Utilização do método de Gauss-Jordan no ensino médio

Abstract

This work is oriented to teachers and students in the high school. It aims to show the usage of Gauss-Jordan’s Elimination Method to solve systems of linear equations, calculation of inverse matrices and determinants. The motivation behind the selection of this topic is that, more and more, the study of matrices, determinants, and consequently, systems of linear equations has been ignored in the high school. Firstly, an abridgement is done on what equivalent matrices and elementary operations are. Secondly, it explains about the cofactor of an element of a matrix and about adjoint matrices, needed for the calculation of the inverse matrix using determinants. A little introduction of Gauss and Jordan’s histories is made, and then, the method itself. It is also shown what happens with the method when the matrices are not invertible, the systems are possible but undetermined, or, the systems are not possible. Concerning determinants, their properties are presented and the method’s efficacy for determinants of order n 3 is shown and furthermore, it is shown the application of the determinants in the calculation of inverse matrices and resolutions of systems using Cramer’s Rule. Finally, some suggestions for exercises are presented with brief resolutions.