Three results in connection with inverse matrices

First we show that the Moore-Penrose solution of an arbitrary system of linear equations is a convex combination of the solutions of all uniquely solvable partial systems. The other two results concern the elements of inverse Toeplitz band matrices, namely the asymptotic behavior of a determinant appearing in a formula of D. S. Meek and a modification of a formula of W. D. Hoskins and P. J. Ponzo for matrices with binomial coefficients in the limit case.