can someone please help me with this? please do not upload answers on c'hegg i have looked at them they are all wrong and i dont understand them

Consider the vector space C[L, L] of continuous functions on the interval [413,15], endowed with the inner product L (Lg) = [L x) go) in vs g e CIL, L]- Let U...I be the subspace of C[L, L] spanned by a. set of n + 1 vectors shwe)w(s)mm(s)}l where n 2:: 0 is a positive integer. (i) Show that on is orthogonal with respect to the inner product. Normalize the vectors in n to obtain an orthonormal basis for U\". (ii) Find an explicit expression for the best approximation of a function f(:s] E C[L, L] in the subspace U\