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For the system Ax = b, if rank(A) < rank(augmented matrix A|b), the system has:

AA single unique solution exists
BInfinitely many distinct solutions
CTwo distinct solutions to the system
DNo solution (inconsistent system)
Answer & Solution
Correct answer: D. No solution (inconsistent system)
rank(A) < rank(A|b) → b is NOT in column space of A → system is INCONSISTENT (no solution). **For consistency:** rank(A) = rank(A|b). Unique solution needs both = n.
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