Part BCSIR NET December 2024row-space-complement-is-the-null-space

Row space complement is the null space

Let $v = (a, b, c) \in R^{3}$ be a nonzero vector that lies in the orthogonal complement (with respect to the standard inner product) of the row-space of the matrix A = [[2, 2, 7], [3, 1, 4]]. If a, b, c are all integers, then what is the smallest possible value of |a + b + c|?

A.5
B.10✓
C.15
D.20

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Row space complement is the null space

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