Linear algebra proof with annihilator

[ptolema]

Homework Statement

V is a finite-dimensional vector space over F.
For subspaces W₁ and W₂ of V, prove that

Homework Equations

V^* is dual space of V, defined V^*=the set of all linear functionals

For every subset S of V, define annihilator

The Attempt at a Solution

I'm not really sure where to start. I proved in a previous part of the problem that the annihilator is a subspace of V^*. I tried to argue that for two subspaces of a vector space, one of the subspaces is a subset of the other, but I don't know if that's even a valid theorem. Could someone shed some light on this?

 

[LCKurtz]

Just use the basics. You have to show W_1=W_2 \Leftrightarrow W_1^0=W_2^0

So start by showing W_1=W_2 \Rightarrow W_1^0=W_2^0 which looks to be trivial. So what about the other way: W_1^0=W_2^0\Rightarrow W_1=W_2

If W₁ ≠ W₂ then ...