Discussion
Under what condition does a homogeneous system have non-trivial solutions?
Answer: D
Correct answer: the rank is less than the number of unknowns
With \( r < n \) there are \( n-r \) free variables, so solutions other than the zero vector exist. For a square system this is the same as saying the coefficient determinant vanishes. If instead \( r = n \), the only solution is the trivial one, and having more equations than unknowns does not by itself change anything.
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