A is a 3 × 4 real matrix and Ax = b is an inconsistent

A is a 3 × 4 real matrix and Ax = b is an inconsistent system of equations. The highest possible rank of A is

C = [A: B]_{3 × 5}
∴ ρ [C_{3 × 5} ] <e; min [3,5}
Since the system is inconsistent
ρ(A) < ρ(C)
∴ ρ (A) < 3
Hence, the maximum possible rank of A = 2