  Motivated by many practical applications, in this paper we study {\em budget
feasible mechanisms} where the goal is to procure independent sets from
matroids. More specifically, we are given a matroid
$\mathcal{M}=(E,\mathcal{I})$ where each ground (indivisible) element is a
selfish agent. The cost of each element (i.e., for selling the item or
performing a service) is only known to the element itself. There is a buyer
with a budget having additive valuations over the set of elements $E$. The goal
is to design an incentive compatible (truthful) budget feasible mechanism which
procures an independent set of the matroid under the given budget that yields
the largest value possible to the buyer. Our result is a deterministic,
polynomial-time, individually rational, truthful and budget feasible mechanism
with $4$-approximation to the optimal independent set. Then, we extend our
mechanism to the setting of matroid intersections in which the goal is to
procure common independent sets from multiple matroids. We show that, given a
polynomial time deterministic blackbox that returns $\alpha-$approximation
solutions to the matroid intersection problem, there exists a deterministic,
polynomial time, individually rational, truthful and budget feasible mechanism
with $(3\alpha +1)-$approximation to the optimal common independent set.
