  Let A be an m \times n matrix in which the entries of each row are all
distinct. Drisko showed that, if m \ge 2n-1, then A has a transversal: a set of
n distinct entries with no two in the same row or column. We generalize this to
matrices with entries in a matroid. For such a matrix A, we show that if each
row of A forms an independent set, then we can require the transversal to be
independent as well. We determine the complexity of an algorithm based on the
proof of this result. Lastly, we observe that m \ge 2n-1 appears to force the
existence of not merely one but many transversals. We discuss a number of
conjectures related to this observation (some of which involve matroids and
some of which do not).
