New Method for Solving Linear Systems of Algebraic Equations | ||||
| Advances in Basic and Applied Sciences | ||||
| Volume 4, Issue 1, March 2025, Page 73-85 PDF (934.72 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/abas.2024.306139.1048 | ||||
 View on SCiNiTO | ||||
| Author | ||||
Usama Wadie 
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| Computer and Systems Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt. | ||||
| Abstract | ||||
| This paper presents a method for solving linear systems of algebraic equations. The proposed method can find all solutions, can deal with any order of square linear systems in a fast and an easy way, and produces an explicit formula for the solution. The proposed method has been organized and structured in an easy way that facilitates the solving using a computer or manually. It has been developed to be complete, easier, faster, stable and effective. The main idea of the proposed method is to gradually transform any square linear system of algebraic equations into a square linear system with two variables. To achieve this, I deduced the proposed method using second-order determinants and the substitution method. The results of extensive experiments on many examples demonstrated the robustness of the proposed method, on various types of linear systems of algebraic equations, where the proposed method showed superior performance against many other methods as well. | ||||
| Keywords | ||||
| Coefficients; Determinants; Levels; Substitution | ||||
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