1. ## Finding a subspace

Here's the problem:

For each k in {0, 1, 2, 3, 4} find a subspace of R4 of dimension k.

I don't know where to start with this, any help would be appreciated!!

2. ## Re: Finding a subspace

Otherwise, let $e_1,e_2,e_3,e_4$ be your basis vectors (standard or otherwise) for $\mathbb{R}^4$

What is the dimension of the subspace spanned by $e_1$?

What is the dimension of the subspace spanned by $e_1$ and $e_2$?

What about the subspaces spanned by $e_1,e_2,e_3$ or $e_1,e_2,e_3,e_4$?

3. ## Re: Finding a subspace

The dimension of the subspace spanned by e1 would be 1, spanned by e1 and e2 would be 2, spanned by e1, e2 and e3 would be 3 and the last would be 4.

4. ## Re: Finding a subspace

Great! So do it!

5. ## Re: Finding a subspace

I feel like I'm just missing something obvious here... Would I say "the dimension spanned by ek gives us a dimension of k"? I understand the concepts of dimension and subspace, I'm just confused.

6. ## Re: Finding a subspace

Originally Posted by widenerl194
I feel like I'm just missing something obvious here... Would I say "the dimension spanned by ek gives us a dimension of k"? I understand the concepts of dimension and subspace, I'm just confused.
You already said the subspace spanned by e1 is one dimensional. So that is a one dimensional subspace you're looking for. Likewise for higher dimensional subspaces. If it makes you feel better you can write down a coordinate representation of e1,e2,e3,e4.