**ABSTRACT**

We extend results of Campbell of the linear systems of differential equations 𝐴 𝑥̇+ 𝐵𝑥=𝑓 when 𝐴 and 𝐵 are rectangular, and results of Kanan of solution of a class of singular linear systems of difference equations 𝐴 𝑥𝑛+1+ 𝐵𝑥𝑛=𝑓𝑛 when 𝐴 and 𝐵 are square, to such systems of difference equations when 𝐴 and 𝐵 are rectangular. Explicit solutions of the last one are derived for several cases. One such is, when the matrix (𝜆𝐴+𝐵) is one-to-one, another case is when such matrix is onto, for a scalar 𝜆∈ℂ. Also, explicit solutions are derived for the case that 𝐴 is onto, and for the case that 𝐵 is onto.

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