2.18 Let V be the vector space of all polynomials, with inner product

(!,g)= J0

"' f(x)g(x)e-x dx Let W be the subspace ofV spanned by {1, x, x2

}.

a) Use Gram-Schmidt to orthogonalize {1, x, x2}.

b) Find the orthogonal projection of f(x) = x3 onto W.