Linear Algebra for Data Science

1. True or False: Matrix multiplication is commutative (AB = BA for all matrices A and B).

True

False

2. True or False: The rank of a matrix equals the number of non-zero eigenvalues.

True

False

3. What is the condition number of a matrix used for?

Measuring numerical stability and sensitivity to perturbations

Computing the rank of the matrix

Finding eigenvalues

Determining matrix invertibility

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6. What does Singular Value Decomposition (SVD) express any matrix as?

A product of an orthogonal, diagonal, and orthogonal matrix

A sum of rank-one matrices

A product of upper and lower triangular matrices

A linear combination of eigenvectors

7. True or False: Every square matrix has a real eigenvalue.

True

False

8. Which norm measures the largest singular value of a matrix?

Spectral norm

Frobenius norm

L1 norm

L∞ norm

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10. What is the null space of a matrix?

All vectors x such that Ax = 0

All vectors in the column space

The set of eigenvalues

All zero rows of the matrix

11. What is the rank of a matrix?

The number of linearly independent rows or columns

The total number of rows plus columns

The determinant of the matrix

The sum of all diagonal elements

12. Which decomposition is commonly used for solving least-squares problems in regression?

QR decomposition

Cholesky decomposition

Schur decomposition

Polar decomposition

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14. If matrix A is 5×3 and matrix B is 3×4, what are the dimensions of AB?

5×4

3×3

5×3

The product is undefined

15. What is the determinant of an identity matrix?

0

1

-1

Undefined

16. In Principal Component Analysis (PCA), what does the first principal component represent?

The direction of maximum variance in the data

The mean of all data points

The smallest eigenvalue

The correlation between variables

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18. What is the trace of a matrix?

The sum of diagonal elements

The product of all eigenvalues

The determinant of the matrix

The Frobenius norm

19. If a square matrix has eigenvalue λ = 0, what does this tell you about the matrix?

The matrix is singular (non-invertible)

The matrix is diagonal

The matrix is orthogonal

The matrix has full rank

20. Which operation is NOT valid for matrix multiplication?

Multiplying a 3×2 matrix by a 2×4 matrix

Multiplying a 2×3 matrix by a 3×2 matrix

Multiplying a 4×2 matrix by a 2×4 matrix

Multiplying a 3×3 matrix by a 4×3 matrix

DataX Linear Algebra for Data Science Quiz

1. True or False: Matrix multiplication is commutative (AB = BA for all matrices A and B).

2.

What first name or nickname would you like us to use?

2. True or False: The rank of a matrix equals the number of non-zero eigenvalues.

3. What is the condition number of a matrix used for?

4. If A is an n×n invertible matrix, then det(A⁻¹) = ____.

5. The column space of a matrix consists of all possible ____ of the matrix's columns.

6. What does Singular Value Decomposition (SVD) express any matrix as?

7. True or False: Every square matrix has a real eigenvalue.

8. Which norm measures the largest singular value of a matrix?

9. An orthogonal matrix Q satisfies Q^T Q = ____.

10. What is the null space of a matrix?

11. What is the rank of a matrix?

12. Which decomposition is commonly used for solving least-squares problems in regression?

13. A matrix is symmetric if it equals its ____.

14. If matrix A is 5×3 and matrix B is 3×4, what are the dimensions of AB?

15. What is the determinant of an identity matrix?

16. In Principal Component Analysis (PCA), what does the first principal component represent?

17. Two vectors are orthogonal if their dot product equals ____.

18. What is the trace of a matrix?

19. If a square matrix has eigenvalue λ = 0, what does this tell you about the matrix?

20. Which operation is NOT valid for matrix multiplication?