This is the linear transformation im working with:
T(x,y,z) = x - 3y + 2z
I'm asked to find a basis for the kernel of T.
I'm also asked what are dim(ker(T)) and dim(Im(T)).
I don't have a clue how to do either. Any advice? Thanks.
You should have definitions. What's a 'kernel'? Something about mapping to zero should come to mind.
You're not in Algebra I any more. Rote memorization of techniques will not help you. You must begin to have a new vision of rigor of thought, rather than rigor of pencil.