申論題

5.(25%)下面的問題共有四個子題,只要寫出每個子題的答案即可(不需寫出計算過程),例如； (a)1||xll=1,θ=30°或θ=π/6。 Consider the inner product space C[0, 1] with (f, g) := f(x)g(x)dx and the norm||f||:. Denote S := spanfy{1, x} as a subspace of C[0, 1].

(c) (6%) Find the vector p(x) in S that is closest to on [0, 1].