Transformações elementares nas linhas de uma matriz como ferramenta adicional para o cálculo de matrizes inversas e resolução de problemas

Abstract

Determine the inverse matrix, when this exists, and solve a linear system of equations are tasks that increase as the order of the array and the size of the system also increases the difficulties of being performed. Usually, the books of school work determining an inverse matrix using the matrix product as the product of a matrix with its inverse is equal to the identity matrix and solving a linear system by Cramer's rule and scheduling system equations. In this work, we propose to introduce high school students the concept of Elementary Transformations in the rows of a matrix and use it as a new tool for the determination of a matrix inverse and solving a system of linear equations. Elementary Transformations are, in a way, simple operations and lighter, especially compared to calculations performed to find inverse matrices of order greater than or equal to three and solutions of linear systems larger than a two-by-two system.