Question

Find the dimension of the subspace U = span {1,sin^2(θ), cos 2θ} of F[0, 2π]

Find the dimension of the subspace U = span {1,sin^2(θ), cos 2θ} of F[0, 2π]

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Answer #1

To find the dimension of Span(U), we need to find a basis of Span(U). One way to do this is to note that the third vector is the sum of the first two vectors. Also, it's clear that the first two vectors are linearly independent. is a basis of Span(U).

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