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Homework Help: Proof about bases for subspaces

  1. Apr 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that all bases for subspace V of R[tex]\hat{}N[/tex] contain the same number of elements.


    2. Relevant equations



    3. The attempt at a solution

    I have absolutely no idea where to start this proof. Do I need to do something with finding an equation of the subspace, or not?
     
  2. jcsd
  3. Apr 28, 2010 #2
    R^n

    like, real numbers in all dimensions. I tried typing it using LaTeX and failed.
     
  4. Apr 28, 2010 #3
    I think I got started

    assuming I have 2 bases of V, (w1, w2, ....wn) [tex]\in[/tex]O R[tex]\hat{n}[/tex]

    and (v1,v2,...vp)[tex]\in[/tex]O R[tex]\hat{n}[/tex], I'm supposed to be showing that n=p

    But I'm not sure how to do that.
     
  5. Apr 28, 2010 #4

    lanedance

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    Homework Helper

    a basis is a linearly independent set that spans the space, thus any element of V can be written in terms of W and vice versa...
     
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