4.1 - Eigenvalues and Eigenvectors

Question 1

T/F: Given any matrix A, we can always find a vector x where Ax = x

Answer 1

False

Question 2

When is the zero vector an eigenvector for a matrix?

Answer 2

Never. If it was, then every number would be an eigenvalue because A0 = λ0 = 0 no matter what λ is.

Question 3

If v is an eigenvector of a matrix A with eigenvalue of 2, then what is Av?

Answer 3

2v

Question 4

T/F: If A is a 5x5 matrix, to find the eigenvalues of A, we would need to find the roots of a 5th degree polynomial.

Answer 4

True