Linear Transformation, Nullity and rank...

Find bases for both N(T) & R(T). Then compute the nullity and rank of T, and verify the dimension theorem. Use the appropriate theorems to determine whether T is 1-1 or onto..

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

I'm not too sure where to go from finding the N(T)...I think I have a clue about the R(T)...but not totally sure...

All I got so far is that N(T) : a1 + a2 = 0

2a1 - a2 = 0 which gives a matrix...

| 1 1 |

| 2 -1 | this matrix can be reduced to

| 1 0 |

| 0 1 | and we can see that a1 = 0 and a2 = 0? Which means that the Basis of N(T) is (0,0) meaning dim N(t) = 0, and thus nullity of T = 0....this is what I got so far