A method is given by means of which a computer program for Linear Programming can be used to produce, in one run, the solution of a set of simultaneous linear equations and the inverse of the matrix of coefficients. The non-negativity rule usual in Linear Programming places no restriction on the problems that can be dealt with. The method can also be used for inversion of matrices not associated with simultaneous equations. Many programs have special features which will render parts of the procedure outlined superfluous, but these possibilities have been left out of account.