Let p (x) = ao + a¡x + a2x² and q (x) = bo + b1x + b2x² be vectors in P2 with inner product < p, q >= aobo + a¡b1 + azb2 . Consider the polynomials in the set {2 + x², –1 + x + x² } 1. Show that the polynomials in the set do not form an orthonormal set. 2. Use the Gram-Schmidt orthonormalization process to form an orthonormal set from these polynomials. Keep the order, and show work for the orthogonalization, then normalization. 3. Do the polynomials in the orthonormal set (from question 2) form a basis for P2 ? Why or why not?

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