Question: (a) If A is an m x n matrix and M = (A | b) the augmented matrix for the linear system Ax = b.

(a) If A is an m x n matrix and M = (A | b) the augmented matrix for the linear system Ax = b. Show that either
(i) Rank A = rank M, or
(ii) Rank A = rank M - 1.
(b) Prove that the system is compatible if and only if case (i) holds.

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