Discussion
A homogeneous system of 3 equations in 3 unknowns has coefficient rank 2. Its solution set is
Answer: D
Correct answer: a one-parameter family of non-trivial solutions
The number of free variables is \( n - r = 3 - 2 = 1 \), so the solution set is a line through the origin - every scalar multiple of a single non-zero vector. It contains the trivial solution as the point where the parameter is zero, but it is not confined to it, since the rank is less than the number of unknowns.
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