For p(t) = azt? + azt + ao and r(t) = byt? + bit + bo in Rz[t], define (p(t), r(t)) := a2b2 + 2a bi + 4apbo. (a) Show th

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For P T Azt Azt Ao And R T Byt Bit Bo In Rz T Define P T R T A2b2 2a Bi 4apbo A Show Th 1 (20.12 KiB) Viewed 42 times

For p(t) = azt? + azt + ao and r(t) = byt? + bit + bo in Rz[t], define (p(t), r(t)) := a2b2 + 2a bi + 4apbo. (a) Show that (pt) r(t)) as defined above is an inner product on Ry[t). (b) If r(t) = t - 1 and s(t) = 6t? - t, compute ||s(t)|| and dér(t), 8(t)). (c) Let S = {t? - 2t +3). Using the given inner product defined above, compute for a basis of St (show that the set you obtained is indeed a basis of S-).