SHORT APPROACH OF SOLVING A SYSTEM OF LINEAR ALGEBRAIC EQUATIONS

Authors

  • Larissa Bazarbayeva https://orcid.org/ 0009-0002-3451-3720, SDU University, Kaskelen, Kazakhstan
  • Aiman Shakulikova https://orcid.org/0009-0001-8873-0678, SDU University, Kaskelen, Kazakhstan
  • Aziza Aipenova https://orcid.org/0000-0002-5104-7429), SDU University, Kaskelen, Kazakhstan

Keywords:

system of linear algebraic equations, Gaussian method, matrix rank, Kronecker-Catelli’s theorem, pivot element, solution of a system of linear algebraic equations, reduced echelon form of matrix, echelon form

Abstract

This article discusses a very popular topic in all courses of Linear Algebra, studied by all technical specialties mainly in the first year. The solution of systems of linear equations is carried out by several methods. Of these, the most common is the Gauss method. Its description takes up a lot of space in books and requires a fairly long period of time to fully master it. Our method, the improved Gauss method, allows you not to spend much effort to transform systems to reduced echelon form and solve many related issues. This method allows students to answer the main questions of the tasks without paying attention to the calculation process, find a solution to the system by analyzing the ranks of the system. The purpose of this article is to illuminate these important concepts in a way that is accessible and interesting to all readers

Published

2025-02-24

How to Cite

Larissa Bazarbayeva, Aiman Shakulikova, & Aziza Aipenova. (2025). SHORT APPROACH OF SOLVING A SYSTEM OF LINEAR ALGEBRAIC EQUATIONS. Scientific Results, (9). Retrieved from https://ojs.publisher.agency/index.php/SR/article/view/5356

Issue

No. 9 (2025): Scientific Results

Section

Physical and Mathematical Sciences

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.