n this paper, we introduce a recursive solution approach to linear systems of the form Ax=b, where A is non-singular and its corner minors are all non-zero. For the first time in the literature, we show how one can exploit (possible)useful information provided by corner sub-matrices of A towards an efficient solution approach to the linear system. This is going to initiate a thorough study of solution methods whose goals are to fully exploit available information within the given linear system.
