Existence Theorems for Linear Systems
This chapter is concerned with the existence of solutions to dual homogeneous linear systems. In this regard, we shall deal with pairs of finite systems of homogeneous linear equations and/or inequalities in which the variables are either nonnegative or unrestricted in sign. Specifically, these systems are structured in a fashion such that there is a one-to-one correspondence between unrestricted variables in one system and equations in the other; and between nonnegative variables in one system and inequalities in the other. Moreover, the coefficient matrix in one system is the negative transpose of the coefficient matrix of the other.
KeywordsLinear System Coefficient Matrix Existence Theorem Dual System Finite System
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