Finding a subspace

• Apr 23rd 2013, 04:16 PM
widenerl194
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!!
• Apr 23rd 2013, 07:03 PM
Gusbob
Re: Finding a subspace

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

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

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

What about the subspaces spanned by \$\displaystyle e_1,e_2,e_3\$ or \$\displaystyle e_1,e_2,e_3,e_4\$?
• Apr 25th 2013, 10:17 AM
widenerl194
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.
• Apr 25th 2013, 12:27 PM
HallsofIvy
Re: Finding a subspace
Great! So do it!
• Apr 25th 2013, 01:15 PM
widenerl194
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.
• Apr 26th 2013, 03:12 AM
Gusbob
Re: Finding a subspace
Quote:

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.