Eigenvectors and Eigenvalues

Show that if v is an eigenvector for A with eigenvalue L then so is 3v.

More general, if v is a (non-trivial) eigenvector of A with eigenvalue L, then kv with k a scalar is too.

We are given: Av = Lv, so A(kv) = k(Av) = k(Lv) = L(kv).