Question: Problem 9 - (15 points) Define the polynomials P1, Pz, Pa, PA E Pa as PI(r) = +21, Pz(x) = x'41+3, Pa(x) = 2r+1, PA(r)

Problem 9 - (15 points) Define the polynomials P1, Pz, Pa, PA E Pa as PI(r) = +21, Pz(x) = x'41+3, Pa(x) = 2r+1, PA(r) = -2r'+x-21+3 for all r ER (a) Show that the set S = {P1, Pa, Pa, PA) is a basis for P3. (b) Let p Pa be defined as p() a + + + 1, Determine the coordinate vector of p with rapect to S - {pi, Pa. Pa, Pak

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