How the Existence of Inconsistent Solutions in Systems of Non Homogeneous Linear Equations can be Tamed

Résumé

In this paper the issue of the long aged existence of inconsistent solutions to systems of non-homogeneous linear equations has been given another look,and some of the causes of for inconstancy in solutions were discovered. This paper has shown that inconsistent solutions are caused by an ill-posed or ill constructed equation in the system of equations,and when the ill constructed linear equation is identified and correction is effected,the system of equations will have a unique solution when the problem is solved guidelines are given on how to idetify correctly.To prove the wort of the discoveries made in this paper,example problems were taken from well known standarded text books in Linear Algebra,Tne need to tame the existence of inconsistent solutions so that students are not discouraged from having interest in mathematical problems involving non-linear systems of linear equations in future and to avoid unnecessary wast of valuable time solving problems that lead to false statements like; “ 0 =5!”.In a reduced echelon form when any of the equations,or any of the rows have two variables that makes that particular equation to become a homogeneous system,the use of the mirror image method(MIM) makes what will have resulted to the system having infinitely many solutions to have a unique solution.

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