Systems of Linear Equations
A x = b.
A is the system matrix, x is the vector of unknowns and b is the vector of the right-hand side.
A unique solution only exists, if det(A)≠0.
If det(A)=0 and rk(A)=rk(A|b), we can find a general solution, that depends on parameters (λi).
The number of necessary parameters equals the difference between the number of unknowns and the rank of the system matrix.
It is possible to define auxiliary parameters, that can be used in the system matrix and the vector of the right-hand side.