1. The problem statement, all variables and given/known data Let T be defined on F^2 by (x1,x2)T=(w*x1+y*x2, z*x1+v*x2) where w,y,z,v are some fixed elements in F. (a) Prove that T is a homomorphism of F^2 into itself. (b) Find necessary and sufficient conditions on w,y,z,v so that T is an isomorphism. 3. The attempt at a solution I already proved (a). Part (b), I'm not sure what it means. For T to be an isomorphism it has to be one-to-one and onto. To show one-to-one, I need to show that the kernel is 0. Is showing that T is into F^2 the same thing as saying it is onto F^2? If not, what's the difference?