Prove Finite Dimensionality of Subspace of Finite Dimensional Vector Space

[torquerotates]

Homework Statement

Prove that the subspace of a finite dimensional vector space is finite dimensional

Homework Equations

dim(V)=#basis vectors

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.

 

[morphism]

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