Question

Consider the linear transformation T: R4_R2 defined as T(11,12,13,14)=(-211 +12 +214,-312-14). Find the standard matrix for T: sina) a dr f -2 1 0 2 -3 0-1 2 What is the dimension of ker(T)? Is T one-to-one? NO Enter one: yes no Write the standard matrix for HoT where H is the reflection of R2 about the line y=I. ab sina) 518 8 a 22

I need help with the last part of this question (ie: Write the standard matrix for H∘T, where H is the reflection of R2 about the line y=x.)

Answer 1

3p2 reflection about the Now as Jere the transferernation is given by 7441,42,43, 14) (-rata 2+2, -342-24) TOR1 and HER² R2 such the n is the line y=x weg know that we we reflect a point beint across tha line yen the a-coordinate and y-cocrcalinata Change places (goe (114) = (y,x) HOT Cnida, daina) ne given by. lel B - {e,, 22, 63, en? be the standard basiz off C, = (1,0,0,0) ,, -10,1,0,0), 3-10,0,1,0), PA= (0,0,0,1) HOTle) = HAT (1,0,0,0)) H(-290) (0,-2) CAD> HOTCO) = (0,-2) = 0(8,0) + -2(0,1) 70.0, +-2102) where standard basis of R33 Hot (2) HCT 01,0,0,0 HI 1,-3) = (-3,1) -31110)+1(011) HOT (e): H(T(0,0,1,0)) Hoo) Cou) 011,09 +0.000) Hot 104) = H ( 110,0,0,0) = (2,-1) = (-1,2) H(10) +20,4) el

& The sleendared mahix fore Hot is given by 2 - E 3'57: