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ISRN Algebra
Volume 2012 (2012), Article ID 205478, 14 pages
http://dx.doi.org/10.5402/2012/205478
Research Article

The Matrix Linear Unilateral and Bilateral Equations with Two Variables over Commutative Rings

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3-b, Naukova Street, 79060 L'viv, Ukraine

Received 16 January 2012; Accepted 20 February 2012

Academic Editors: I. Cangul, H. Chen, and P. Damianou

Copyright © 2012 N. S. Dzhaliuk and V. M. Petrychkovych. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The method of solving matrix linear equations 𝐴 𝑋 + 𝐵 𝑌 = 𝐶 and 𝐴 𝑋 + 𝑌 𝐵 = 𝐶 over commutative Bezout domains by means of standard form of a pair of matrices with respect to generalized equivalence is proposed. The formulas of general solutions of such equations are deduced. The criterions of uniqueness of particular solutions of such matrix equations are established.