We have to check both Rank[A] as well as Rank[A:B] (the augmented matrix)
- If Rank[A] = Rank[A:B], then only the system is consistent
Now check for what kind of solution it has:
i) If Rank[A] = Rank[A:B] = n (number of unknowns), then a unique solution exists
ii) If Rank[A] = Rank[A:B] $<$ n, then infinite number of solutions exist
- If Rank[A] $\neq$ Rank[A:B], then the system is inconsistent i.e. no solution exists