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The least squares solutions with the minimum norm of the matrix equations${\rm {\bf A}}{\rm {\bf X}} = {\rm {\bf B}}$, ${\rm {\bf X}}{\rm {\bf A}} ={\rm {\bf B}}$ and ${\rm {\bf A}}{\rm {\bf X}}{\rm {\bf B}} ={\rm {\bf D}} $are considered in this paper. We use the determinantal representations of theMoore - Penrose inverse obtained earlier by the author and get analogs of theCramer rule for the least squares solutions of these matrix equations.

Analogs of Cramer's rule for the least squares solutions of some matrix equations