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In this paper, the general solution of the homogeneous matrix dif- ference system is constructed in terms of two fundamental matrix solutions. The general solution of the inhomogeneous matrix dierence system is estab- lished by the variation of parameters formula. A unique solution of the two- point boundary value problem associated with the matrix dierence system is constructed by applying the QR-algorithm and the Bartels-Stewart algorithm.

First order difference system- existence and uniqueness