that corresponds to a row–leading 1 in the reduced row echelon form of A. Since the reduced row echelon form of A is unique, the pivot positions are uniquely determined and do not depend on whether or not row interchanges are performed in the reduction process. Also, the pivot of a row must appear to the right of the pivot in the above row in row echelon form. References R. L. Burden, J. D. Faires, Numerical Analysis, 8th edition, Thomson Brooks/Cole, 2005. G. H. Golub, C. F. Loan, Matrix Computations, 3rd edition, Johns Hopkins, 1996. . Numerical linear algebra Exchange algorithms sv:Pivotelement