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Subspace base math question

  1. Jul 3, 2005 #1
    I'm stumped by this problem:

    let W be the subspace of C[0,1] spanned by S={sin^2(x),cos^2(x),cos2x}

    a) explain why S is not a basis for W

    it's because S not linearly independent

    b) find a basis for W

    please help me with this one...

  2. jcsd
  3. Jul 3, 2005 #2


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    This one is easy think about trig identities and try to express one function in terms of the others. See which function is superfluous.
  4. Jul 3, 2005 #3


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    show each one is superfluous.
  5. Jul 3, 2005 #4
    Oh..sorry for the confusion. I just needed help with b). I already know how to do a).
  6. Jul 3, 2005 #5

    matt grime

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    and they answered b for you. they span a space of fewer then 3 dimensions, so it's 0,1 or 2, but obviously 0 or 1 is nonsense so you just need to find two of them that aer independent. as mathwonk says any two will do.
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