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For real parameters α and β, consider the homogeneous system λ x + (sinα)y + (cosα)z = 0, x + (cosα)y + (sinα)z = 0, -x + (sinα)y - (cosα)z = 0. The collection of all x-values for which this system admits a non-zero solution is:

1. [0,√(2)]
2. [-√(2),0]
3. [-√(2),√(2)]
4. None of these

Correct answer: [-√(2),√(2)]

Solution

For a nonzero solution the coefficient determinant must vanish: λ = √2·sin(2α+π/4). As α varies this expression takes every value in [-√2, √2], so that is the required set.

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