Applications Of The Rational Canonical Form Of Matrices To Systems Of First Order Linear Differential Equations With Constant Coefficients

The theory of matrices plays an integral role in applied and pur® mathematics. In recent years, matrices have become very essential in many different fields of study. They are used in applications in engineering, physics, economics, and many other fields. It is the purpose of this paper to use matrix theory to study systems of first-order linear differential equations with constant coefficients with respect to (l) existence of solution; (2) uniqueness of solution; and. (3) form of solutions. This study will have the following form: Chapter I will include some basic definitions and notations used in differential equations and matrix theory. Chapter II contains the basic theorems used. Chapter III will show the existence, uniqueness, and form of solutions. Chapter IV Includes applications of systems of first-order linear differential equations with constant coefficients and Chapter V gives the aumbry. The bibliography follows Chapter V