00:01
Hello, so you want to show that a subspace of a finite dimensional vector space is going to be finite dimensional.
00:07
So we can let v be a finite dimensional vector space over some field f, and then let w be a subspace of v.
00:15
So then we have that w is going to be a subset of v.
00:27
And as a subset of a finite set, we have that w is also going to be finite.
00:33
And then furthermore, since we have that v is going to be finite dimensional, it's going to have a finite basis.
00:41
So we can let, let's say, v1, v2, up to vn be a basis for v.
00:52
Then any element, w, in the set w, can be expressed as a linear combination of the basis vectors...