Matrix Algorithms Online Test

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Matrix Algorithms

Description: This quiz covers fundamental concepts and algorithms related to matrix operations and transformations.
Number of Questions: 15
Created by: Aliensbrain Bot
Tags: matrix operations matrix transformations linear algebra

What is the result of multiplying a matrix by its transpose?

A symmetric matrix
A diagonal matrix
A skew-symmetric matrix
A singular matrix

Which of the following is a valid elementary row operation?

Swapping two rows
Multiplying a row by a nonzero constant
Adding a multiple of one row to another row
All of the above

What is the determinant of a diagonal matrix?

The product of its diagonal entries
The sum of its diagonal entries
The difference of its diagonal entries
None of the above

What is the rank of a matrix?

The number of linearly independent rows
The number of linearly independent columns
The number of nonzero rows
The number of nonzero columns

Which of the following is a valid matrix decomposition?

LU decomposition
QR decomposition
Singular Value Decomposition (SVD)
All of the above

What is the purpose of Gaussian elimination?

To solve systems of linear equations
To find the determinant of a matrix
To find the inverse of a matrix
To find the eigenvalues and eigenvectors of a matrix

What is the trace of a matrix?

The sum of its diagonal entries
The difference of its diagonal entries
The product of its diagonal entries
None of the above

Which of the following is a valid matrix norm?

Frobenius norm
Euclidean norm
Spectral norm
All of the above

What is the purpose of the Gram-Schmidt process?

To orthogonalize a set of vectors
To find the eigenvalues and eigenvectors of a matrix
To solve systems of linear equations
To find the determinant of a matrix

Which of the following is a valid matrix factorization?

Cholesky factorization
QR factorization
LU factorization
All of the above

What is the purpose of the power iteration method?

To find the largest eigenvalue and eigenvector of a matrix
To find the smallest eigenvalue and eigenvector of a matrix
To find all the eigenvalues and eigenvectors of a matrix
None of the above

Which of the following is a valid matrix transformation?

Rotation
Scaling
Translation
All of the above

What is the purpose of the singular value decomposition (SVD)?

To find the eigenvalues and eigenvectors of a matrix
To find the rank of a matrix
To find the determinant of a matrix
To find the null space of a matrix

Which of the following is a valid matrix norm?

Frobenius norm
Euclidean norm
Spectral norm
All of the above

What is the purpose of the QR algorithm?

To find the eigenvalues and eigenvectors of a matrix
To find the rank of a matrix
To find the determinant of a matrix
To find the null space of a matrix

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