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 sum of all singular values:\n[[-3, 16, 0, -3, 14, 12, 3, 1, -13],\n [16, -16, 13, -6, -5, -11, 0, -5, -8],\n [16, 17, -16, 6, -6, -3, 9, 8, -9],\n [-1, -11, -12, 3, -10, 10, 18, 10, 9],\n [2, 14, 7, -4, -17, -7, 14... | 237 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[12, -15, 11, -15, 12, 15, -15, 1, -1],\n [-11, -17, -10, -3, 3, -7, -14, -4, -11],\n [5, 0, 18, -1, 2, -5, -4, -16, -8],\n [-16, 11, -13, -13, 12, 3, 2, -13, 10],\n [-8, 3, -13, 1... | 60 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-16, 17, 12, 6, 5, -18, 12, 18, -8],\n [-16, -7, 1, 11, -9, -4, 2, -1, 13],\n [0, 11, 14, 3, 10, 5, -15, -7, 17],\n [-15, -14, 0, 12, -12, -7, -9, 10, 2],\n [-6, 4, -13, 12, -10, 5, -3, -8, 17],\n [-... | 56 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[7, -10, -15, 12, -14, -12, 9, -5, 5],\n [-14, 15, 9, -11, 2, 5, 5, -6, -4],\n [6, 9, -11, 12, -12, -2, 16, 3, -12],\n [-9, 9, 10, 16, 3, -10, 17, -11, 11],\n [11, 12, 3, 12, 9, -14, -2, -8, 3],\n [6, -6, 17, -8, -14, -5, 3, -16, ... | 242 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-12, -3, 17, -15, -1, 13, 13, -1, 18],\n [9, -17, 18, 18, -17, 0, -14, -6, 3],\n [-12, -17, -5, 6, 7, -14, 1, -7, 17],\n [12, -2, -3, -9, 16, 14, 16, 8, -12],\n [8, -7, 14, -6, -17, -... | 228 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[12, 6, -2, 7, -2, 0, 8, -12, 7],\n [-14, -17, -3, -8, 4, 16, -13, 18, -18],\n [14, -1, -16, 0, -9, 1, -8, 13, 1],\n [13, 18, 3, -15, -6, -13, 10, -17, 6],\n [13, 7, 7, 3, -9, 4, -... | 56 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 10, 11, -4, -15, 14, -10, -3, 7],\n [8, -8, 7, -5, -18, -8, 11, 5, -15],\n [3, -11, -3, 14, 14, -9, -17, -15, 4],\n [8, 14, 14, 1, -6, -8, 0, 13, -16],\n [-6, 9, 3, 0, 12, 1, 5... | 51 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-5, -18, 1, 3, 12, 12, 9, -7, -3],\n [14, 16, -15, -9, 15, -16, 12, 12, -18],\n [-14, -14, -17, -4, -18, 2, 18, -12, -8],\n [7, -17, 11, -5, -14, 12, 13, 15, -9],\n [12, 8, -1, -14, -2, -8, -14, 18, ... | 60 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[16, 5, -9, 5, -1, -11, -6, -3, -5],\n [-10, -10, -14, -8, 0, -9, -3, 10, -14],\n [-1, 16, 17, 3, 5, -7, -7, 16, 0],\n [18, -5, 4, 3, -8, -17, -9, -14, 11],\n [2, 14, 6, -12, 9, -3, 18, -16, 0],\n [-7, 0, -8, -16, -17, 7, 3, -2, 1... | 232 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[11, 3, -14, -17, 14, -3, -12, 2, 16],\n [3, 3, -13, 14, 6, -1, 16, 5, 4],\n [14, 10, -9, -4, -9, 7, 10, 15, -1],\n [-17, 6, 2, 12, 3, -10, 8, 6, 6],\n [8, -9, 11, -15, 2, 11, 14, 7, -17],\n [4, 12, -... | 49 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[1, 4, 7, -5, 12, 8, -10, 4, -9],\n [4, -9, -17, 18, -18, -1, 16, -12, 3],\n [6, 4, -10, 8, -8, 8, 9, -1, 17],\n [15, -6, 11, 9, 3, 5, 11, 1, -13],\n [14, -4, -4, 13, -5, -11, 17, 3, 1],\n [5, 2, 9, 4, 5, 4, -15, -15, 11],\n [9, 12, 1... | 56 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[16, -10, -4, 0, 18, -13, 17, -14, -16],\n [-9, -6, -15, 14, 15, 17, 14, 2, -14],\n [-6, -2, -9, -9, -17, 2, -18, 11, -1],\n [16, 3, -16, -13, 17, -3, ... | 55 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-17, -14, -17, -9, 12, 14, -13, -5, -5],\n [-4, 14, 12, -2, -4, 1, 2, 10, -10],\n [10, 15, -10, 11, -2, -15, 13, 13, -12],\n [13, -14, -16, 1, -2, -3, -8, -6, -1],\n [-5, 15, -7, 3, 2, 7, -17, -3, 15],\n [-8, 0, 11, ... | 56 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-9, 0, 12, -9, 18, -6, -2, -14, 2],\n [1, -12, -4, -4, 4, 14, -17, 13, -4],\n [-12, -10, 9, 3, -16, -17, 3, 6, 6],\n [13, -12, 12, 18, -15, 14, -4, -10, -13],\n [12, 15, -6, 17, 13, 3, 10, -8, -13],\n [-14, -18, -9, -9, 5, -12, 3, 2,... | 60 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 16, 8, 1, 12, -3, -5, 13, 13],\n [-17, 3, 18, -2, 13, -2, 15, -12, 10],\n [-2, 5, -11, 4, 14, 10, 0, -14, 18],\n [4, 7, 5, 2, 14, 7, -9, 10, 16],\n [9, -7, -12, -3, 1, 10, 16, 9, -12],\n [3, -5... | 51 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, -5, -10, 8, 0, 6, 13, 3, 10],\n [9, -6, 9, -16, 11, -8, -17, -10, 14],\n [7, -3, 6, -18, 2, 1, -14, -2, -18],\n [-6, -1, -15, -5, -14, 14, 7, -15, 11],\n [-2, 9, -13, 8, 17, -12, -18, -9, -6],\n [13, -5, 14, 11, -10, -13, -9, -8, ... | 58 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[16, 18, 14, 18, 16, -1, 0, -9, -15],\n [11, 14, -15, -10, -2, 5, -6, 7, 0],\n [-2, 11, 7, -6, -1, 2, 15, -10, 11],\n [10, 10, 0, -11, -2, -7, -4, -14, 15],\n [-16, -14, 15, -10, 5, -14, 8, 1, -17]... | 63 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, 5, -1, 11, 9, -5, 2, 15, -14],\n [12, -16, 4, 11, 11, 17, -12, -14, -13],\n [-5, -8, 18, -17, 12, 8, -3, -17, 7],\n [-3, -10, -10, -14, 17, -12, 13, 10, 18],\n [-16, 11, 12, 8, -13, 10, -10, 1, -8],\n [0, -9, -14... | 52 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[14, 18, -18, 16, -9, 0, -8, 16, -17],\n [-16, -4, 9, -17, 11, -14, -13, -14, -7],\n [-15, 5, 6, 7, 14, 2, 4, 18, 18],\n [-7, 18, 2, -6, 14, -13, -7, 11, 18],\n [-1, -3, -12, -18, 9, -16, ... | 58 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[12, 9, 18, -3, -10, -17, -17, 13, -3],\n [-6, 8, 12, 14, 2, 0, -6, 0, 16],\n [16, 14, -16, 2, 4, -8, -15, -15, -4],\n [9, 17, -11, 5, 15, -4, 4, 8, -5],\n [-17, 16, -12, -3, 3, 9, 13, -12, 3],\n [-17, -11, -12, 2, 3, 16, -1, -10,... | 265 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-3, -5, 11, 13, -7, 8, 7, 10, 4],\n [3, 1, -3, 12, -16, 2, -14, 1, 4],\n [13, -10, -16, 8, 8, -9, -3, 5, 4],\n [-10, -17, -13, 18, 16, -12, -4, 2, 17],\n [4, 10, -6, -14, -18, 1, -18, 16, -12],\n [16, 15, -14, 10, 8,... | 57 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-1, -4, -16, 4, -17, -15, 7, 0, -9],\n [3, -13, -18, -3, -12, 5, 16, -5, -15],\n [-4, 4, 0, -5, 8, 17, 3, -8, -15],\n [13, 5, 15, -16, -17, 4, 1, -11, 16],\n [-16, 13, 12, 12, -18, -7, -1... | 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[[9, 5, -14, -6, -1, -2, 11, 0, 3],\n [-1, 7, -4, 9, 11, 9, 1, -15, -15],\n [18, -4, 15, -8, 4, 16, 16, -8, -17],\n [-4, 9, 12, 13, 15, 3, 10, -11, 3],\... | 47 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[10, -7, -15, 7, -15, -8, -17, 12, -16],\n [6, 15, -18, -14, 12, 17, -16, -7, -3],\n [-11, -8, -5, 8, -1, -11, 14, -15, 11],\n [1, 11, 8, 6, -13, -14, -5, -5, 15],\n [6, -1, 1, -11, 7, 2, ... | 55 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-6, 0, -13, -1, -10, -2, -15, -13, -8],\n [7, -8, -11, -16, -17, -1, -17, 7, -7],\n [18, 7, 17, -3, -5, -17, 2, -12, -8],\n [10, 18, 9, -15, -15, 8, -13, 15, -1],\n [11, 14, 1, 17, -14, 16, 0, -7, 7],\n [0, -8, 1, -10, 1, 8, -14,... | 248 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-14, 0, -12, 3, 7, 6, -13, -14, 3],\n [12, 3, -8, 13, -2, 3, -3, -4, -11],\n [-16, -6, 11, 9, -10, -7, 6, 18, 2],\n [0, -11, -16, 3, -18, 0, 2, -6, 8],\n [-2, 1, 11, -8, 8, 9, 7, ... | 44 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[6, 16, -14, -16, 15, -7, 8, -14, 3],\n [-15, 9, -12, 15, -17, -10, -4, 12, 17],\n [-4, 14, 12, 8, -17, -10, -18, 0, -10],\n [-17, 18, -18, -7, 7, -9, -18, -18, 12],\n [-8, -14, 16, -8, -15, 2, 17, 9, -11],\n [1, 2, 16, 13, 17, -14, -... | 63 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[8, -5, 4, 1, -13, 5, 4, 17, -7],\n [-17, 8, 13, 10, 14, 10, 14, 17, -2],\n [-9, -18, -2, 9, 17, 8, 18, 6, 15],\n [-16, 10, 16, -9, -18, -18, 13, 3, 0],\n [16, -13, 15, -4, -16, 18, 3,... | 251 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, -8, -14, 10, -13, -7, -12, -7, 14],\n [0, 17, 0, 2, 0, -10, 3, 0, 18],\n [-8, 6, 16, -14, 12, -5, -6, 15, 15],\n [-1, -13, 2, -14, -17, -13, -11, -17, 4],\n [1, -15, -4, 11, 1, 5, -10, 2, -6],\n... | 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[[6, 14, -9, 5, -14, -9, 8, 17, 14],\n [9, -16, 12, 10, 2, 13, 9, 2, 16],\n [11, -2, 10, -17, 14, -15, 6, -14, -15],\n [10, 18, -11, 1, -13, 17, 13, -14... | 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[[9, 12, -6, 6, -13, -16, 3, 13, 11],\n [-12, 6, -17, -11, 14, 9, -9, -1, -6],\n [2, 14, 4, -18, 2, -14, 16, -1, 17],\n [10, 7, 17, -1, 10, 12, -6, 11, ... | 48 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 3, 12, 6, 11, -15, 7, -12, -7],\n [-18, -13, -18, -11, 14, -15, -13, -16, -4],\n [-13, -13, 18, 8, -14, -2, 4, -2, 4],\n [14, -17, -9, 0, -10, -4, 5, -7, 3],\n [-1, -17, -4, -10, 3, -2, -5, 12... | 243 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-16, -6, 2, 3, 10, 6, 4, -7, 4],\n [-14, 10, -14, 16, 16, -2, 11, -17, -4],\n [4, 7, -8, 5, -10, -5, 5, -12, -9],\n [14, 14, 8, -11, -5, -12, -1, 7, -4],\n [14, -8, 0, -1, 3, 17, -1, ... | 224 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[17, -16, 0, -11, 9, -18, 11, -8, 10],\n [12, -9, 16, 10, 18, -17, -18, 13, 5],\n [-17, -16, -10, 5, -7, 15, 15, 4, 0],\n [13, 9, 7, -7, 12, -8, -15, -1, 10],\n [12, 9, 8, 11, -8, -5, -15, 17, -18],\n [18, 14, 2, 5, -6, 15, 10, 17... | 255 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-14, -6, -15, -17, 18, 15, -13, 7, -8],\n [-18, 15, 2, -9, -14, 7, 0, 2, 15],\n [10, -4, -3, -1, -18, -8, 17, 13, 9],\n [-13, -12, 5, -9, 11, -2, -11,... | 52 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[8, 7, -12, -8, 3, 0, 1, 0, 0],\n [17, 8, -2, -1, 1, -11, -8, 11, -7],\n [4, -13, 16, -4, 9, -12, -13, 8, -17],\n [-13, 13, 10, 15, -18, -4, -9, -9, -9],\n [18, 13, 17, 6, -4, -10,... | 53 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-13, -2, -11, 16, 5, -16, -2, 17, -2],\n [11, 6, 3, 18, -8, -7, 2, -4, -7],\n [3, 16, -3, 14, -5, -1, -3, -16, 7],\n [-4, 17, 8, -2, -5, -17, 8, 5, 16],\n [-15, 7, 17, -15, 15, -6, -1... | 260 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, 3, -3, 9, 6, -5, 2, 0, -6],\n [-17, 17, -5, 15, -1, 5, 11, 0, 17],\n [2, 0, 7, 16, -15, 2, -16, -14, 10],\n [0, -2, 15, 1, 9, -10, -16, -9, 2],\n [-15, 3, -12, -7, -8, 3, 10, 8, 1],\n [-5, -12, -... | 49 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-16, -11, 6, 17, 2, 15, 8, -10, -9],\n [8, 6, -6, -15, -3, -7, 6, -3, -17],\n [-10, -6, -5, -7, 16, 3, 2, -16, 3],\n [-10, -16, 12, 18, -13, -5, 0, -1, -12],\n [17, 10, -16, -6, 17, 6, 9, -8, -10... | 243 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-10, 8, -4, 6, -1, 11, 18, -3, -7],\n [-2, 6, -4, 6, 2, 0, 5, -12, -7],\n [-8, 14, 6, 15, -8, -3, 13, -4, -4],\n [-12, 18, -17, -13, 17, 9, 3, 18, -14... | 44 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -17, -7, 3, 3, 3, -13, 18, 1],\n [-13, -10, 10, 18, -14, -6, 8, 4, 18],\n [15, 6, 18, 4, 9, 7, -7, -16, -10],\n [-4, -11, 9, 7, -3, 15, 1, -18, 5],\n [10, -15, -15, -16, -17, 10, 9, -7, -4],\... | 251 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-12, -4, 6, 3, 4, -9, 17, 18, -12],\n [6, 5, -14, 2, 1, 10, 18, 1, -1],\n [-15, -8, 3, -5, 9, -15, -3, 4, -6],\n [1, -14, 0, 2, -14, -5, 17, -13, -14],\n [5, 10, 10, -17, -13, 15, -7, 3, ... | 57 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[15, -16, 13, -17, -3, -2, -7, -14, -15],\n [-3, -1, 1, -10, -3, 16, 10, 11, 1],\n [3, 4, 17, 3, -18, 2, 0, -11, -14],\n [10, -1, 10, -4, 12, -4, -16, 14, 5],\n [5, -6, 8, 14, 0, 6, -13, 14, 6],\n [4, -2, 2, 1, -7, -6, -1, 3, 5],\... | 221 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-9, 9, 2, 9, 3, 0, 5, 9, -6],\n [-10, -10, 2, 5, 12, 10, -9, -15, -16],\n [-6, 2, -11, -10, -18, -5, -7, 17, 3],\n [17, -3, -8, -16, 15, 6, 7, -16, 1],\n [12, -18, 7, 6, -8, -3, 1, -17, 10],\n [-12, 6, -15, 15, 6, -11, 13, -1, -8],\n... | 54 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[9, -18, -5, 0, 12, -4, 0, 13, 12],\n [18, 7, 6, -11, -15, 12, 13, 15, -16],\n [7, -15, -17, 0, 4, 6, -12, -11, -16],\n [4, 14, 9, 3, 16, 15, 11, 17, -5],\n [-10, 3, 9, -5, -4, 18, 5, 15, -16],\n [4, 1, -4, -3, -1... | 244 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, -14, -17, -9, 7, 5, 7, -3, 6],\n [-13, -7, -10, -11, 12, 13, -12, 13, 6],\n [14, 9, -8, 12, -9, -17, -15, 3, 9],\n [-9, -17, 12, 4, -3, -10, -13, 6, -15],\n [-7, 5, 8, -16, -7, 11, -7, 3, -4],\n [9, -2, 6, -1... | 238 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, -7, 1, 15, 17, 2, 0, 16, -11],\n [3, -1, -11, -17, 1, -14, 11, -1, 4],\n [-17, 18, 13, -18, -18, 12, -11, -16, -7],\n [15, 6, 17, -12, -4, 2, 6, 18, -3],\n [-18, 18, -5, 15, -17, 12, 0, 0, 4]... | 267 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, 8, -14, -14, -10, 8, -15, 5, 8],\n [-18, 13, -3, 4, 9, 1, -2, 17, -11],\n [-1, -6, -10, 18, 11, 9, -1, 1, 17],\n [0, -14, 15, -2, 9, 17, 11, -1, -13],\n [7, -4, -18, -2, 12, -17, 17,... | 62 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[17, 0, 12, 11, 18, 6, -6, -7, -10],\n [-10, 8, 12, -13, 10, 11, -8, -13, 12],\n [16, -7, -13, 7, 18, 13, -15, -16, -17],\n [1, 0, -7, 17, 9, -10, -8, 11, -17],\n [14, -12, 2, -7, 2, 4, -13, -5, 13... | 51 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-4, 6, -5, 5, -17, 15, 4, -11, -14],\n [10, 14, 1, -3, 18, 18, 5, 10, 16],\n [-10, 3, 1, -15, 17, -7, 4, -11, -9],\n [4, 10, 13, -5, -3, -2, 1, -7, -10],\n [-11, 18, 2, 13, 18, -1, 10, -12, 18],\... | 253 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-14, 2, 3, 1, -7, -13, 10, 16, -8],\n [14, 6, -5, 10, -6, -4, -11, 14, -8],\n [-4, 2, 17, -13, 6, -18, 14, 13, -17],\n [6, 14, -8, 0, 6, 9, -9, 12, -3],\n [-1, 3, 16, -7, 9, -10, 11, -1, 5],\n [0, -5... | 53 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 6, -4, -2, 17, 10, 14, 13, -11],\n [-6, -2, 2, -5, 6, 5, 14, -11, 9],\n [0, -8, -9, -18, -14, -3, 1, 1, 9],\n [-14, -16, 11, 4, 15, 9, -18, 8, 15],\n [12, 13, -12, 15, -15, 0, 3, 10, 15],\n [1... | 261 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[1, -6, 3, -4, 12, 13, -6, 6, 2],\n [-15, -4, 2, -11, 12, -9, 2, -2, -14],\n [-6, 2, -7, 6, 9, -17, 2, 3, -17],\n [11, -18, -6, -16, 1, -14, -17, 7, 10],\n [-1, -10, 3, 9, -7, 18, -1, 15, -16],\n ... | 234 | 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, 14, 13, 17, 17, 15, -17, -6, -9],\n [-12, -16, 8, -5, 11, 15, 4, -2, -4],\n [-12, -16, -10, -16, 16, -11, 7, -4, -14],\n [-6, -4, -7, 16, -11, -9... | 50 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 11, -17, -2, -12, 3, -9, 7, -6],\n [9, 17, -8, -10, -3, -2, -14, -14, 12],\n [-17, 8, 0, 6, -6, 10, 0, 16, 6],\n [-10, 16, -4, 3, -6, 11, 2, 6, 6],\n [3, -16, -10, 5, 13, -2, 5, -11, -13],\n [... | 218 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, 9, 11, -4, 2, -7, -8, -13, -16],\n [-4, 15, -15, 15, -13, 3, 18, 13, 9],\n [7, -15, -9, 8, 1, 17, -14, -2, 13],\n [16, 4, -6, -18, 12, 0, 4, 15, -15],\n [15, 11, -9, -13, -7, -7, -1, 17, 16],\n [6, 3, 11, 10,... | 258 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[3, -8, -9, -11, 9, 4, -13, -5, 5],\n [-10, 6, 11, 3, -17, 6, 5, 18, -16],\n [7, 11, 10, -12, -10, 11, -3, -5, 7],\n [18, -9, 11, 3, 11, 13, -5, 4, -2],\n [17, 10, 5, -8, -4, 3, 8, 15, 14],\n [2, 5, 1, -15, 18, 18, 14, 12, 15],\n ... | 243 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[13, -4, 3, -11, -11, 17, 1, 18, -11],\n [-5, 1, 16, 6, -1, 2, 18, 12, -13],\n [1, 9, 17, 7, -6, -15, 15, 18, 15],\n [-3, 4, 4, -4, 6, 10, 17, -4, 18],\n [16, 18, ... | 53 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[11, -13, -18, -15, 6, -8, 18, -7, 10],\n [15, -1, -10, -7, -10, -18, -12, 15, 13],\n [9, 7, 17, -5, 12, -3, -8, -8, -7],\n [-10, 3, -10, -16, 16, 11, 7, -11, 13],\n [3, -11, -17, -5, -14,... | 55 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, 7, -18, 7, -10, 16, -1, 0, -3],\n [9, -16, -1, -6, 8, 5, 10, 3, 7],\n [1, 5, -7, -1, -7, 13, 4, -15, -7],\n [-2, 2, 18, 10, -13, 9, -11, 12, 1],\n [-3, -6, -4, -6, -17, 1, 9, -1, -12... | 51 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[7, -7, 7, 3, -18, -7, 5, 11, -5],\n [4, -17, -16, -13, 0, 2, 1, 2, -15],\n [6, -12, -12, 14, 7, -2, -11, 7, -4],\n [1, 0, -12, -18, 18, -1, -11, -4, -13],\n [18, 3, -8, 7, -11, -10, -... | 260 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[11, -14, 18, 7, 9, 0, 2, 9, 0],\n [17, -8, 0, -14, -17, 6, 7, 11, -2],\n [2, 1, -1, -3, 9, -7, -13, 5, -13],\n [-2, 0, 9, 10, -12, 0, -11, -11, -14],\n [15, 2, -15, 17, -14, 4, 0,... | 58 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -9, 7, 4, -2, 11, 8, -8, -15],\n [-1, 0, 17, 7, -18, 1, -8, 6, 0],\n [13, -18, -18, -16, 13, 17, -11, 11, 15],\n [-11, 6, 7, 8, 0, 4, -3, -11, 11],\n [-11, -8, -12, 2, 15, 2, -14, -2, ... | 59 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -4, 18, -2, 1, -15, 15, 15, 12],\n [15, -16, 9, 18, 10, -4, 17, 16, -9],\n [-2, 11, -11, 4, 0, 18, 17, -15, 7],\n [8, -6, 15, 14, 7, 1, -11, -3, -14],\n [15, 8, 17, -15, -12,... | 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[[-15, 15, 10, 2, 7, 13, 3, -5, 15],\n [18, -18, 13, 13, 5, 2, -7, 1, 18],\n [1, -17, -5, -2, 5, 11, -4, 15, -11],\n [-16, -8, 8, -10, -4, 13, -8, -16, ... | 52 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, -15, 5, 0, 5, 2, -2, -11, 12],\n [0, -8, 4, 18, 9, 4, -7, -3, -3],\n [-5, -12, 2, 2, 16, 5, -18, -5, 1],\n [9, -1, -16, 8, -13, -15, -18, 2, 16],\n [9, -1, 16, 2, -3, 7, -10, 4, -17],\n [-16, 14, 5, 4, -13, 2,... | 243 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-16, 16, 14, -12, 16, -16, -1, -16, 8],\n [-10, -2, -14, -15, -5, 10, -8, 3, -14],\n [-7, 2, -4, 5, -6, 13, 7, 7, 17],\n [11, -10, 5, -1, -10, 3, 2, -12, -7],\n [... | 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[[6, 2, -6, -6, 11, -6, -12, -7, -17],\n [-5, -2, -6, -18, -18, 7, -6, 15, -10],\n [0, 4, 9, 11, -12, -5, -17, -7, -17],\n [9, 9, -7, 11, 3, -1, -5, 6, ... | 52 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, 8, 9, -7, -14, -11, -2, -11, 15],\n [4, -1, -9, -14, -2, -8, 0, 2, -16],\n [-18, 5, 17, -13, -9, 15, 5, 4, 1],\n [16, 15, 17, -3, 4, -18, -10, -7, 18],\n [-2, -16, 10, 12, 16, 7, -6, 0, 13],\n [8, -6, 15, 0,... | 236 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, -14, 14, 16, 15, 14, -9, -16, 10],\n [16, 12, -4, -18, 0, 18, 8, 2, -12],\n [14, -17, -5, -16, -5, -14, -2, -18, 9],\n [-5, -2, -4, -12, -12, 5, 7, -5, 0],\n [7, -3, 15, -17, -18,... | 272 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[4, 12, 11, -16, -3, -15, 17, 9, 9],\n [-16, 7, -6, -12, -6, -15, -3, 9, -6],\n [-9, -14, 17, 0, 11, 9, 12, 17, -18],\n [-10, -7, 4, -7, -10, 7, 11, 1, -3],\n [-6, 16, -15, 6, -6, 9, -7, 5, 9],\n [... | 48 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-9, 12, 15, 12, -8, 17, 13, 4, -16],\n [9, 6, 9, 0, 0, 10, 0, -1, 5],\n [-3, -1, -6, -15, -6, 16, -15, 0, 5],\n [14, 14, -10, -16, -16, 11, -1, -17, 13],\n [-10, -17, 1, 8, 17, 0, -3, 7, -5],\n [-1, ... | 53 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[2, 1, -10, 12, -10, -12, 14, -18, 0],\n [-16, -7, 11, -3, -6, 5, -2, 8, 10],\n [-5, -14, -13, 5, 14, -10, -16, 4, 2],\n [3, -11, 1, -5, 11, -11, 0, 17, -13],\n [15, -9, 12, -8, 16, -8, 13... | 52 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, -11, -11, 16, 0, -9, 16, -10, -11],\n [-11, -11, 1, -12, 3, -2, -14, 15, 6],\n [-4, 12, 0, 12, -7, 4, 4, 17, -8],\n [3, 11, -14, 18, 1, -9, 3, 11, 11],\n [3, -12, 17, -5, -8, -12, 13, -1, 15],\n [-17, -12, 1... | 245 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-5, -4, -12, -12, 14, -12, 1, -12, -5],\n [-4, -1, -9, 16, 8, -18, 9, 15, -16],\n [-16, -8, -15, 11, 13, -3, -2, -8, 17],\n [13, 16, 8, 15, -14, 6, 9, -1, -16],\n [9, -17, 15, 3, 3, 11, 15, -18, 10],\n [0, 0, 10, 14,... | 52 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[2, 7, 9, 3, -16, 9, 17, -17, 1],\n [17, -11, 6, -4, 11, 15, -15, 3, 6],\n [-10, 4, -7, -5, -12, 12, -13, 4, 0],\n [2, 0, 0, 15, -6, 17, 6, 14, 2],\n [15, 6, -1, -8, 0, 15, -17, 11, -4],\n [-8, 5, ... | 49 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-6, 12, 4, -16, -8, 10, -1, 6, 15],\n [-1, -18, 9, -15, 2, -13, 2, 18, 11],\n [1, 13, 12, 17, 6, -14, -11, -2, -4],\n [1, 10, 17, 9, -11, -5, 14, 15, 10],\n [3, -16, 4, -16, -13, 4, -... | 262 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[3, 4, 5, 13, 14, 9, -2, 7, -1],\n [-4, 3, -1, 2, 0, -17, 11, 6, 7],\n [-2, -3, 8, -16, 10, -17, -5, -7, 5],\n [9, -1, 6, 18, -13, 11, 12, 15, 0],\n [9, -11, -8, -3, 7, -18, 12, 8,... | 46 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[12, 4, 8, 14, 1, 9, -11, 3, 16],\n [12, 5, -4, 12, -14, 3, -2, 9, -16],\n [0, 8, -2, 13, 18, 2, 18, -8, -18],\n [11, 7, 17, 7, 8, 7, -1, 14, 17],\n [18, 15, 7, 3, 5, -7, -8, 2, -3],\n [17, -12, 9, 5, -6, -5, 12, -11, -18],\n [-2, -6,... | 51 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 13, -11, -8, -6, 1, -18, -17, -8],\n [11, -14, -12, 5, 12, 11, -4, 17, -9],\n [-18, -12, 7, 11, -18, -4, 1, 3, 6],\n [17, 18, 8, 0, 0, -3, 2, 14, 12],\n [15, -4, 17, 7, 11, 12, 6, -15, -7],\n [0, -10, 6, -12, ... | 256 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-5, -14, -3, 2, -8, -12, -11, -2, 11],\n [-5, 14, 5, -12, -4, 6, -2, 14, -17],\n [-9, -5, -7, -2, -5, -9, 10, -13, 12],\n [18, -10, 14, -12, -11, 15, -2, -2, 11],\n [-1, -4, 1, 6, -5, 8, 16, 9, -13],\n [12, -5, -... | 224 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, 15, -17, 17, 4, 5, 13, -6, 14],\n [-5, -2, -3, 13, -4, 12, -7, 14, -16],\n [-8, -14, 8, -3, 16, -3, -3, 3, -15],\n [13, 8, -4, 0, 7, -4, -9, 15, 7],\n [-11, -3, 10, 13, 2, 13, -7, -9, -13],\n [18, -1, 12, 16, -16, -14, 15, 14, 17... | 55 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, 6, 16, -17, -3, -5, 10, -17, -9],\n [-17, 8, -6, -17, -5, -2, 17, 15, 10],\n [4, 4, -3, -12, -18, 0, 14, 15, -18],\n [-7, 6, 4, 6, 12, 5, -9, -17, 14],\n [18, 4, -17, -15, 4, 4, -7, 5, 10],\n [9,... | 58 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-6, -12, -18, 12, 16, 5, -16, 0, -15],\n [9, 11, 17, -15, 4, -8, -15, -8, 5],\n [1, -2, -6, -2, -4, -15, -1, -10, -16],\n [8, -1, -2, -9, 18, 10, -14, -13, 16],\n [-14, -4, 8, 14, 5, 2, -17, 0, -1],\n [-9, 18, 4, -18, -13, -18, -1, 8... | 56 | 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, 11, -7, 6, 0, -17, 3, 11, 17],\n [-16, 4, -15, 9, -5, -13, -13, 18, -12],\n [-6, -18, 5, 15, -9, -13, -15, -11, -4],\n [-7, -13, 2, 13, 13, 8, -8, ... | 49 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-15, -16, -4, -15, -2, -10, 6, -18, -17],\n [14, 3, -7, 8, -8, -5, -5, 3, -10],\n [-4, 14, 0, 12, -1, -7, 18, -18, 15],\n [-12, -17, 3, -15, 1, -16, -10, -1, -3],\n [-10, 0, -13, -4, -13, -14, 10, 8, 7],\n [9, 13, 6, -12, 11, 12, -7,... | 52 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, -2, -9, -3, 5, 10, -5, -9, 10],\n [9, -2, -14, -17, 17, -10, 17, -14, -4],\n [-10, 6, 9, 8, 14, 14, -11, -15, 17],\n [12, -9, -11, 11, -5, 16, -16, 10, -3],\n [-9, -15, -15, -17, -8, -4, -8,... | 254 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[16, -2, -1, 6, 16, -3, 6, -3, 5],\n [-7, 16, -10, 18, 13, 0, 3, 15, 0],\n [-7, -1, -14, 7, 8, 1, -11, -3, -17],\n [-18, -14, 12, 4, 2, -7, -15, 18, -8],\n [-10, 7, 8, 10, 6, -1, 11, -11, -17],\n [3, 2, 7, 10, -14... | 233 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, -3, 11, 15, 3, 10, -14, -18, 6],\n [-13, 4, 14, -5, 17, -1, -9, -7, 4],\n [-12, 6, -6, 0, 3, -8, -16, 0, 8],\n [-12, 18, 8, 15, -8, -14, -12, 17, -14],\n [-14, 8, 10, 8, 13, 6, 15, -4, 15],\n [16, 1, 5, 15, 15, ... | 50 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[15, -5, -11, 6, -15, 12, 2, 13, -5],\n [9, 6, 9, -4, 3, -13, -17, -13, 4],\n [7, -8, -18, 9, 3, -6, 17, 3, -15],\n [-1, -2, 6, -2, 10, -11, 10, -4, 14],\n [-9, 18, -8, 16, 15, 13, 3, -15, -17],\n [14, -10, 16, 12... | 246 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-1, -16, 13, -16, 11, -13, 8, -17, 1],\n [-2, 14, -2, 18, 10, -10, -15, -6, -13],\n [-10, 7, -5, 15, -15, 2, 12, 2, 10],\n [5, -3, -10, 2, -17, -17, 1... | 51 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[15, -15, 6, 13, -7, -17, -7, 7, 2],\n [18, 17, -1, 5, 11, -2, -3, -2, -7],\n [8, -15, 16, -18, -7, 10, -11, -11, -7],\n [17, 15, 17, -15, -8, -16, -9, -7, -10],\n [2, 15, 3, -1, -13, 6, -4, -18, -1],\n [12, 1, 6, 14, -9, 10, 0, 9, 8]... | 56 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, -4, 13, 16, -7, 2, -7, -18, -8],\n [6, -10, 8, 10, 8, 9, -1, -4, -3],\n [4, 11, 17, 16, 9, -16, -3, -4, 0],\n [-9, -15, 3, -1, 3, -3, -16, 16, -3],\n [2, 2, -18, 11, 15, 4, 15, 11, 14]... | 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[[-12, 16, 14, -7, 4, -14, 12, -3, 14],\n [-18, 3, 9, -14, -15, -18, -4, 18, 5],\n [4, -12, 12, -12, -6, -15, -1, 0, -3],\n [-1, -3, 12, 6, -17, 9, -3, ... | 51 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[11, -15, 17, -16, -9, 8, -1, -8, 17],\n [16, -6, 4, -10, -15, 12, -16, 17, -2],\n [-3, -17, -14, 14, -6, -7, 0, 3, -11],\n [-15, -12, 3, -1, -13, -15, -7, 18, -17],\n [-16, 2, -6, -5, 11, -1, -6,... | 238 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, -13, 0, 7, -10, -6, 7, 1, -17],\n [-15, -12, 0, 16, -8, 0, 13, -5, -14],\n [6, -5, -7, 1, -1, -18, -15, -7, 7],\n [13, 18, -4, 16, 7, -4, -11, 9, 11],\n [-16,... | 50 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[6, 2, 0, 15, -13, 16, -16, 14, -10],\n [-12, 8, -18, -1, 16, -2, -8, 18, -8],\n [-16, -6, 9, 15, 9, -17, -17, 18, -3],\n [-11, -8, -4, -15, 4, -11, -3, -3, 5],\n [-9, 15, -1, -3, 17, -11, 1, 4, -... | 231 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, 6, -18, 5, 14, 18, -12, 5, -4],\n [-8, -2, 4, -15, 12, 15, -9, 18, -9],\n [-8, 12, -9, -11, -8, 1, 5, -12, 2],\n [-13, 12, -7, 18, -6, 12, -10, 8, -2],\n [-11, 8, -4, -13, 13, -11, 16, 12, 7],\n [5, -17, -18... | 242 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, 16, 14, -11, 18, 16, 1, -2, -6],\n [-15, 11, -13, -17, -4, 15, 1, -3, 10],\n [8, -18, -6, 13, -16, -5, 9, 7, 2],\n [-8, 8, -18, 14, -1, -17, -15, -15, -2],\n [-3, -10, 7, -9, -12, -10,... | 61 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[17, -4, 14, -14, 10, -2, 8, -2, -15],\n [-7, 4, -8, 17, -7, -10, 5, -1, 8],\n [-10, 14, -13, 14, -13, -15, -16, -6, 7],\n [15, -6, -11, -7, -11, 0, -9, 13, 2],\n [4, 8, 6, -12, 16, -17, 9, -12, -... | 215 | MATH |
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