3. Matrix Range, Rank, and Pseudo-inverse Let A e Cmxn and b E C. Show that the following three statements are equivalent: - There exists a vector x E C" such that Ax = b, - Rank(A) = Rank ([A b]) where [A b] = Cmx(n+1) is a matrix obtained by appending b after the last column of A, and - AA¹b = b.

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