Solving Linear Systems with Column Reduction

Abstract

Summary In order to solve a system of linear equations, students or teachers are used to performing a row reduction with the Gauss method. In this paper we propose to adopt a column point of view through two fundamental subspaces of a matrix—its kernel and its image—linked to the homogeneous system and to a particular solution of the system. This paper provides a method to find the set of solutions of a system by performing a column reduction of a double augmented matrix of the system.