T:R2-->R3 defined by T(a1,a2)=(a1+a2,0,2a1-a2)

I need to prove that is a linear transformation, and find the bases for both
N(T) and R(T). then compute the nullity and rank of T. finally say where it is one -2- one or onto.

I already got the anwsers but I need to know in detail especially for computing the nullity and rank of T. and onto or one 2 one.
Thanks