Thank you Give an example of a linear transformation T V rig

Thank you.

Give an example of a linear transformation T: V rightarrow W of finite dimensional vector spaces that is one-to-one but that is not onto.

Solution

Let, V=R2,W=R3

T(x,y)=T(x,y,0)

Let, T(x,y)=T(p,q)

(x,y,0)=(p,q,0)

x=p

y=q

HEnce transformation is one to one

But clearly not onto as it only maps to vectors of the form

(x,y,0) in R3