  We consider partial and total reduction of a nonhomogeneous linear system of
the operator equations with the system matrix in the same particular form as in
paper [N. Shayanfar, M. Hadizadeh 2013]. Here we present two different
concepts. One is concerned with partially reduced systems obtained by using the
Jordan and the rational form of the system matrix. The other one is dealing
with totally reduced systems obtained by finding the adjugate matrix of the
characteristic matrix of the system matrix.
