give an example for a transformation T:R^3 -> R^3

in which $\displaystyle (ImT)^{\perp}=\{(x,y,z)|x-3y+2z=0$

and find T(x,y,z) formula

??

i solvled this x-3y+2z=0 equation

i got two vectors then i took V=(a,b,c)

and said that V*U1=0 and V*U2=0

and that v is ImT

the result is Im T=sp{(-1,3,0)}

i got 2 thing to do here

the first one:

T(0,0,1)=(-1,3,0)

T(0,1,0)=(-1,3,0)

T(1,0,0)=(-1,3,0)

correct?

regarding the second one:

how to find T(x,y,z) formula

?