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20. Inner Products Let V = P2(x) and define (f,g) = 2/(0)g(0) + f(D)g(1) + 3/(2),(2). (a) Prove that this is an inner product. (You may use the fact that a quadratic polynomial with three roots must be zero.) (b) Let /(2) = 1 + r and g(x) = 2' - 3. Compute |If|| and Ilgll. (c) Let f(x) = 1 + a and g(x) = 23 -3. Compute Proj,g and the projection of g orthogonal to f.If U is a subspace of an inner product space V, prove that U- is a subspace of V and that Unu- = {0}