We thank the reviewers for their comments.  We address specific reviewer points below.$ - - - - - Reviewer_1:  We agree that subspace clustering and identifiability are different. We will make it clear in the paper. Technically, we only need to know an upper bound on the dimension of each subspace, and so r in our results can be taken to be this known upper bound. Regarding the distinction between one subspace and K-subspaces: The identifiable observation patterns for low-rank matrix completion (LRMC) and subspace clustering with missing data (SCMD) are similar, but differ in a non-trivial way. SCMD requires stronger conditions, which we derive in Theorem 2. The main differences are described in lines 299-302. In fact, the exponential-time algorithm you suggest in your review needs to search for identifiable SCMD patterns. Searching for identifiable LRMC patterns alone can lead to incorrect subspaces, as in Example 3. Algorithm 2 and our deterministic conditions for SCMD are similar to those in Pimentel-Alarcon et al (2015a) for LRMC.  We tried to make it clear that we used these and other results from the literature, but we are happy to clarify it in the introduction. Thanks for the pointers to general position assumptions in the literature. We will add citations. - - - - - Reviewer 2: Intuitively, A1 ensures that with probability 1, columns will not lie in polynomial varieties defined by other points by mere chance.  For example, under A1, any combination of r columns will be linearly independent.  It may be possible to extend the results to discrete distributions, and this is a interesting direction for future work. About the relation to coherence, A1 essentially discards pathological cases with measure zero, like subspaces perfectly aligned with the canonical axes (which would yield entries equal to zero), or identical columns. In contrast, typical results require bounded coherence. This essentially asks that the subspaces are not too aligned with the canonical axes (which discards a set of subspaces with positive measure), but indeed allows some identical columns, or entries to be zero.  We point out that coherence does not imply A1, nor vice-versa. - - - - - Reviewer 3: We have not explored the relation to expander graphs yet, but we certainly will.  We appreciate the comment and will investigate this potential connection. As mentioned to Reviewer 1, our results for SCMD are similar (but non-trivial) to those in Pimentel-Alarcon et al (2015a) for LRMC.  We can certainly discuss this at the beginning of the paper.