A question about the projection matrix


at the top of page 9 of this document about augmented reality:


it talks about the projection matrix, considering it, as you see, as a 3x4 matrix.

But i just found out, projection matrix in opengl is a 4x4 matrix!

So, the first term ((x y 1)) of the relation is not correct.

So, What is the correct relation?

Another question:

I have drawn a point 3d at (10, 10, 10) in my opengl space and my projection matrix is this:

0.0075 0.0000 0.0000 0.0000
0.0000 0.0100 0.0000 0.0000
0.0000 0.0000 0.0050 0.0000
0.0000 0.0000 0.0000 1.0000

when i multiplicate it by the coordinate (10, 10, 10) i get this coordinates (0.075, 0.1, 0.05, 1.0)

I thought they would be the coordinates of the projection of that point. so they will be something like (10,10) or (23,23), but im wrong, it thinkā€¦

What are this last coordinates (0.075, 0,1, 0.05, 1.0) and what is the relation with the projection of the point 3d?

you have here answers: