Discussion
What solution does every homogeneous system certainly possess?
Answer: C
Correct answer: the trivial solution with all unknowns zero
Setting every unknown to zero satisfies \( AX = 0 \) whatever \( A \) is, so a homogeneous system is never inconsistent. The only question is whether anything else satisfies it as well, and that is decided by the rank - which is why the interesting question about a homogeneous system is always whether non-trivial solutions exist.
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