Scaling

To scale a point relative to the origin, you want to multiply the x,y components by scaling factors sx and sy, respectively. In addition, you want no translation during the scaling operation. Here's the matrix you want:

    |sx  0   0|
Ms =|0   sy  0|
    |0   0   1|

Eg. p = [x y 1]


                      |sx  0   0|
p' = p*Ms = [x y 1] * |0   sy  0| = [(x*sx) (y*sy) 1]
                      |0   0   1|

Again, this is the desired result for scaling; that is

x' = sx*x
y' = sy*y