The matrix completion problems are about completing a partially filled matrix to achieve the lowest possible rank. As they can be interpreted as an understanding of a certain algebraic variety, we consider a corresponding algebraic matroid and desire to characterize its bases. Polyhedralizing via tropical algebra may help us to figure out this characterization. We begin the talk with brief introductions on matrix completion problems, algebraic matroids, and tropical algebra. No pre-knowledge is assumed. This is based on ongoing work with May Cai, Cvetelina Hill, and Josephine Yu.