Diagonalização de matrizes 2X2 e reconhecimento de cônicas

Abstract

This paper deals with the recognition of TAPER using the method of matrix diagonalization 2X2. At first, it shows the definition of conics, standard equations followed by their names and geometric representations. Then follows the ideas of eigenvalues and eigenvectors of a linear transformation that are the basis for the diagonalization of matrices.Immediately after that, the linear independence eigenvector is discussed, as well as its properties of forming a basis of a vector space. The condition for any square matrix to be diagonalizable is shown below, as well as the particulars of a symmetric matrix. The demonstration that all 2×2 symmetric matrix is diagonalizable is made from a matrix, elegant and elemental approach. The recognition of conics is made from basic calculations using some content widely exploited in high school such as matrices, determinants, linear systems and algebraic equations. At the end it is presented a way of teaching conical school using educational software Winplot.