 Both the pivotal column and pivotal row may be computed directly using the solutions of linear systems of equations involving the matrix B and a matrix-vector product using A.These observations motivate the ""revised" simplex algorithm", for which implementations are distinguished by their invertible representation of B.In large linear-programming problems A is typically a sparse matrix and, when the resulting sparsity of B is exploited when maintaining its invertible representation, the revised simplex algorithm is much more efficient than the standard simplex method.