Linear dynamical systems (LDS) are mathematical models that describe dynamical processes. They are used for analysis, design and simulations of linear systems and for approximating the behaviour of non-linear dynamical systems. This paper presents some of the methods used in solving linear dynamical systems and what needs to be taken into account when choosing which method to use on a given system. The least-squares and least-norm methods yield remarkable solutions. QR factorization, quadratic form and singular value decomposition are factorization methods for matrices that give matrix forms which are easy to compute with and do operations on and which have a significant effect on the speed of doing the computations and also on interpreting the systems. Two classes of systems are defined, autonomous and systems with inputs and outputs, and various methods for solving them are discussed along with considering the interpretations of the systems’ properties.