The set S = 1 1 3 , 1 2 x, #3 2 x2 #2 3 2 is an orthonormal basis for P2 with respect to

Chapter 7, Problem 23

(choose chapter or problem)

The set S = 1 1 3 , 1 2 x, #3 2 x2 #2 3 2 is an orthonormal basis for P2 with respect to the evaluation inner product at the points x0 = 1, x1 = 0, x2 = 1. Let p = p(x) = 1 + x + x2 and q = q(x) = 2x x2. (a) Find (p)S and (q)S . (b) Use Theorem 7.1.4 to compute p , d(p, q) and p, q.

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