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Using elementary linear algebra, we develop a technique that leads tosolutions of two widely known problems on nonnegative matrices. First, we givea short proof of the result by Vavasis stating that the nonnegative rank of amatrix is NP-hard to compute. This proof is essentially contained in the paperby Jiang and Ravikumar, who discussed this topic in different terms fifteenyears before the work of Vavasis. Secondly, we present a solution of theproblem of Cohen and Rothblum on rational nonnegative factorizations, which wasposed in 1993 and remained open.

The nonnegative rank of a matrix: Hard problems, easy solutions