Study of systems of linear equations for compatibility

Before attempting to solve a system of linear equations, it should be examined for compatibility. Preliminary research simplifies the analysis of systems of linear equations that describe logistic and production processes. If the system of linear equations is compatible, it has solutions.

Compatibility of systems of linear equations is assessed through the application of Kronecker's theorem–In the course of the analysis, it is determined whether the ranks of the main and extended matrices are equal, if they are equal, compatibility can be asserted, inconsistency is observed in all other cases.

If the system is definite, it has exactly one solution, if it is indefinite, it has several. The definiteness of a compatible system of linear equations is observed when the rank of the main matrix equals the number of unknowns.