This answer explains what is null space very effectively. In brief Null Space is the set of vectors which have 0 effect on the system when applied. So, what is the use of finding null-space? Is it just that it gives us what not to use and whether the matrix is invertible or not or is there a better use for null space? May be something like, "we know adding null-space-vectors won't change the system but improves the stability of the system?" (I'm just guessing)
Any practical examples (like the ones given in the answer referred) are greatly appreciated. Theoretical ones will also be helpful.