Question

Let A and B be matrices .

Answer 1

You know that \(Av=\lambda v\) and \(Bv=\mu v\). How else can you write \((A+B)v\)?

Answer 2

you can distribute the v to both A and B and then use equalities?

Answer 3

so you would get (lambda+ mu)v..

Answer 4

That's basically it (with a few steps skipped). So \(\lambda+\mu\) is an eigenvalue of \(A+B\) for \(v\).