  In this paper we will consider Rohde's general form of {1}-inverse of a
matrix A. The necessary and sufficient condition for consistency of a linear
system Ax=c will be represented. We will also be concerned with the minimal
number of free parameters in Penrose's formula x = A^(1) c + (I - A^(1)A)y for
obtaining the general solution of the linear system. This results will be
applied for finding the general solution of various homogenous and
non-homogenous linear systems as well as for different types of matrix
equations.
