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The aim of this work is to show the consistency of all systems of non-homogeneous linear difference equations of the form, whereis a finite potent endomorphism of an arbitrary vector space  V  and. An algorithm to compute the set of solutions of these systems is given. In particular, the method offered is valid for computing the explicit solutions of the system of non-homogeneous difference equations, with  A  being a finite square matrix.

Explicit solutions of non-homogeneous difference equations from finite potent endomorphisms