# 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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