Let λ be an eigenvalue of A. Prove that λ+a is an eigenvalue of A+aI.

Question

Let λ be an eigenvalue of A. Prove that λ+a is an eigenvalue of A+aI.

That is a question I may find in a test next monday. I think my approach is valid, but if it is, the question looks too simple to be in the test!

Av = λv, v≠0

Av + av = λv + av

(A+aI)v = (λ+a)v

Is that it? Thanks guys

Answer 1

That's correct! (Answering as community wiki so this question may be closed as answered)