In this paper we will consider a partial reduction for nonhomogeneous linear systems of the operator equations with the system matrix in the companion form and with different operators. As a result of this method we will get an equivalent system consisting of the linear opera\-tor equations having only one or two variables. Homogeneous part of the equation in one unknown is obtained using generalized characteristic polynomial of the system matrix. We will also look more closely at some properties of the doubly companion matrix.