Analogs of Cramer’s rule for the minimum norm least squares solutions of some matrix equations

The least squares solutions with the minimum norm of the matrix equations AX=B,XA=B and AXB=DAXB=D are considered in this paper. We use the determinantal representations of the Moore–Penrose inverse obtained earlier by the author and get analogs of the Cramer rule for the minimum norm least squares solutions of these matrix equations.