Hi, I'm reviewing some linear algebra this summer as a refresher. I've come across the following proof problem, and have found myself stuck. Apparently, I'm supposed to use induction to solve this, but I'm not really sure exactly WHAT to use induction on. Anyway, here's the problem:

Prove that if W is a subspace of a vector space V and w(1), w(2),...,w(n) are in W, then a(1)w(1) + ... + a(n)w(n) is in W for any scalars a(1), ... ,a(n).

Any help on this? :-(