For p(t) = azt? + ait + oo and r(t) = bizt? + bit +bo in R2[t], define (p(t),r(0)) := a2b2 + 2a76, + 4apbo. (a) Show tha

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For P T Azt Ait Oo And R T Bizt Bit Bo In R2 T Define P T R 0 A2b2 2a76 4apbo A Show Tha 1 (20.11 KiB) Viewed 32 times

For p(t) = azt? + ait + oo and r(t) = bizt? + bit +bo in R2[t], define (p(t),r(0)) := a2b2 + 2a76, + 4apbo. (a) Show that (p(t), r(t)) as defined above is an inner product on R2[t]. (b) If r(t) = + - 1 and s(t) = 6t-t, compute || s(t)|| and dr(t), s(t)). (e) 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-).