Question

isomorphic?

Answer 1

let W is subspace of the vector space of all continuos real-valued functions spanned by \[\left\{ \cos ^{2}t,\sin ^{2}t,\cos 2t \right\}\].

Answer 2

find a basis for W and state the dimension of W.do you think W and\[\mathbb{R} _{2}\] are isomorphic?

Answer 3

I'm thinking \[\cos(2t) = \cos^{2}(t) - sin^{2}(t)\]This gives us a clue about what sort of dimension we have.