How to use microsoft office excel to solve systems of linear equations

Abstract

The article shows how to use Microsoft Office Excel table tools to solve some problems in algebra and number theory. In particular, it presents the method of solving of system of linear equations using Gaussian (complete exclusion) elimination in Microsoft Office Excel table tools and presents advantages that this method has over traditional one. Author gives an example of Kronecker-Capelli theorem that answers the question about compatibly of the system of linear equations of any rank and gives the solution in case if the system is compatible. Author shows that Ms Excel is suitable for using Cramer’s, Gaussian, and elimination methods to solve a system of linear equations that helps to develop programming skills and to save a considerable amount of time.
Given the fact that the hours dedicated to the study of mathematics is being reduced, the importance of using IT is increasing in the process of learning of particular topics in high mathematics permit to diversify the way of studying, to rise student motivation, to give students a possibility to study new material by themselves in the short terms and an experience to be used in the work environment. The use of the computer during a lesson will multiply 4-5 times the amount of studied material and will help students to develop the capacities of programming, self-control, and self-evaluation. The article admit that the use of computer technology helps to reduce the time teacher spent to prepare exercises and to grade student papers. The examples of such exercises are also given in the article.
This method of solving of systems of linear equations can also be used to some problem of matrix analysis, of vector algebra, of the problem of optimization in mathematical programming etc. It needs to be studied further.