Okay, what is the dimension of W? It cannot be any larger than the dimension of F[x] can it? And a basis is the largest possible independent set of vectors.(b) Suppose here that and such that for all . Prove that is linearly dependent.
A hint was provided as follows: What is the dimension of ?
I'll try to do some of this, but there's a lot of info that I'm unfamiliar with (primarily the change of basis parts).