Question

show work pls!

Let L :P2 →P3 be the linear transformation given by L(p(t)) = 5p"(t) + 3p' (t) + 1p(t) + 4tp(t). Let E = (e1, C2, C3) be the basis of Pề given by ei(t) = 1, ez(t) = t, ez(t) = 62. and let F = (f1, f2, f3, f4) be the basis of P given by fi(t) = 1, fz(t) = t, f3(t) = ť, fa(t) = {'. Find the coordinate matrix LFE of L relative to the ordered bases E and F. LFE =

Answer 1

Given that & = henesieg} is the basis for pt eat catat effl=p F = {fi fortifer} is the basis for ip3 fictial facts=t fa(t)= t fact=t Gived that LCpti) = Sp"(t)3P|4) 4 Pt) tatprt) Let us find the action of linear transformation arte basis of pie Ę. Llect)) = 4(1)=6426149)+ 35 (40+)4 lt+ afeck) 1 = 5.0+ 3.0+ 1 fat (1) Hect) = 144 [Lect)= # Lofict) + 4€44) + 0.ff (t) + 0.) 242 de lekcu)= sed de + Ca(49+ afe24) = 5.64 3.1'44 +46(H) = 3-4 teat2 L(4) = 3f(t) + 1624+1+4 +24)+ o. fect) Lesti) = S(+3.+ eft) + 4f5964) = 5.2 + 3(24)4 +&43) Left= 10+66 +4+¢f3 a tof,C4)4 6fect) + #sct) fact) AFE = [1 3 107 [recenti] [Llengua | 4 6 1o 4 (Liga)] = 177 Looq hositing [Lectly [Llegetilly [Llegte as the colours of CS Scanne che hatrin he get tell hfE