3D to 2D projections via a matrix

Thanks to my new book I just got in the mail I finally figured out my problem with 3D to 2D projection.

I was on the right track but just couldn't sort it out.

IM=identity matrix

p=[p1,p2,p3,1][IM]=[p1,p2,p3,p3] or **p'**, for p3!=0

so w=p3.------------------->^

This is vector in homogenous space - to map it back to three dimensions divide each component by w.

so

*V*(x,y,z,w)= (x/w,y/w,z/w,w/w)=(x/w,y/w,z/w,1)=(x/w,y/w,z/w)=x

Pretty simple really, dunno why I couldn't derive it.