Here's the problem:

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

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

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- Apr 23rd 2013, 04:16 PMwidenerl194Finding a subspace
Here's the problem:

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

I don't know where to start with this, any help would be appreciated!! - Apr 23rd 2013, 07:03 PMGusbobRe: Finding a subspace
Do you understand what a subspace is? If not, please read your text/consult your notes before even thinking about this question.

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 AMwidenerl194Re: Finding a subspace
The dimension of the subspace spanned by e

_{1}would be 1, spanned by e_{1}and e_{2}would be 2, spanned by e_{1}, e_{2}and e_{3}would be 3 and the last would be 4. - Apr 25th 2013, 12:27 PMHallsofIvyRe: Finding a subspace
Great! So do it!

- Apr 25th 2013, 01:15 PMwidenerl194Re: 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 AMGusbobRe: Finding a subspace