In this thesis we consider several distinct problems in linear systems theory and encompass the implementation of such work via the symbolic computational language Maple. Our analytical contribution is split into three main areas these being: the solution to a regular, discrete-time ARMA-representation; the computation of the generalised inverse of a rational matrix P(s)ER(s)n×m; and the computation of the invariant direction vectors associated with a regular polynomial matrix description (PMD).