What is the basis for the subspace W spanned by {sin^2(x), cos^2(x), cos2x}?

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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...

TIA.
 
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physicsss said:
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...

TIA.
This one is easy think about trig identities and try to express one function in terms of the others. See which function is superfluous.
 
show each one is superfluous.
 
Oh..sorry for the confusion. I just needed help with b). I already know how to do a).
 
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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