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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
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