If the system of linear equation
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0, where a, b, c ∈ R are non-zero and distinct; has a non-zero solution, then :
(1) a, b, c are in A.P.
(2) a + b + c = 0
(3) a, b, c are in G.P.
(4) 1/a, 1/b, 1/c abc are in A.P.