Are there similar results for more general systems of linear equations?

　　The answer is yes. Before introducing Clem's law, we first introduce the concept of -element linear equations.

        A system of linear equations containing unknowns

 　　 (1)

is called a system of linear equations of variable. When the constant term on its right end is not all zero, the system of equations (1) is called a system of non-homogeneous linear equations. When is all zero, the system of equations (1) is called a system of homogeneous linear equations , that is

  　　(2)

        The determinant formed by the coefficient  of the linear equation system (1) is called the coefficient determinant of the system of equations , that is

.

　　Theorem ( Clem's law) If the coefficient determinant of the linear equation system (1)

,

Then the system of linear equations (1) has a unique solution, and its solution is

,

among them, the determinant is the determinant obtained by correspondingly replacing the element 

,,,

 of the -th column in with the constant term 

,,,

 of the system of equations while leaving the remaining columns unchanged.

　　Note: The [ proof ] of this theorem is given in Chapter 2 .