The Existence and Representation of the Solutions to the System of Operator Equations AiXBi + CiYDi + EiZFi = Gi(i = 1, 2)

In this paper, we give the necessary and sufficient conditions for the existence of general solutions, self-adjoint solutions, and positive solutions to the system of AiXBi+CiYDi+EiZFi=Gi(i=1,2) under additional conditions. In addition, we derive the representation of general solutions to the system of AiXBi+CiYDi+EiZFi=Gi(i=1,2), and provide the matrix representation of the self-adjoint solutions and the positive solutions in the sense of the star order.