A Note on Solutions of Linear Systems. (1st August 2013)

• Record Type: Journal Article
• Authors: Malešević, Branko; Jovović, Ivana; Makragić, Milica; Radičić, Biljana
• Other Names: Jaballah A. Academic Editor.; Lee E. W. H. Academic Editor.; Marko F. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2013(2013)
• Publication Date: 2013-08-01
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.1155/2013/142124
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : 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 A x = 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. These results will be applied for finding the general solution of various homogenous and nonhomogenous linear systems as well as for different types of matrix equations.