Question

Linear algebra

Chapter 8, Section 8.2, Question 22b Let T1:R2 → R2 and T2:R2 → R2 be the linear operators given by the formulas T1(x, y) = (x + y, x - y) and T2(x, y) = (2x + y, x - 2y) Find formulas for Tīl(x, y), , Tz?(x, y), , and (T2• Tı) (x, y). Tīl(x, y) = Edit T'(x,y) (0,5 Edit (T2T1)-1(x, y) = Edit Click if you would like to Show Work for this question: Open Show Work By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor.

Answer 1

Solution: Let's Recall the facts ; 6 het GR 12 he a lines transtamation defined by GCX, X3-, 962), (0.84 +*+ Gn&, aantt landln ,.... An alt annat ...+ Amln) Then the transformation I can be Representeel as Je with respect to . [ Ja ( Or.....Ali A2 aan. Ami aun The Standard buser Bu Sever , en) and Bm-{e ser, een} where eo-Co,...,0,1,0,...,0) ER and -position. ei (0,...,0,1,0,...,0) 11,0,...,O) GRM posestion

2. Ako Suppi That ProR" Rm I: RR be elmas transformation, then the lines map Ti ole : R Raube represented as the matur [1, 5, = [1][T, The usual math.be Devoluct.

% het TilRn Rh he a lines map Such that 0 an invertible matin , then the corresponding matrix for 18 you can be Represented as [ ] = [27-1

% het TilRn Rh he a lines map Such that 0 an invertible matin , then the corresponding matrix for 18 you can be Represented as [ ] = [27-1

→IR? Here I: R² R² and 5201R2 are his fiusformatteos.defineel by Ti coliy) = (x+y, 7-y), 146964)=(87c+y; ot- 1-2y)

[9] = 2 3 => [117-(-:-) and a) With respect Standard bases B 1 (011), (1,0) ? = 7,17 - [7]" Adi (1) det [. - 2 (+ -) = (hh) Hence Tina no Can be expressed Ji (1, y) = (/ h 26 // / as 21 alty 91-y 2 / Also Ⓡ = 3= [1,]" Ad (T2) detta)

(**) 2/ / % -2% Home TR² I 2 : 122 D² Can he bogascared as 응 26) -2/ ant (2 8/5 C Yo Anety Oy 5. 5 Now Oo [lable] = [1,1-[5] 276) 2 24 3 - 1 3 (i Sunday =>(5:09,) WW (Tula) - det 9.5.544(1.55) 93) Card to

. +7 (9209.7778_71R2 Can be expressed as Gacil (ay) ) *(3 ( % -10 Yo / ID 32-4 +3y 10 10