On version of Farkas lemma of alternative

TL;DR

This paper introduces a novel version of Farkas lemma that uses different matrices with various dimensions for alternative linear systems, potentially improving computational efficiency.

Contribution

It proposes a new approach to Farkas lemma involving diverse matrices, expanding the traditional framework for alternative linear systems.

Findings

New version of Farkas lemma with variable matrices

Potential computational advantages in solving linear systems

Different dimensional matrices improve flexibility

Abstract

A new version of Farkas lemma of alternative linear systems is proposed. One and the same matrix $A$ and vector $b$ have always been used in alternative linear systems. The paper shows a different way of alternative systems involving application of different matrices with various dimensions, which can be advantageous from computational point of view.