The solution is unique if and only if the linear system A has a unique solution. Furthermore, if B, then the

**above**linear system becomes C, which has a unique solution if and only if D has full column rank.

Here

*above*refers to "linear system A" from the previous sentence. Somehow

*above*doesn't sound quite right, because the thing that is said to be "above" could actually be on the same line, and thus not really above. I think

*aforementioned*is for things that are mentioned much earlier, and

*previous*seems a little ambiguous. What do you think?