İn 1932, S. Banacii stated that if A is a re\'ersibie matrİK, then the System of egnations k=o a‘.nk-^Xk, has a unique solution given by X = vl + By, where B — is the uniqııe right inverse cf A, By = s Yk k=o co I , vGc, xgc4^ and v — (v )* e In 1953 MacPhail shovzed that v need n=o ‘ a o not belong to by giving a simple reversible matrix with v ubounded. It is the purpose of this paper to extend Banach’s work on c-reversible matrices to bv-re- versible matrİces and construct matrices which are bv-rever»ible matrices but not c-reversible; the first one with v bounded and the second one with v unbounled. Notations: s; c; bv; bs; l^,; Ca i 0; 8; X* will denote the set of ali sequences; convergent secjuenccs; sequences of bounded variation that is, sequences such that S | | 00 k=o and lim X]j exists; bounded series, that is, sequences x such that ’eo n sup I S X]j I k=o 00; bounded sequences; convergence domain, that is, cx = {xes; Axec}; S (1. 1, ...), 8*^ X* the continuous dual of X respectively. n=o (0,0,...,0,1,0;...)