Question

Please, give me an example to illustrate this expression
T is linear transformation on C
Tz = az + comples conjugate (z)

Answer 1

why is everyone doing linear algebra today :/

Answer 2

@ikram002p
if \(z = \alpha x + \beta i y \), then Tz = \(a(\alpha x+ \beta iy -\beta iy = a\alpha x\)
@hba why not?

Answer 3

I have to prove/disprove it is invertible but not sure how to translate the question.

Answer 4

no idea?

Answer 5

sry was afk , ill check this :D

Answer 6

I appreciate your quickly response whenever I tag. :)

Answer 7

when z= ax+Biy
conjugate (z)=ax-Biy

so ur exampl
Tz=a(ax+Biy)+(ax-Biy)
Tz=(a^2+a)x + (aB-B) y

Answer 8

so , ok x , y still in linear mood
a,b constant right ?
then it work

Answer 9

but need to make sure that
Tz is not = aax in the example u gave

Answer 10

I don't think a in Tz =a z is a in z = ax + bi y
that's why I put z = \(\alpha x +\beta iy\) to make them separate

Answer 11

i see so u have a and alpha ?

Answer 12

well , it wont change it well still linear
cuz x,y both linear exchange

Answer 13

Thanks for your explanation. I think I can work now. hihihi

Answer 14

good !
gtg now , good luck with the rest of it :D

Answer 15

:)