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International Journal of Engineering Mathematics
Volume 2016, Article ID 9382739, 14 pages
http://dx.doi.org/10.1155/2016/9382739
Research Article

On the Extension of Sarrus’ Rule to Matrices: Development of New Method for the Computation of the Determinant of Matrix

Department of Mechanical Engineering, University of Lagos, Lagos, Nigeria

Received 14 June 2016; Revised 8 August 2016; Accepted 30 August 2016

Academic Editor: Giuseppe Carbone

Copyright © 2016 M. G. Sobamowo. 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 determinant of a matrix is very powerful tool that helps in establishing properties of matrices. Indisputably, its importance in various engineering and applied science problems has made it a mathematical area of increasing significance. From developed and existing methods of finding determinant of a matrix, basketweave method/Sarrus’ rule has been shown to be the simplest, easiest, very fast, accurate, and straightforward method for the computation of the determinant of 3 × 3 matrices. However, its gross limitation is that this method/rule does not work for matrices larger than 3 × 3 and this fact is well established in literatures. Therefore, the state-of-the-art methods for finding the determinants of 4 × 4 matrix and larger matrices are predominantly founded on non-basketweave method/non-Sarrus’ rule. In this work, extension of the simple, easy, accurate, and straightforward approach to the determinant of larger matrices is presented. The paper presents the developments of new method with different schemes based on the basketweave method/Sarrus’ rule for the computation of the determinant of 4 × 4. The potency of the new method is revealed in generalization of the basketweave method/non-Sarrus’ rule for the computation of the determinant of () matrices. The new method is very efficient, very consistence for handy calculations, highly accurate, and fastest compared to other existing methods.