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Question

If the system of linear equation x+2ay+az = 0, x+3by+bz = 0, x+4cy+cz = 0 has a non zero solution, then a, b, c
  1. Are in A.P.
  2. Satisfy a +2b + 3c = 0
  3. Are in G. P.
  4. Are in H. P.


Solution

The correct option is D Are in H. P.
∣ ∣12aa13bb14cc∣ ∣ = 0,     [C2  C22C3] ∣ ∣10a1bb12cc∣ ∣ = 0,     [R3  R3R2, R2  R2R1] ∣ ∣10a0bba02cbcb∣ ∣ = 0 ; b(cb)(ba)(2cb) = 0
On simplification, 2b = 1a+1c
a, b, c are in Harmonic progression.

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