Algorithm For Solving Systems of Linear Equations: Exploring the Applications and Theory of Matrices and Gaussian Elimination

Abstract

We review here some of the basic definitions andelementary algebraic operations on matrices. There are many applications aswell as much interesting theory revolving around these concepts, which weencourage you to explore after reviewing this article. Gaussian elimination isan algorithm for solving systems of linear equations. It can also be used tofind the rank of a matrix, to calculate the determinant of a matrix, and tocalculate the inverse of an invertible square matrix. Row pivoting, columnpivoting, complexity theory etc. explained in this article.