A note on solutions of linear systems

2013/04/30 by Branko Malesevic, Ivana Jovovic, Malesevic, Branko +5
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1304.7890

Published in the ISRN Algebra, Vol. 2013

arxiv created 2013/07/21 · arxiv updated 2013/07/23

Abstract

In this paper we will consider Rohde's general form of 1-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free parameters in Penrose's formula x = A^(1) c + (I - A^(1)A)y for obtaining the general solution of the linear system. This results will be applied for finding the general solution of various homogenous and non-homogenous linear systems as well as for different types of matrix equations.

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