Part CCSIR NET June 2024free-coordinate-from-a-basis-vector

Free coordinate from a basis vector

Let V be the subspace spanned by the vectors $v_{1} = (1, 0, 2, 3, 1), v_{2} = (0, 0, 1, 3, 5), v_{3} = (0, 0, 0, 0, 1)$ in the real vector space $R^{5}$ . Which of the following vectors are in V?

A.(1, 1, 1, 1, 1)
B.(0, 0, 1, 2, 4)
C.(1, 0, 1, 0, 1)✓
D.(1, 0, 1, 0, 2)✓

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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Free coordinate from a basis vector

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