Proof about bases for subspaces

[cookie91]

Homework Statement

Prove that all bases for subspace V of R$$\hat{}N$$ contain the same number of elements.

Homework Equations

The Attempt at a Solution

I have absolutely no idea where to start this proof. Do I need to do something with finding an equation of the subspace, or not?

 

[cookie91]

R^n

like, real numbers in all dimensions. I tried typing it using LaTeX and failed.

 

[cookie91]

I think I got started

assuming I have 2 bases of V, (w1, w2, ...wn) $$\in$$O R$$\hat{n}$$

and (v1,v2,...vp)$$\in$$O R$$\hat{n}$$, I'm supposed to be showing that n=p

But I'm not sure how to do that.

 

[lanedance]

a basis is a linearly independent set that spans the space, thus any element of V can be written in terms of W and vice versa...