The value of k for which the set of equations 3x + ky - 2z = 0, x + ky + 3z = 0 and 2x + 3y - 4z = 0 has a non-trivial solution is-
Step-by-Step Solution
Key Concept: For a homogeneous system of linear equations to have a non-trivial solution, the determinant of the coefficient matrix must be zero.
The system of equations is homogeneous. For a non-trivial solution, the determinant of the coefficient matrix must be zero: |[3, k, -2], [1, k, 3], [2, 3, -4]| = 0. Expanding along the first row: 3(-4k - 9) - k(-4 - 6) - 2(3 - 2k) = 0. This simplifies to -12k - 27 + 10k - 6 + 4k = 0, which gives 2k - 33 = 0, so k = 33/2.
Correct Answer: 3