Matrices Determinants Sequences Series

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

  1. satisfy a + 2b + 3c
  2. are in G.P
  3. are in A.P
  4. are in H.P

Answer

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.