Question

(1 point) Let S = {1, 2, 3} and T : Fun(S) + Rº be the transformation T(f) = (f(2) – 2 f(1), f(2) + f(3), f(1)) and consider the ordered bases E = {x1 X1, X2, X3 > the standard basis of Fun(S) F = {xı – X3, 2X1 + X2, X3 – x2} a basis of source Fun(S) E' = {(1,0,0), (0,1,0), (0,0,1)}the standard basis of R3 G = {(-2, –1,1), (1,-1,0), (0,1,0)} a basis of target R3 In the parts below you will use the change of basis formula to compute MF (T) = M (Id) ME (T) M (Id). A. ME (T) = B. M (ID) = C. ME(ID) = D. M (T) =

Answer 1

Page No. Dale ap basis E = 1.5 S2, S3 be the standard basis of Funist | Dues.) Ange Given s={1, 2, 3} Ti Fum(s) - R3 I(f) = (f(z) -2 f (1), 7(2)+ f(3), f(1) F = {4-ho, 24, +42, fi - 42 } be the of Fusks) E' = {(1,0,0), (0,110);(0,0,1). bethe Standard basia G= {(-2,-1,1),(1,-1,0), (0,1,0)} be the basis of 1R3 I here Sig is Charaitentic funetion Sub that feos if t=8 if tas ay O Fun (S) = set of all function to s → IR {f fos IR? Also Fun (S) 14 a vector space A) For MECT 3x3 ET SB This ita toordinate vertoo tort besit & (55) = ( 59623–2510, 6,(2) + S;(3), $,0)

Date 0 (9t5 ,201 - ه) = (ر) 1 * (ا هر2 - ( ,۵۵) ۱۰ + (ماه) .0+ (5,5) 2- ع (a linear combination of veeter (6ے b Coordinate vector of T(41) في و مر والله 0 T) - ( 2) - 25 (1), (2) + (3) ) Smilarly (1 - 2.0, 140, 5) (مله) سے ( ره) .10 ( 50) .1- (150) ۱۰ - عملیات 2 Similarly ($ 2+2 21- (عادي) = (ن )1 (هرا +200 - 0) = (هلهم (0.001 + ( 59) .( د (قفل):): - عين للفظ

Page No. Date ร ME CODE O - o 6 B) For M (3d) 3x3 [ickas tie Elfirade Tal2x +Xal] clearly gd gedentity Map gl (x,x) = x - X3 EX,+ o. X2-1.73 (30(2,-23)] Similarly Id (2X + X2) = 22, + X₂ = 2.7, + 1.X2 +0.73 2 [Jel (2X, 4 X ₂ Je 8 O Similarly gel (X3-X) = X3 X2 = 0.x,-1.762 +1.83 6 [1473-60-

Page No. Date 0 - 2. O M (d) - O M(94) fgelcor order [gd (1,00d [zel lololo Ja (10070) = (1,0,0) (۵/e) (ه,اسط + (1 ,(2) = -2a +b=1, laro b=1 -a-bt czo (C=1 Je (1,0,0) (1,0,0) 0.(-2,-1, 1+1,(1,-1,0)71.001110) ( gelli 10,2 G 2 fo Similarly 90 Colo) = (0,110) = a(-2,-)11) + b.(147,0)+((01/19 => -22+6=0; -9-67,cel, (a = 6] (12) bao Jd (0,1101 = (01110) 50.(-24-11170.(174,90+1.0,19 Igelloilo Jor

Page : Date + C (011) Similarly 20 (0/071) - (0.011) 24-(-2/-1,1) + b(10-110) -7 -241b20 4-b1(20, बचा 1652 | c - 3 ।। Id(0,0,1) Go 2 H 3 1 6 0 2 १ Mण (24) - म 3 Mr) = Mण (d)M FCI) M. (१) D.) Now Foo MOLT) 모 + ० -1 2 -- + - 3 -- e छ -2 -3 m 2 + 2 a O या D -- 근 6 - 4 Also that verify for first column you can

Page No. Date £ (X32-85ܢܐ0(X , ) ( 2 ) -2xx-ܕ݁ܥܳܓ -(;IX , -X ܕܠܢܛܰܢܠܳܚܕܡܓܟ܂ܢ-)* ܐ||| -oro- ܘ_;(- ܐ)2- ܘ-o ܕܐܙܐ ܝܐ-)2 (ܘܝ | . ) to .- ;, O ) , to (ܙܨܐ-2-):( ܪܝܠܐܥܠ ܐ - ܕ%)J] 2 2 6 2