Discussion
When does a consistent system have infinitely many solutions?
Answer: B
Correct answer: when the common rank is less than the number of unknowns
Consistency requires the coefficient and augmented ranks to be equal. If that common rank \( r \) is less than the number of unknowns \( n \), then \( n-r \) of the unknowns can be assigned freely and the rest follow, giving an \( (n-r) \)-parameter family. The rank can never exceed \( n \), so the fourth option describes an impossibility.
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