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## Homework Statement

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.

## 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?

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