Introduction of the Kifilideen’s Extermination and Determinant of Matrix (KEDM) Method for Resolving Multivariable Linear Systems with Two, Three and Four Unknowns

Abstract

The Gaussian extermination technique poses significant challenges when applied to systems of linear equations with three or four unknowns, as it involves multiple steps and requires a high number of arithmetic operations, making the method less efficient and more complex to implement and understand. Furthermore, the Jacobian and Gauss-Seidel methods produce approximate solutions that may not accurately represent the true solution. Additionally, LU decomposition method can introduce round – off errors, leading to inaccurate solutions. The graphical method is also impractical for systems with more than two unknowns, as visualization and interpretation become increasingly difficult. Cramer’s rule, used for resolving large systems of linear equations, is computationally complex and inefficient due to complexity of determinant calculations. Therefore, a simpler and more efficient technique is needed for resolving linear systems of simultaneous equations with two, three, and four unknowns. This study introduces Kifilideen’s Extermination and Determinant of Matrix (KEDM) Method for resolving multivariable linear systems with two, three, and four unknowns. The KEDM method employs a progressive extermination technique to narrow down the number of unknowns of a system of simultaneous equations using a determinant of matrix layout. This method was developed to efficiently determine the solution of linear systems of simultaneous equations. The KEDM method was tested on linear systems of simultaneous equations with two, three and four unknowns to evaluate its effectiveness and simplicity. The results show that the KEDM method involves only 2 × 2 determinant of matrix calculations, making it simpler, easier, more intuitive, less computationally expensive and more efficient to implement and understand.