  We present a simple, accurate method for solving consistent, rank-deficient
linear systems, with or without addi- tional rank-completing constraints. Such
problems arise in a variety of applications, such as the computation of the
eigenvectors of a matrix corresponding to a known eigenvalue. The method is
based on elementary linear algebra combined with the ob- servation that if the
matrix is rank-k deficient, then a random rank-k perturbation yields a
nonsingular matrix with probability 1.
