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If the system of linear equations x + ky + 3z = 0, 3x + ky - 2z = 0, 2x + 4y - 3z = 0 has a non-zero solution (x, y, z) then (xz)/(y²) is equal to
- -10
- 10
- -30
- 30
Correct answer: 10
Solution
The system of equations has a non-zero solution if the determinant of the coefficient matrix is zero, which leads to a specific relationship between the variables. Solving for the ratio (xz)/(y²) using the values derived from the equations shows that it simplifies to 10.
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