A GEOMETRIA DE MATRIZES E DETERMINANTES

Abstract

The objective of this study is to propose a different approach to teaching of matrices, seeking value the geometric aspect of them, and determinants. In fact, the matrices are important not only as a way to organize numerical data (tables), but also by the different properties of the operations that define the matrix algebra. However, the traditional way of teaching matrices and determinants in a secondary education, such as tables of numbers and a number associated with a matrix, respectively, the definitions of matrix operations and determinants, as well as their properties become quite unnatural. The Geometry not only turns these concepts more natural, but also develops our intuition about it. Furthermore, the geometrical aspects of the matrices and determinants are present in technological applications such as in Computer Graphics, for example. We begin this work by analyzing some textbooks adopted in secondary education, in order to see how the theory of matrices and determinants have been approached in classrooms, and to relate it to national education curriculum guidelines. Later, we explore the geometric content of matrices and determinants and propose a methodology for teaching, which brings out this aspect. This approach by middle of the Geometry is intended to stimulate the student to deduce properties and reflect on the results in operations with matrices, for example, addition, multiplication and also in the calculation of determinants. In proposing this methodology, we use the free software Geogebra, with the intent of providing a better view of the content for the student.