Solutions of systems of linear differential equations with matrix

A variety of solutions to systems of linear differential equations are known. In this study, except for these methods, systems of linear differential equations are solved in different ways with the help of matrices. In this study, section of the matrix, according to a program is considered to be used in solutions of systems of linear defferential equations and is deepened at this state. In the section of the matrix, issues such as elementary transformations, elementary matrices, equivalent matrices, the canonical way of transforming the matrix, polynomial matrices, equivalent polynomial matrices, elementary transformations for equivalent polynomial matrices, the canonical form of equivalent polynomial matrices (Smith Normal Form), exponential matrix, eigenvalues and eigenvectors of a matrix, canonical forms are focused.Systems of homogeneous linear differential equations with constant coefficients are solved by elimination method, determinant (cramer) method, eigenvectors method, smith normal form, rational canonical form, triangular matrix method and matrix exponential method. Systems of non-homogeneous linear differential equations with constant coefficients are solved by elimination method, determinant (cramer) method, diagonalization method, variation of parameters method, smith normal form, rational canonical form, triangular matrix method, matrix exponential method. Systems of homogeneous linear differential equations with variable coefficients and systems of non-homogeneous linear differential equations with variable coefficients are solved with the help of the matrices. In addition, systems of homogeneous linear differential equations with variable coefficients are solved by Peano-Baker method.