Abstract
In this research, an alternative technique to Gauss Elimination Method for Determinants is presented. It gives exact determinants. It is free of fractions, free of roundoff errors and can be applied for all types of square matrices. This alternative technique is illustrated in four different examples.
Highlights
In civil engineering applications, the linear system of algebraic equations, AX = B, arises, for example, in the solution of ordinary and partial differential equations, interpolation, curve fitting, networks of roads and Truss problem
Before using analytical or numerical methods to solve the linear system of algebraic equations or to find A-1 it is better to find the determinant value
The value of the Vandermode determinant of a system of linear algebraic equations is small but there is a solution to the linear system of algebraic equations
Summary
Determinants of 3rd order are evaluated analytically by the diagonal method or Laplace expansion method ( called the cofactors method) ([2]-[4]). Gauss elimination method is a numerical method used to find the value of a determinant |A|. By using Gauss elimination method the determinant value of. It is clear that the analytical evaluation of the determinant using the diagonal method gives |A| = 0 This is due to the round off errors result from the numerical technique used. In this research an alternative technique to Gauss Elimination Method for determinants is presented. It is free of fractions, free of round off errors, reliable and can be applied for all types of square matrices.
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