Part BCSIR NET December 2024check-membership-before-orthonormality

Check membership before orthonormality

Consider $R^{4}$ with the standard inner product. Let V be the subspace of $R^{4}$ spanned by the vectors (1, 0, 0, 1), (0, 1, 0, 1), and (0, 0, 1, 0). Which of the following is NOT an orthonormal basis of V?

A.{ $(- 1/ 2, 0, 0, - 1/ 2), (- 1/ 6, 2 / 3, 0, 1/ 6), (0, 0, 1, 0)$ }
B.{ $(1/ 2, 0, 0, 1/ 2), (- 1/ 6, 2 / 3, 0, 1/ 6), (0, 0, 1, 0)$ }
C.{ $(1/ 2, 0, 0, 1/ 2), (- 1/ 6, 2 / 3, 0, - 1/ 6), (0, 0, 1, 0)$ }✓
D.{ $(1/ 2, 0, 0, 1/ 2), (1/ 6, - 2 / 3, 0, - 1/ 6), (0, 0, 1, 0)$ }

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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Check membership before orthonormality

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