Matrices Quiz

What is an orthogonal matrix?

• A matrix with all elements equal

• A matrix where the transpose is equal to the inverse

• A matrix with all elements zero

• A matrix with no specific properties

Which of the following is an example of an orthogonal matrix?

• [1 0; 0 1]

• [1 2; 2 1]

• [0 1; 1 0]

• [1 0; 0 -1]

What is the property of the transpose of an orthogonal matrix?

Evaluate responses using AI:

OFF

What is a unitary matrix?

• A matrix with all elements equal

• A matrix where the conjugate transpose is equal to the inverse

• A matrix with all elements zero

• A matrix with no specific properties

Which of the following is an example of a unitary matrix?

• [1 0; 0 1]

• [1 2; 2 1]

• [0 1; 1 0]

• [1 0; 0 i]

What is the property of the conjugate transpose of a unitary matrix?

Evaluate responses using AI:

OFF

What is the rank of a matrix?

• The number of rows

• The number of columns

• The number of non-zero elements

• The maximum number of linearly independent rows or columns

How do you find the rank of a matrix?

Evaluate responses using AI:

OFF

What is the rank of the identity matrix?

Evaluate responses using AI:

OFF

If A is a matrix with rank r, what is the rank of A^T?

Evaluate responses using AI:

OFF