Question: Exercise 1: In lesson 12, we have seen that the set S = {po, P1, P2}, Po(x) = 1, P1(2) = = x, P2(20) (1

Exercise 1: In lesson 12, we have seen that the set

Exercise 1: In lesson 12, we have seen that the set S = {po, P1, P2}, Po(x) = 1, P1(2) = = x, P2(20) (1 32), is an orthogonal set. 1. Find the norms of po, P 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, 5 (19) marca) = laran polis) + (po, f) (P1,8) (P2, S) Pif) ||P: 112 - Pi( 2 Po( 2) ||po|l2 21 ||p1/12 P1(x)+ ||p2||2 P2(x)

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