We have that the general expression for the projection fo a vector w onto another vector v is the following:

in this case, we have that v = (0,1,-3), then, if w = (x,y,z), we have that the transformation matrix is the following:

then, the transformation matrix is T(w) = (0, -1/10 (y-3), 3/10 (y-3z) )
for part b, let w = (1,2,4), then, the transformation matrix of this vector is:

therefore, T(1,2,4) = (0,1,-3)