Question: Let V = P (R) be equipped with the inner product (p, q) = Sp(x)q(x)dx and V R, be given by (p) = (-1)p+

Let V = P (R) be equipped with the inner product (p, q) = Sp(x)q(x)dx and :V R, be given by (p) = (-1)p+

Let V = P (R) be equipped with the inner product (p, q) = Sp(x)q(x)dx and V R, be given by (p) = (-1)p+ (1)p, vp V (a) Show that is a linear functional on V. (b) Given that if L. (x) = 12, 1, (x)=x, L: (x) = 33 (x - 4) then B = (Lo, L1, L2) is an orthonormal basis for Lo 1 12 V, compute the unique polynomial P 212 EV for which (p) = (q, P), Vq V

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