Gauss Elimination Family of Methods
In this chapter, we study the commonly used methods for the solution of general square systems of linear equations as well as for the inversion of matrices. The same processes yield, as a by-product, the determinant of a matrix, thereby also detecting any singularity or ill-conditioning of the matrix. All these methods use elementary transformations and tend to decouple the scalar equations so as to make the solution either trivial or easy.
In the Gauss elimination family of methods for solving linear systems, Gauss-Jordan elimination is conceptually the most straightforward one. It involves complete reduction of the coefficient matrix up to the identity matrix. If the system is to ...