13],\n [7, 15, -13, 18, 14, 3, 2, -13, -13],\n [-15, 11, -8, 11, 12, 5, -10, -16, 12],\n [18, 17, 5, 12, -13, -17, 1, 9, -8],\n... | 61 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-18, 18, -10, -2, -10, -8, -4, 5, 16],\n [11, 12, -14, -5, -8, -10, 15, -7, 16],\n [16, -18, 3, 10, -11, -8, 18, -5, 11],\n [16, 2, 18, -14, 0, -5, 7, -15, 6],\n ... | 60 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[10, -15, -7, -17, 8, 12, 17, 17, 7],\n [8, -14, 1, -8, -9, -13, -11, 4, 7],\n [-7, 7, -6, -1, 6, 14, -7, 17, -15],\n [-14, 18, -11, 9, 12, -10, 10, -5, 3],\n [-8, 4, -18, 18, 2, 7, 17, 4, -18],\n [-4... | 54 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[13, -6, 11, 4, 0, 13, 11, 10, 10],\n [11, -3, 0, -1, -18, -5, -17, 9, 11],\n [-15, -18, -11, 10, -16, 13, -9, -9, 0],\n [15, 14, 4, 9, 13, -12, 10, -11, -18],\n [-16, 5, 4, -11, 1... | 56 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, -10, 15, 16, 3, 5, -2, -9, 11],\n [4, 13, -2, -2, -5, -10, -17, 6, -10],\n [3, -15, 7, 10, 15, 4, 18, -8, -13],\n [-1, 2, 17, 15, -2, 18, 6, -7, 4],\n [3, 2, 8, 12, -13, 8, 15, -7, -12],\n [-9, -2, 7, 2, 9, -17, -18, 17, 7],\n [1... | 58 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-16, 18, 11, 15, -7, 0, 18, -2, -9],\n [-7, -3, 5, 0, -11, 12, 2, -2, 4],\n [18, -3, -13, -11, 6, -1, 6, -7, -4],\n [7, 7, 13, -9, -3, -12, -2, 4, 7],\n [2, 3, -1... | 45 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -3, -9, 11, 6, 1, -14, -18, 11],\n [-16, -5, 11, -15, -1, 18, 6, -18, -4],\n [-10, -4, 5, -15, -7, 18, 18, -13, 5],\n [-8, -6, 15, 6, -12, -15, -11, 1, 10],\n [-9, 15, 7, -16, -13, -14, -14, 4, -10],\n [16, 1... | 240 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-1, -13, 18, -6, 9, -14, -6, -2, 13],\n [10, -16, 15, 8, -6, 14, -13, 5, 0],\n [-3, 9, 14, -6, 6, 17, 8, -12, -14],\n [12, 4, -9, 13, 11, 12, -1, 17, -17],\n [-5, -6, 10, -7, -17, 13, -6, 8, -2],\n [12, 15, 5, 16, -13, 0, 11, -12, -9... | 59 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[16, -7, -12, 10, -8, 14, -13, -4, 13],\n [-8, 4, 7, 15, 15, 10, -15, -2, 16],\n [-6, -4, 10, 10, -8, 13, -17, -5, 1],\n [3, -8, 8, -16, -2, 9, 10, 2, -3],\n [18, 1, -13, 0, -14, -16, ... | 235 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -11, 2, -1, 11, -1, 12, 13, -8],\n [6, 14, -11, -8, 3, 5, -2, -7, 13],\n [-4, -3, 3, 9, 1, 14, -9, 13, 14],\n [-17, 14, 14, -6, 11, 14, -6, 7, 3],\n [-17, 7, -4, 15, -8, -16, -13, -10, -13],\n [-... | 46 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[13, -16, 9, -9, 16, 10, -4, 14, -12],\n [-7, 11, 2, 12, 5, 1, 18, -15, 9],\n [1, 5, 13, 17, 15, 17, -17, -4, 15],\n [17, -13, -7, -16, -1, 2, -4, 14, 16],\n [7, -11, 17, 11, 4, -5, -5, -17, 18],\n [-14, -5, 6, 1, -17... | 60 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[18, 18, -7, 18, 9, -4, -13, 1, -5],\n [-17, -10, 18, 1, 7, 10, -18, 16, -13],\n [18, -14, 14, -5, -7, 1, 5, 15, 6],\n [10, 12, 4, 1, 4, -3, -11, 2, -18],\n [-11, 10, 13, -14, 3, 15, -18, 7, -9],\n [11, -1, -2, 7,... | 256 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-6, 4, 0, -8, -18, 5, -12, 6, 2],\n [-4, -18, -7, -12, -4, 2, 0, 10, 6],\n [14, 13, 16, 7, -8, 16, -11, -5, -9],\n [-17, -10, -16, 2, 7, -11, -17, -13, 9],\n [10, 7, 6, -7, -14, 15, 18, -4, 17],\n [-... | 55 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[12, -9, -6, 12, -12, 17, 1, -15, -12],\n [-18, -6, 3, 2, 3, 9, -10, 7, -10],\n [-4, -9, 5, -11, 5, -3, 7, 8, 18],\n [-15, 5, 0, 17, -9, 6, -1, 0, 17],... | 59 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-14, 8, 13, 2, -11, -11, -16, -16, 3],\n [-13, -17, 4, -17, -2, 16, 15, 4, 11],\n [-11, 3, 17, -14, -6, 10, 12, -3, 11],\n [-3, -7, -2, -3, -7, -11, 1, -16, -3],\n [11, 4, 9, -14, 1, ... | 243 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[11, -5, -13, -16, -3, -12, -5, -10, -4],\n [2, 16, -17, 8, -17, 16, -1, -5, 1],\n [-1, -9, 6, -17, 6, 14, 17, 12, -5],\n [-18, -3, -16, 16, -13, 6, -6, 15, -11],\n [2, 15, -15, 6,... | 53 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-15, -2, 18, 10, 17, 18, 16, -12, 8],\n [9, 3, -5, -12, 18, 3, -14, -17, 8],\n [2, -4, 2, -9, 4, -14, -18, -6, 2],\n [7, 2, -1, 18, 13, 17, -2, 16, -8],\n [2, 7, -15, 15, -1, 16, ... | 54 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 12, 17, -8, -4, 0, -12, 9, -14],\n [-14, 11, 13, -11, -9, 13, 9, -2, 12],\n [-11, 6, -10, -17, -4, -16, 17, -15, -5],\n [6, -9, 2, 17, -7, 8, -17, -6, 13],\n [12, -3, 13, 13, 15, -8, -9, -4, -2... | 53 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[8, 12, -4, 4, 5, -6, 3, 18, 14],\n [-16, 0, 4, 10, 11, 6, 18, -11, -3],\n [-11, -18, -14, -16, -18, -15, 16, 13, 15],\n [6, -9, 2, 8, 8, -17, -6, -10,... | 50 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[3, 5, -7, 11, 12, 17, 0, 17, 11],\n [14, -1, 9, -8, 14, -2, -13, -15, 1],\n [8, -4, -13, -5, -8, -10, 7, -3, -14],\n [-9, -16, -6, 11, -13, -2, 0, 16, 7],\n [-14, 10, 18, 1, 2, -9, -14, 17, -13],\n [7, -15, 16, -18, 5, 17, -13, 12, 1... | 52 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[8, -12, -13, -4, -1, 13, -8, 1, 5],\n [-4, -12, 2, 7, -5, 18, 2, -1, -14],\n [-16, 4, 7, 18, 5, 0, 6, 2, -7],\n [14, -15, -12, 3, 14, -2, 5, 15, 9],\n [3, -2, 15, -13, -13, 15, -18, -... | 228 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, 0, -14, -8, -7, -9, -11, 5, 9],\n [17, 18, 2, -11, -10, -4, -1, 1, -13],\n [-7, -17, -12, -3, -16, -16, 8, 14, 9],\n [-18, -11, 18, 13, 18, -15, 11, -13, 0],\n [13, -10, -7, -8, -3, -1... | 59 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[14, 2, 16, 15, -1, -8, 4, 3, -2],\n [-14, -8, 11, -4, 8, 16, 14, 1, -3],\n [15, -17, 16, 9, -13, -10, 1, -18, -11],\n [4, -16, -15, 6, -4, 2, 16, -5, 17],\n [-7, -2, -10, 16, -6, -4, -1, 14, -13],\n [8, 4, 8, 15,... | 236 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, 16, -5, 11, -15, -15, 9, -11, -17],\n [3, -3, 10, 11, -7, 16, -8, 2, 2],\n [-14, 1, 18, -16, 14, -10, -10, -15, 16],\n [-2, 15, 5, 13, -18, -11, 4, -7, -7],\n [-4, 0, 7, 10, 3, 2, 1, 10, -15],\n [-12, 9, 9, -... | 242 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[7, 2, -10, 5, 18, -2, 5, 2, -6],\n [-8, 0, -8, -6, -18, 0, -7, -11, -11],\n [-7, 14, 7, 9, -14, -11, 6, 8, 4],\n [11, 4, 1, -1, -1, -17, -15, 11, 14],\n [17, -1, 18, 0, 9, 1, 14, -7, -4],\n [-17, 10, -9, -17, -8, -6,... | 63 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[17, 16, -10, 11, 15, 13, -16, -16, 9],\n [-4, 4, -8, 13, 17, 14, 5, 15, 9],\n [18, -12, -15, 18, -18, -18, 1, 0, 10],\n [-9, -1, 9, 16, 12, 8, -8, -14, -11],\n [15, -7, -18, 12, -15, -14, 11, 5, -16],\n [-8, -15, 7, 8, 8, -13, -4... | 279 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-18, 9, 5, 16, -6, 15, -8, 17, -2],\n [16, -1, 3, 5, 0, 18, 2, -11, 9],\n [-14, -2, 18, 17, 0, 8, 15, -8, -7],\n [2, -8, 9, -14, -2, 1, -7, -13, -2],\n [0, 7, 13, -13, 17, -8, 14,... | 49 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[11, 11, 16, 0, -11, 7, -12, 11, -12],\n [-16, -18, 17, 6, 18, -18, -4, 18, -6],\n [-11, -14, -10, -18, 17, 16, -17, 4, -10],\n [15, -5, -15, 11, 12, -... | 56 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[3, 11, -15, -6, 4, -11, -1, -7, 12],\n [-5, 15, -1, 15, -8, -7, -4, 12, 10],\n [7, -1, 13, 3, -2, 4, 5, -11, -13],\n [-14, 10, 9, -8, -18, 0, -10, 8, 15],\n [-15, 17, -1, -4, -6, 0, -13, -7, 18],\... | 53 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-1, 18, -6, 17, 12, -17, -3, -10, -10],\n [-8, 3, 14, 17, 4, 15, -10, 5, -11],\n [-12, 17, -1, -16, 9, -13, 2, 9, -18],\n [17, 2, 16, -6, -9, -9, -6, 18, 5],\n [-17, 3, -2, 17, -5, -9, 16, 6, -16]... | 59 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 4, 6, -11, 3, -15, -16, 10, 10],\n [15, 15, 9, -6, -4, 4, 7, -15, 7],\n [-10, -14, 13, 1, -8, -4, 13, 9, 3],\n [-2, 7, -12, 7, 6, -9, 0, -8, -6],\n [-11, -15, 12, 9, -8, -18, 5, 12, 7],\n [-14, 1... | 54 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-8, 18, 6, -1, 0, 4, -1, 7, -13],\n [-15, 10, 15, -2, -3, -17, 15, -11, -6],\n [-11, 11, 13, 17, 11, -18, -2, 1, 5],\n [3, 10, 3, -10, 18, -9, 17, 18, 9],\n [9, 2, 5, -17, -11, 8, 3, 18, 8],\n [10, -16, -6, -9, 1... | 245 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-14, -18, -2, 3, 15, 10, -15, -14, -8],\n [2, 16, -7, 7, 0, -12, -12, 7, -14],\n [2, -5, -15, 4, 1, -4, 10, -11, 0],\n [9, 8, -15, -4, 16, 18, -18, -16, 5],\n [8, 17, 15, 10, 5, 5, -15, -16, 15],\... | 56 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -8, 13, -9, 3, -2, -15, 6, 2],\n [18, -18, 6, 17, -2, 5, -17, -4, 13],\n [-13, -18, 4, -2, 15, 10, -10, -6, -13],\n [-13, 1, -16, -2, -7, -18, -2, -16, 7],\n [-4, 17, 13, 13, ... | 51 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, -11, 14, -7, -8, -14, 8, -7, -2],\n [-13, 14, -14, 9, -5, -14, 14, 0, 3],\n [-14, -17, 11, -15, 14, -6, 1, -12, -4],\n [4, -5, 4, 0, 10, 1, 10, 5, -1],\n [-9, -11, 7, 10, -9, -2, -17, -13, -14],\n [9, -14, -1, 7, 1, 8, -7, -12, -... | 51 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-10, 14, 13, -13, 17, -17, 10, -15, -18],\n [0, 7, 6, -9, -4, 3, 2, 3, 17],\n [15, 11, 6, 9, -18, -15, -12, -10, 17],\n [0, -18, -9, 17, -10, 13, 13, -13, -2],\n [-9, 8, 16, 2, 6, 9, -4, -15, 10],\n [-10, 8, 7, 0, 9,... | 59 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-10, -1, 2, -17, 17, 18, -4, 9, -1],\n [15, 3, -8, -6, -15, 3, -12, 5, -15],\n [9, -4, -18, -16, -5, -18, 2, 10, -14],\n [-9, 9, 2, -12, -16, 1, 0, 16, -15],\n [-14, -18, -15, -7, 8, 4, 6, 2, 5],\n [6, 13, 13, -1... | 243 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[14, 11, -2, 13, -5, -9, 17, 15, -10],\n [9, -8, -5, 0, -4, 9, 5, -11, -10],\n [14, 14, 0, -16, -9, -18, 10, 15, -6],\n [-18, 15, 10, -6, 10, 5, 7, -2, -12],\n [-6, -14, 7, -16, -12, -18, -2, 6, -16],\n [-4, 10, 13, 7, -3, 6, 9, -10, ... | 52 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[1, 10, 10, -16, 0, -16, -5, -15, -8],\n [12, 13, 8, 11, -17, -10, 9, 12, 15],\n [-4, 6, 17, -11, -10, 18, 13, -2, 16],\n [18, 0, 10, -12, 9, -10, 9, -13, 10],\n [-2, -3, 4, 12, -1... | 53 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -4, -15, 13, 4, -13, 5, 1, 18],\n [1, -7, 14, 9, -11, -18, 18, 3, -13],\n [2, 13, 16, -4, -14, -13, 6, 10, -12],\n [-6, -1, -17, -11, -8, 14, 8, 1, -7],\n [12, 8, 13, -9, -16, 8, 16, 12, -4],\n [... | 56 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, -14, -14, 2, -7, -15, 1, 6, -5],\n [-8, 13, -8, -1, 8, -1, 4, -8, 2],\n [-14, 4, 6, -9, 3, 0, -18, -12, -15],\n [-18, -4, -7, 3, 3, -2, 10, -5, 1],\n [14, -4, -7, 1, 11, -16, 9, 7, 11],\n [-6,... | 205 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[11, 10, 0, -8, 15, -12, 15, 1, 5],\n [-9, 13, -4, 18, 1, -16, 18, -11, 4],\n [-8, -11, 10, 11, -9, 9, 17, -6, 13],\n [17, 18, 7, 3, -15, 12, -1, 5, 4],\n [3, -17, 12, -8, 9, 13, -14, -9, 5],\n [16, 4, -2, -18, 12, 12... | 49 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 13, -6, -2, 18, -13, 0, -6, 7],\n [-5, 12, -15, -11, 6, -6, 13, 9, 11],\n [-16, 9, -16, 15, -3, 3, 13, -11, -11],\n [-13, -5, 13, 16, -9, -16, -7, 12, 10],\n [-14, 6, 12, 2, 1, 3, -15, -6, 1],\n [-6, -2, 17, 14, -18, -4, -6, -2, 5... | 53 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-10, -9, 12, 4, 11, 14, -10, -18, 16],\n [-8, 15, -3, -10, 13, -4, -7, 14, -5],\n [-11, -11, 8, -7, -18, -8, 12, -2, 14],\n [13, 10, 2, 2, 4, -13, 3, 18, -11],\n [16, -8, 5, 2, -1... | 56 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -9, 0, -16, 5, -14, -16, 8, -3],\n [-4, 16, -7, 7, 15, 4, 12, 1, -7],\n [4, -15, 4, -18, 6, -17, 11, -16, 2],\n [6, 1, 3, 2, 14, -4, -4, 6, 2],\n [5, -14, -13,... | 53 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[2, -4, -2, 3, 16, -3, -11, -2, -2],\n [7, -6, -2, -2, -5, -13, 16, -5, -11],\n [-4, 8, -6, 12, 16, -13, -14, 3, 4],\n [6, 15, 7, -14, 7, 1, -13, -13, -1],\n [-15,... | 56 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, -12, -3, 16, 11, -9, -1, -14, 10],\n [15, 4, -14, 11, -13, -15, 10, 4, -13],\n [13, -1, -4, 13, -10, 18, -9, 1, -13],\n [-16, -8, -2, 13, -15, -15, -2, 0, -14],\n [13, 3, -13, 16, 3, -18, 1, 3, -8],\n [-6, -16, -10, -7, 4, -... | 240 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-7, -1, -8, -3, -1, 16, 7, -3, -13],\n [-7, -6, -15, -17, 7, 8, 8, -4, -11],\n [-12, -7, -6, -2, -2, 17, 2, -11, -14],\n [7, -3, 17, 9, 10, -7, 18, 11, 4],\n [-3, -5, -9, -12, 18, 10, -16, -4, 17],\n... | 56 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[1, 4, -8, 18, 3, -15, 10, 15, -6],\n [-10, 12, -12, -15, 0, 11, 12, 16, 2],\n [12, 0, 12, 13, -17, -9, -17, -17, 5],\n [-2, 13, -3, -3, 12, 5, -18, -8, 2],\n [-15, -12, 7, -7, 12, -2, 14,... | 57 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-17, -7, -10, -7, 7, -10, -9, 13, 15],\n [1, -17, -18, 17, 5, 8, -17, 12, -5],\n [-17, 10, -4, -7, 18, 9, 1, 5, 2],\n [-9, -5, 18, -1, 5, -5, 15, -7, 3],\n [-13, 17, 17, 3, -5, -3, 17, 6, 13],\n [14, 17, 1, -1, -16, 4, 13, -3, -14],\... | 57 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 13, -6, 1, 16, -14, -10, 10, -13],\n [6, 12, 3, -17, -14, 8, 6, -11, -18],\n [1, 4, 13, -8, 5, -8, 10, 7, -3],\n [16, 1, -16, -18, -18, -2, -17, 10, 1],\n [-13, -11, 10, 14, -16, 16, -14, 8, -7... | 50 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-11, -12, -8, -15, 6, -7, 7, -7, 18],\n [5, -3, -6, 6, -15, -8, 13, -12, -8],\n [9, 4, 4, 9, 7, 6, 10, 0, 14],\n [17, -5, -5, 16, 11, 9, -2, -16, -3],\n [11, 10, ... | 58 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[11, 11, 3, -8, -17, -7, 11, 17, -1],\n [7, -12, -18, 7, 4, 7, -13, -13, -11],\n [5, 3, 0, 18, -1, 12, 18, 11, 14],\n [-9, 18, -7, 11, 8, -10, 2, -7, 1... | 52 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[16, -13, -7, -6, 10, 0, -16, -11, -11],\n [1, -15, 2, -16, -11, 4, -3, -6, -16],\n [-10, -5, -6, -12, -4, -12, 15, 3, 5],\n [18, -18, -9, -3, -11, 6, -7, 6, -2],\n [7, -5, 17, 4, -13, -14, 6, -1,... | 233 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-18, 3, 4, 0, -1, -7, 9, 9, 14],\n [0, 9, 18, 7, 16, 15, 16, -3, -6],\n [4, 3, -3, 9, 16, -11, 3, 2, 7],\n [2, 6, -18, -13, 4, 4, 4, 13, 11],\n [-6, -1, 4, -4, 14... | 52 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[15, 6, -3, 15, 10, 0, 4, 0, 6],\n [-3, -10, -18, 0, 14, 15, -3, -1, 15],\n [6, -13, 2, -13, 13, 12, -9, 11, -1],\n [5, -10, 12, -4, -15, -10, -10, 7, -15],\n [-2, -3, -4, 16, -14,... | 52 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-6, 9, -13, -16, 16, -1, -8, 1, -14],\n [0, 3, 0, -3, 5, -15, -4, 6, 16],\n [-5, 0, 17, -12, 11, 0, 6, -3, -11],\n [-1, 9, -3, 0, -2, -6, -12, 8, -9],... | 48 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-2, 16, -14, 13, -16, 16, -5, 12, 12],\n [-2, 5, 4, -1, -5, -4, -4, -13, 8],\n [-4, 17, -11, -4, -16, -6, 15, 5, 13],\n [13, 11, -6, -18, 15, -4, -5, ... | 53 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[10, 14, -1, -12, -18, 14, -18, 5, -15],\n [-15, -1, 8, 13, 14, 9, 17, -13, -3],\n [15, 4, 5, -6, -1, -6, 18, -2, -4],\n [-1, 4, 11, 15, -15, -16, -12, -1, -12],\n [-13, 3, -18, -1... | 49 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-13, 18, -18, -18, 8, 2, -3, 7, -3],\n [9, -18, 17, -9, -2, 4, -12, -12, -4],\n [15, -15, -5, -5, -3, -12, 13, 0, -17],\n [-9, -2, 18, -7, -13, 3, 13, 1, -18],\n [-13, 0, -1, -13,... | 52 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-12, 7, 15, 11, 17, 2, -2, 14, -9],\n [-7, -3, 13, -4, 8, 9, -2, -17, 17],\n [-12, -6, -4, 6, 4, 3, 7, 14, -8],\n [-9, 6, 18, 5, 14, -2, 5, 18, -17],\n [13, 5, -10, -15, -2, -2, 11, -8, 2],\n [2, -1, 10, 5, -9, -2, -... | 55 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[14, 0, -2, 14, -7, -16, 7, 16, -11],\n [17, -12, 17, -3, 5, -18, 6, -9, -3],\n [-3, -11, 10, 9, -13, -3, 1, -3, -12],\n [-5, 7, 7, -5, -12, 14, 7, 1, -16],\n [-15, 7, -8, -17, -5, 11, -7, 7, 14],\n [-6, -5, 5, 15, 7, 2, 9, 17, -1... | 227 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, 1, 8, 18, -12, -14, -8, -4, -16],\n [-14, 4, 18, -10, -4, -16, 10, -13, -2],\n [7, 2, -11, 2, -8, -11, 5, 16, -5],\n [-5, -9, -7, 15, -9, -2, -2, -16, 12],\n [-18, -7, -15, -6, 1... | 235 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-9, -13, -2, 5, -9, -11, 2, -13, 2],\n [5, 14, -1, 9, 13, -7, 8, -9, 13],\n [7, 6, -8, 4, 15, 4, 10, 12, -12],\n [14, 2, -17, -1, 14, 18, 15, 1, 16],\n [-1, 5, -11, 11, -9, 4, -8,... | 50 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[18, -12, 7, 7, 5, -7, -3, 4, -10],\n [13, -4, 18, -6, -14, -8, -9, -6, -4],\n [-12, 9, 13, 16, -4, 17, 2, -13, -18],\n [-15, -8, 7, 18, 4, 10, 2, 8, -6],\n [4, -3, 11, -15, -3, 12, 6, -7, 7],\n [1... | 58 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[17, 18, -16, -10, -1, 16, 15, -5, -15],\n [10, -4, 9, -3, -7, -14, 15, -18, 13],\n [7, -2, 8, 5, 16, 7, 4, 3, -15],\n [-10, -15, -12, 4, -17, 5, 12, 1... | 52 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[13, -6, -14, -9, -9, 8, 2, -11, -18],\n [9, -5, 2, 11, 2, -10, -2, -14, 12],\n [0, 17, 14, -6, -5, 14, 10, 17, -9],\n [12, -13, -18, -12, 8, 2, 9, -3, 4],\n [1, 6, 9, -14, 2, -1, ... | 58 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[11, -7, -15, 5, 10, -10, -15, 5, -5],\n [-14, -1, 0, -7, -1, -2, 11, 5, -8],\n [16, 4, -2, -18, -4, 13, -10, -4, 9],\n [5, 16, 3, 8, 0, -7, 1, -18, 2],\n [-18, -9, 13, 3, -1, 13, 8, 9, -1],\n [10,... | 50 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-14, -7, -1, -17, -9, -4, 11, -2, -15],\n [-12, 12, 15, -13, 15, -4, -5, -13, 18],\n [13, -16, -16, 3, 3, -9, -16, -7, 10],\n [-2, -12, -6, -17, -15, -9, 5, -2, -13],\n [0, -14, 13, -9, -10, 8, -6, 0, 2],\n [5, -15, ... | 56 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[14, -3, 16, -16, -14, 7, -8, -12, -9],\n [15, -16, -11, 12, -8, -12, -17, -13, 13],\n [1, 15, -3, 6, -7, -12, -2, -8, -13],\n [4, 8, -13, -17, 3, 1, 6, -4, 10],\n [-11, 18, 14, 3, -14, -1... | 58 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, 14, -8, 8, 14, 2, 12, -17, 8],\n [17, -8, -1, -18, 16, 16, 12, 9, -18],\n [6, 1, -16, -17, -1, -9, -14, -10, -17],\n [15, 12, -9, -7, 17, 2, -13, -16, -9],\n [-14, 7, 2, 7, 7,... | 52 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, 10, -3, 9, 12, -5, 14, -10, 8],\n [5, -6, 7, 10, 9, 9, -11, 4, 10],\n [-14, -12, 17, 8, -17, 6, -10, 8, -18],\n [4, -9, 6, -16, -13, -13, -17, -1, 4],\n [-17, -7, 3, 18, 1, 5, 1, -... | 232 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-12, -16, -7, -12, 7, 14, 18, -4, -17],\n [-12, 13, -15, 1, 17, 13, 9, -6, -18],\n [16, 11, 17, 6, -3, 0, -18, -14, 3],\n [5, 18, 17, 17, -15, 17, -1, -3, -1],\n [3, -17, 2, 17, 10, 7, 2, -2, -3],\n [12, -10, 12, -5,... | 61 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[6, -4, -13, 10, -4, 10, -15, -1, -3],\n [-8, -5, -16, -1, 1, 6, -6, -15, -5],\n [14, 9, 18, -11, 15, -14, -14, 12, -10],\n [13, 14, -16, 11, -7, 10, -16, 7, 11],\n [-10, 7, -17, -16, -15, 6, -6, 16, 4],\n [-10, -17, 12, -17, 13, ... | 265 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 6, 0, -14, -8, -4, -11, 0, 4],\n [8, 13, 7, 8, 0, 10, 14, 0, 18],\n [0, 14, -3, 4, -12, 7, 13, -7, -11],\n [-14, 9, -14, 7, -14, 3, -4, -6, 9],\n [14, 4, 14, -1, 11, 7, -3, -6, 14],\n [7, -18, -17, -13, 5, -1, 8, -11, 9],\n [-9, -... | 48 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-13, 0, -16, -1, -10, -7, -14, -16, -8],\n [11, -15, -14, -18, 8, 9, 10, -1, -7],\n [-6, -17, 18, -3, 5, 16, 3, 17, -8],\n [10, 16, -4, 12, -3, -9, 13... | 60 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -17, 8, 16, -17, 18, 2, -14, 2],\n [10, 1, 1, 6, -17, 13, 7, -13, -16],\n [14, -18, -14, -6, 0, -7, 6, 16, -7],\n [11, -14, 15, 3, -6, -16, 1, 12, -14],\n [5, 14, -11, 5, 1, -3, -7, -6, 6],\n [13,... | 51 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[11, 0, -6, -1, 4, 14, -1, -10, 14],\n [13, -2, 0, 8, -13, 16, 18, 15, 1],\n [6, -15, -9, -9, 5, 2, -8, 8, -3],\n [7, 11, -3, -12, -3, 16, -3, -7, 16],\n [2, 17, -2, 13, -13, 5, 8, 1, 6],\n [-17, -10, 9, -16, 1, -13, 14, -18, 18],\n [... | 50 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[0, 11, 9, 16, -8, 12, 17, 11, 4],\n [0, -7, -4, 12, 18, 18, -4, 10, 7],\n [-17, 1, -4, -15, 3, 4, 7, -8, 9],\n [-17, -11, 10, -8, 18, -1, -5, -9, 16],\n [-10, 16, -8, -7, -16, -5, 9, -8, 6],\n [2, -9... | 57 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-2, 13, -12, 11, 9, -5, 11, -2, 13],\n [-13, 5, -13, 8, -1, 5, 18, 5, 15],\n [-4, -8, 3, 5, -18, -1, -7, 9, -12],\n [4, 2, 15, -8, 3, 16, 10, 9, -1],\n [-5, -1, 9, 5, -11, -11, -15, 8, 17],\n [-14... | 49 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, -3, 8, -9, -15, 0, 9, 2, -5],\n [14, -9, 0, 11, 3, -16, 18, -1, -8],\n [-17, -7, -13, 10, 11, -17, -10, -17, 10],\n [14, -9, 15, -11, 18, 14, -13, 0, 13],\n [8, -18, 14, 13, -14, -2, -11, 15,... | 254 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, -9, -10, -16, -8, -7, -9, 6, 6],\n [-8, 17, 7, -5, -18, -15, 11, -7, 16],\n [-6, 12, 4, -15, -3, -12, 3, 10, -8],\n [14, 10, -7, -12, 7, -10, 15, -6, 17],\n [6, 5, -2, -17, -6, 12, 10, 9, 8],\n [-4, 12, -4, 14, 1, -7, 18, -10, 4... | 58 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[4, 10, 1, -3, -2, -3, 0, -11, 10],\n [17, 7, 12, -7, -2, -4, -10, -7, 13],\n [6, -1, -4, 13, -13, 16, 15, -14, -1],\n [-3, -11, 6, 13, 7, 3, 12, -9, -7],\n [9, -13, 1, -14, 4, -10... | 47 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-16, -1, 0, -13, -3, -11, -1, -7, -9],\n [-12, -18, 17, 2, 18, 5, 6, -12, -2],\n [10, 11, -12, 14, -12, 5, -8, -10, -7],\n [16, -15, 17, 9, -6, 4, 0, 18, 5],\n [-3, 14, -7, 15, -12, -8, 12, 10, -6],\n [12, -17, -... | 258 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-10, 6, 14, -18, -13, -1, -9, 9, -8],\n [14, -18, -6, 18, 1, -18, -16, -1, -5],\n [12, 8, -2, 10, 17, 18, 7, -2, 3],\n [6, -17, 3, -14, -15, 17, -13, 2, -6],\n [18, 6, 7, 1, 14, -5, 17, -2, 2],\n... | 233 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, -8, 15, -9, -9, -13, 17, 5, -7],\n [4, 8, 18, -13, -18, -13, 3, 5, 6],\n [-4, 7, -11, 5, -13, 16, -18, 17, -7],\n [-8, -7, -12, -8, 17, 12, 14, -6, -1],\n [5, -10, 12, -9, -17, -4, -16, 12, -13],\n [-16, -8, -4, 9, -9, -12, -4, -1... | 55 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[5, -5, 17, -14, -8, 5, 12, -6, -3],\n [5, -6, 5, 7, -17, -3, -18, -8, 16],\n [10, 18, -2, 9, 10, -16, -9, -5, -7],\n [11, 13, 13, 13, 7, -18, -17, -2, 11],\n [-12, 8, -10, 3, 15, -18, -10... | 61 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-17, 14, 0, -10, 9, 16, -9, -18, 2],\n [-10, -4, 16, -14, 3, 4, -12, 4, 6],\n [8, -13, 15, -10, 14, -13, 18, 12, 15],\n [10, -5, 17, 17, -4, -11, 7, 17, 2],\n [9, -15, -3, 3, -7, -3, ... | 246 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-11, 2, -6, -14, -13, 11, 12, -2, -8],\n [1, -10, -17, 18, -18, -15, 17, 6, -16],\n [-10, 3, 4, -7, -9, 15, -9, 11, 3],\n [-13, -17, 11, -17, 13, -3, -7, -18, -11],\n [-6, -4, -11, -9, -14, 0, -8,... | 49 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-10, 9, -6, 16, -6, 12, 2, 13, 15],\n [-11, -17, 13, 9, 18, -18, -9, -15, 16],\n [-9, -8, -5, -7, -2, -3, 16, -17, -8],\n [-16, 10, -1, 1, -5, 15, 12, -1, 11],\n [6, 0, -11, 9, -11, 12, -16, -16, ... | 52 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, 9, -17, -9, 3, -6, -10, 14, -5],\n [1, -4, 13, 14, -2, 5, 11, -6, -3],\n [-17, -2, 13, -11, -16, -7, 1, -3, -5],\n [-3, 14, 11, -7, -4, -1, 9, 4, -5],\n [11, 14, -4, -12, -4, -8, 10, ... | 56 | MATH |
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 7