Question

Consider the linear transformation T from V = P2 to W = P2 given by Tao + ayt + azt) = (-63, + 2a, + 3a2) + (2a, + 4aq + 2az)t + (220 + 2a, + 3a2)2 Let F = (F1, F2, f3) be the ordered basis in P2 given by f(t) = 1, 72(t) = 1 + t, f3(t) = 1 +t+2 Find the coordinate matrix (TFF of T relative to the ordered basis Fused in both V and W, that is, fill in the b common.) T(f(t)) = x f (t) + 2 X f(t) + 2 f(t) T(f2(t)) = fu(t) + 12(t) + f(t) T(fz(t)) = f(t) + 2(0)+ 7(0) and therefore : [T]FF =

Answer 1

let lotaittat = a filt) to f (A) + Cf (t) = Q +bCI++) +CC14YR them ao+Qit tartha+b+c) +B+7+ CA Aqualang both sides Gefferent of t, fart: ao=albic arabte udac from cada from a=b+c=btara) b ande Dom Qozatbtc = a +9+4pq =) Q5 26 27 kaotant art = (doa) f(t) +(99222) A q840) TCRC) – TC1) = 7C1+0.7toite) 10 . - 660)+0+0) H(201)7040) 743070404 =:-6724+&te ( sono) -66-9867)+2_960+ 2 8:11) F BO) = -8°C4) to f327) +284)

TCP2CH) =TCHA = TttTort?) = 6+601) +2(0)+6) +(204401)+co) ne (267)+241943(0)) {E = 54 +67+47€ .promen) Trepca) 69-6) &CH) +(6-7) BCH) +48 -TCP (A)) = -10 RCA) + 2 f(A) + 4 f (t) fi TCBACH) = TCH1799. 2 13 =66+2+3)+12+9+213 +2+243) =-1+84+7+8 (promo) = 6-0, 6, 9) +(0+ 7603 I TRES) = -97 CH) + f2c8) +788Ct) Tusa -10 91 [Jee = 1 o 2 il m@3) 1. 24 7