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Homework Help: Bases and Dimension questions

  1. Oct 16, 2006 #1
    I'm having trouble understanding bases outside of R^n; I've got a handle on those I think.

    Here are some examples:

    13. In C(-Pi,Pi), find the dimension of the subspace spanned by 1, cos(2x), and cos^2(x).

    14. Find the dimension of the subspace of P3 spanned by x, x-1 , x^2+1, x^2-1

    I really don't know how to begin either of these

    Thanks for any input.
     
  2. jcsd
  3. Oct 16, 2006 #2

    radou

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    Begin with the definition of a span: http://mathworld.wolfram.com/VectorSpaceSpan.html" [Broken].
     
    Last edited by a moderator: May 2, 2017
  4. Oct 16, 2006 #3
    hmm I already know about spans but that might have helped actually. thanks.
     
  5. Oct 17, 2006 #4

    HallsofIvy

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    Science Advisor

    More important, I think, is the definition of "linearly independent". How many of those given functions are linearly independent?
     
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