Solving Linear Systems with Column Reduction

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.

Additional information

Notes on contributors

Romain Boulet

Romain Boulet ([email protected]) obtained his PhD in mathematics in 2008 at the University of Toulouse (France) and he is, since 2012, associate professor in mathematics at iaelyon, school of management (University of Lyon, France); he belongs to Magellan research lab. His research areas include graph theory (especially algebraic graph theory) and network analysis with a particular interest on interdisciplinary collaborations. He teaches algebra (matrix calculus and applications), statistics and data mining at iaelyon, public school of management.