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Math Help - Finding a subspace

  1. #1
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    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!!
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  2. #2
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    Re: 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 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?
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  3. #3
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    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.
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  4. #4
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    Re: Finding a subspace

    Great! So do it!
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  5. #5
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    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.
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  6. #6
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    Re: Finding a subspace

    Quote Originally Posted by widenerl194 View Post
    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.
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