Sistemas lineares homogêneos de recorrências lineares de primeira ordem com duas e três variáveis.

Abstract

Considering the lack of an adequate bibliography on first-order linear recurrence systems with constant coefficients and the use of this tool to solve practical problems, we present an analytical study on the subject, followed by practical applications, considering the two-dimensional and three-dimensional cases when the matrix of coefficients of the system has real eigenvalues. The approach makes use of the Jordan decomposition of the coefficients matrix and a change of variable to simplify the system. Then, the simplified system is solved using suitable techniques for first-order linear recurrences and the solution of the original system is obtained.