Answer is (A) 10
Given:
x + ky + 3z = 0, 3x + ky – 2z = 0, 2x + 4y – 3z = 0
For non-zero solutions, we know that
−3k + 8 – k(−9 + 4) + 3(12 – 2k) = 0
−3k + 8 + 5k + 36 – 6k = 0
−4k = −44 k = 11
Therefore, x + 11y + 3z = 0
3x + 11y + 2z = 0
2x + 4y – 3z = 0
Now, z = t; therefore,
x + 11y = −3t
3x + 11y = 2t