How different is a three variable one?

If T(x,y,z) = (0, 2x+y) is a linear transformation, then you can find a matrix A such that this A transforms (x,y,z) to (0,2x+y). That is

So the matrix should map a 3 x 1 vector to a 2 x 1 vector. This means A must be 2 x 3.

So assume A to be a general 2 x 3 matrix and solve for it to get A as