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Find the value of k for which the homogeneous system 3x + ky - 2z = 0, x + ky + 3z = 0, 2x + 3y - 4z = 0 has a non-trivial solution.

1. 15
2. 16
3. 31/2
4. 33/2

Correct answer: 33/2

Solution

Setting the determinant to zero gives 2k - 33 = 0, so k = 33/2.

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