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Homework Help: Dimension of subspace

  1. Feb 28, 2010 #1
    C[-pi, pi]
    Span(1, cos (2x), cos2 (x))

    Doing the Wronskian here is pain so what other method would be more appropriate?
     
    Last edited: Feb 28, 2010
  2. jcsd
  3. Feb 28, 2010 #2

    Mark44

    Staff: Mentor

    One of the functions is a linear combination of the other two, so the three functions can't be linearly independent.
     
  4. Feb 28, 2010 #3
    How can I go about identifying if one is?
     
  5. Feb 28, 2010 #4
    Use a trig identity for cos2x
     
  6. Feb 28, 2010 #5
    cos2x=2cos^2 x-1 but I don't see how that is a multiple of cos2x sine it doesn't = cos^2 x outright.
     
  7. Feb 28, 2010 #6
    Can cos2x can be written as a linear combination of cos2x and 1?
     
  8. Feb 28, 2010 #7
    I see now.
     
  9. Feb 28, 2010 #8
  10. Mar 1, 2010 #9

    Mark44

    Staff: Mentor

    I realize that you already figured this out, but if you look at what I said, I didn't say that one of the functions was a multiple of another. I said that one function was a linear combination of the other two.
     
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