A full row-rank system matrix generated by the strip-based projection model along one scanning direction was studied recently in [9]. In this paper, we generalize the result to multiple directions. Let Cu = h be a reduced binary linear system generated along two distinct scanning directions by the strip-based projection model in discrete tomography, where C is row-rank deficient. We identify all the linearly dependent rows explicitly through a partition of the rows of C into minimal linearly dependent sets. The removal of these linearly dependent rows results in a full-rank matrix. Consequently, the computational cost for image reconstruction is reduced.