Dimensionality proof

1. Feb 18, 2008

torquerotates

1. The problem statement, all variables and given/known data Prove that the subspace of a finite dimensional vector space is finite dimensional

2. Relevant equations dim(V)=#basis vectors

3. The attempt at a solution
I was thinking about making a summation of the basis vectors in the vector space and the subtracting the summation of the basis vectors in the subspace. That way I get a finite# of basis vectors left over. But that thinking turned out to be flawed because I'm assuming that the #of basis vectors in the subspace is finite(what I'm trying to prove). So I'm back to square 1.

2. Feb 18, 2008

morphism

Can a finite-dimensional space have infinitely many linearly independent vectors?