If the system of linear equations x + 2ay + az = 0, x + 3by + bz = 0, x + 4cy + cz = 0 has a non-zero solution, then a, b, c
- satisfy a + 2b + 3c
- are in G.P
- are in A.P
- are in H.P
For non trivial solution, the determinant of the coefficient of various term vanish.
This implies, (3bc – 4bc) – 2a(c – b) + a(4c – 3b) = 0
2ac/a+c = b
The correct option is D.