Choose 2 vectors in .
We want to show that :
Can you do that? It's just writing out.
Observe that ker . Hence v satisfies .
Find two independant vectors in that satisfy these relations and you have a basis for ker(T).
Find 2 more independant vectors: and you have a basis for Im(T)
(Dim(Im(T))+ Dim(ker(T)) = 4).