(8 points) For p(t) = 22tº+at+ap and r(t) = bet? + bit+bp in Rz[t], define (p(t), r(t)) := 4a2b2 + 2a1bı + apbo. (a) Sho

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8 Points For P T 22to At Ap And R T Bet Bit Bp In Rz T Define P T R T 4a2b2 2a1bi Apbo A Sho 1 (23.84 KiB) Viewed 24 times

(8 points) For p(t) = 22tº+at+ap and r(t) = bet? + bit+bp in Rz[t], define (p(t), r(t)) := 4a2b2 + 2a1bı + apbo. (a) Show that (p(t), r(t)) as defined above is an inner product on Ry[t]. (b) If r(t)=t-1 and s(t) = 6 - 6t, compute |s(t) and dr(t), s(t)). (c) Let S = {t2 +2t - 5). Using the given inner product defined above, compute for a basis of St (show that the set you obtained is indeed a basis of St).