Fundamental and essential matrices

hey, I used the stereo calibration app (using checkerboard) to find the fundamental and essential matrices that describe the scene. Now, according to the theory each corresponding pair of points should satisfy the equation: P1'*F*P0=0.

However, when i'm trying to check that for a set of point extracted from the algorithm (i.e. point on the checkerboard) i get something like P1'*F*P0=f33 (when f33 is the element in 3rd row and 3ed col of F). So what am i missing?

(ps. P0 is a 3x1 vector (x' y' 1)' when x' is x coordinate of the image centered around the principal point and divided by the focal length. same for y').

thanks in advance!