Altering Between Adequate Criterions For Existence Of Solution Of Linear System Using Banach’s Theorem

Abstract

This study explores the presence and singularity of solutions for a system of linear equations through the application of the Banach Fixed Point Theorem. The primary aim is to illustrate how modifying the definition of a metric influences the conditions required for the presence and singularity of solutions in such systems. By examining these changes, the work sheds light on the flexibility of metric-based approaches and their impact on solving linear equations, potentially opening pathways for broader applications in mathematical analysis and computational methods.