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Maximal independent subset

  1. May 10, 2005 #1
    Let V=C[0,1] be the vector space for all-real valued continous functions on [0,1]. If X={1,cosx,cos2x, cos3x, cos^2x, cos^3x}. How do I find a maximal subset of X?
     
  2. jcsd
  3. May 10, 2005 #2

    HallsofIvy

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    Use trigononometric identities. cos2x= (1/2)(1+ cos(2x)) and sin(2x= (1/2)(1- sin(2x)). You can find a similar identity for cos3(x).
     
  4. May 10, 2005 #3
    Thank you.
     
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