9 let v, = (1, 0) v, = (1, -1) and v, = (0, 1), then how many linear transformations t: rr are there such that t(v,) = v t(v) = v t(v) = v,?

see attached , it will clear your doubt..

There doesn't exist any such linear transformation.... T is from R³ into R²... since V1, V2, V3 are vectors in R², so T cannot maps them as these vectors don't belong to their doma...

PFA

in case of R² into R², again there doesn't exist any such linear transformation... see the attachment

see this result...

and

see it

any doubt then ask