COURSE OF PROJECTIVE GEOMETRY

§ 21:

*O81*

Find a 2 by 2 matrix whose determinant is to be 0.

We get x' y' = z' (ρ z' - τ x').

*O82*

By substitution of the coordinates of the five points in the equation we get five linear equations with six unknown variables a_{ij}.
In general, this gives a 1-dimensional solution space, so the coefficients a_{ij} are then unique up to a scalar factor.

(These five linear equations are linearly independent if and only if the five points are freely situated.)