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If the system x - 4y + 7z = g, 3y - 5z = h, -2x + 5y - 9z = k is consistent, then which relation must hold?

1. g + h + k = 0
2. 2g + h + k = 0
3. g + h + 2k = 0
4. g + 2h + k = 0

Correct answer: 2g + h + k = 0

Solution

Because the three left-hand sides are linearly dependent, consistency requires the same dependence among g, h, k; this gives 2g + h + k = 0.

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