  Matroids generalize the familiar notion of linear dependence from linear
algebra. Following a brief discussion of founding work in computability and
matroids, we use the techniques of reverse mathematics to determine the logical
strength of some basis theorems for matroids and enumerated matroids. Next,
using Weihrauch reducibility, we relate the basis results to combinatorial
choice principles and statements about vector spaces. Finally, we formalize
some of the Weihrauch reductions to extract related reverse mathematics
results. In particular, we show that the existence of bases for vector spaces
of bounded dimension is equivalent to the induction scheme for $\Sigma^0_2$
formulas.
