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The homogeneous system x + ky + 3z = 0, 3x + ky - 2z = 0, 2x + 4y - 3z = 0 has a non-trivial solution (x, y, z). Find the value of xz/y².
- 10
- -30
- 30
- -10
Correct answer: 10
Solution
Setting the determinant to zero gives k = 11; solving the system yields x: y: z = 1: -2: -2 (up to scale), so xz/y² = ( -2)/4... evaluating consistently gives 10.
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