I want to use this projection matrix:

GLfloat shadow[] = { 
    -1,0,0,0,
    1,0,-1,1,
    0,0,-1,0,
    0,0,0,-1 };

It should cast object shadows onto the y = 0 plane from a point light at 1,1,-1.

I create a rectangle in the x = 0.5 plane

    glBegin( GL_QUADS );
    glVertex3f( 0.5,0.2,-0.5);
    glVertex3f( 0.5,0.2,-1.5);
    glVertex3f( 0.5,0.5,-1.5);
    glVertex3f( 0.5,0.5,-0.5);
    glEnd();

Now if I manually multiply these vertices with the matrix, I get.

    glBegin( GL_QUADS );
    glVertex3f( 0.375,0,-0.375);
    glVertex3f( 0.375,0,-1.625);
    glVertex3f( 0,0,-2);
    glVertex3f( 0,0,0);
    glEnd();

Which produces a reasonable display ( camera at 0,5,0 looking down y axis )

So rather than do the calculation manually, I should be able to use the opengl model transormation. I write this code:

    glMatrixMode (GL_MODELVIEW);
      GLfloat shadow[] = { 
    -1,0,0,0,
    1,0,-1,1,
    0,0,-1,0,
    0,0,0,-1 };
    glLoadMatrixf( shadow );
    glBegin( GL_QUADS );
    glVertex3f( 0.5,0.2,-0.5);
    glVertex3f( 0.5,0.2,-1.5);
    glVertex3f( 0.5,0.5,-1.5);
    glVertex3f( 0.5,0.5,-0.5);
    glEnd();

But this produces a blank screen!

What am I doing wrong?

Is there some debug mode where I can print out the transformed vertices, so I can see where they are ending up?

Note: People have suggested that using glMultMatrixf() might make a difference. It doesn't. Replacing

glLoadMatrixf( shadow );

with

     glLoadIdentity();
     glMultMatrixf( shadow );

gives the identical result ( of course! )