1 S = {Po, P1, P2} , Po(1) = 1, pi(1) =x, p2(r) =; (1 – 3x²), is an orthogonal set. 1. Find the norms of po, pi and p2. 2. Let f(x) = e*. Find the following inner products on [-1, 1]: (Po; f), (P1,...

Extracted text: 1 S = {Po, P1, P2} , Po(1) = 1, pi(1) =x, p2(r) =; (1 – 3x²), is an orthogonal set. 1. Find the norms of po, pi and p2. 2. Let f(x) = e*. Find the following inner products on [-1, 1]: (Po; f), (P1, f), (P2, f), 3. Find the orthogonal projection of f onto the span of S. That is, (Pi, f), P:(x) (Po, f) Po(x) + l|po||? (P1, f) (P2, f) -P2(x) llP Pi (x) + Note: Notice that the term for i = 0, 1,2 is a real number and can be obtained from the first two questions. Therefore, the projection will be a second order polynomial. If you plot the projection and the function ƒ on [–1, 1] their graphs should be close to each other.