Sistemas lineares com ênfase nas operações elementares e no Teorema do Posto

Abstract

Bearing in mind that mathematical content can be represented in several different ways and with the intention of making teaching simple, in this dissertation, we seek to present a perspective on the study of systems of linear equations, content covered in the 7th and 9th year of teaching. fundamental and in a more complete way in the 2nd year of high school and, in order to make reading easier, we start by bringing a notion of matrices to then present the operations that we can perform with them. All this will be of great relevance a few pages ahead because, after these topics, we will give greater emphasis to elementary operations on lines, where we will use scaling techniques and the application of the Rank Theorem of a matrix to solve a system in question. We will also approach algebraic and geometric representations, where you limit yourself to just a linear system in R 2 and R 3 showing, through graphs built in GeoGebra, the association of equations of the linear system with lines and planes. Finally, we will cite some problem situations in our daily lives involving systems of linear equations with the purpose of presenting the clear need for it in our daily lives.