Describe explicitly a linear transformation T : R3 -> R3 which has as it ranges the subspace spanned by (1, 0, -1) and (1, 2, 2).

This is what I wrote:

T(R3) = a(1, 0, -1) + b(1, 2, 2) for all a, b in K (the underlying field).

Since (1, 0, -1) and (1, 2, 2) span the range, I assume that means that you can take the linear combination of those two vectors and generate the range. But not sure if I did it right.