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If the system of equations 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non-trivial solution (x, y, z), then x/y + y/z + z/x + k is equal to:
- 1/2
- 3/4
- -1/4
- -4
Correct answer: 1/2
Solution
For the system of equations to have a non-trivial solution, the determinant of the coefficient matrix must be zero. Solving for k under this condition reveals that the expression x/y + y/z + z/x + k simplifies to 1/2.
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