Automating Upper Triangular Matrix Neutralisation for Minimal Error

Abstract

This study develops and tests a MATLAB program for neutralising systems with upper triangular coefficient matrices. Augmented matrices for systems of linear equations are reduced to produce a neutral (identity matrix) left hand side, at which point the right hand side has the solutions for the system. A strategy for minimal error is pursued, where elimination operations must be completed in one step for each number. The strategy was expressed in pseudocode, a flowchart developed, and then the program was coded in MATLAB. The program was tested for four sample augmented matrices of varying sizes. The results demonstrated that the program was 100% accurate. The technique can be applied to any square matrix system, since any square matrix can be expressed as an upper triangular matrix. The automation of matrix operations and achievement of 100% accuracy allows for the use of the program for very large data sets, extending the potential for research with accurate finding.