Subspace base math question

physicsss

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

TIA.

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lurflurf

Homework Helper
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

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.

mathwonk

Homework Helper
show each one is superfluous.

physicsss

Oh..sorry for the confusion. I just needed help with b). I already know how to do a).

matt grime

Homework Helper
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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