題組內容

5.(10%)下面的問題共有二個子題,只要寫出每個子題的答案即可(不需寫出計算過程),例如: (a)θ=30或θ=π/6。
Consider the inner product space C[0, 1] with (f, g) :=63083f211fb9e.jpg f(x)g(x)dc and the nomm 63083f3ecf7c0.jpg. Denote S := span (1, x} as a subspace of C[0, 1].

(b) (6%) Find a vector u(x) in C[0, 1], so that {1, u(x)} forms an orthonormal basis for S.