In the first five sections of this paper various properties of a Rao generalized inverse of a matrix are established. A method of computing such an inverse is also given. In order to illustrate the differences between the Rao and other generalized inverses, a survey of results on Penrose-Moore inverses is included.nThe last three sections are devoted to showing how a generalized inverse can be used in the theoretical development of the simplex and modified simplex methods of linear programming. In particular, it is shown that the fundamental equations and iteration formulas of these methods can be derived using matrix notation without requiring the assumption that the linear programming problem has no redundant constraints.
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