Projection matrix to project a point in a plane 
How to determinate the 4x4 S matrix so that the P gets projected into Q, on the XZ (Y=0) plane? 
Q = S P

There's no matrix with this property; if there were, what would it do when multiplied by the coordinates of the point $L$? 
If you represent points with homogeneous coordinates (i.e., append a "1" at the end of each coordinate triple), then there's a $4 \times 4$ matrix that'll do what you want...almost. It'll send $(P_x, P_y, P_z, 1)$ to a point $(R_x, R_y, R_z, R_w)$, with $R_y = 0$, that has the property that when you divide through by $R_w$, you get $(Q_x, Q_y, Q_z, 1)$, except when $R_w$ happens to be zero, as it will when you multiply it by the point $(L_x, L_y, L_z, 1)$. 
The introduction to 2D and 3D transformations section of any computer graphics book will explain this in considerable detail. 
