1112a3 b4ca bc=0C2→C2−2C3 1110 b2ca bc=0R3→R3−R2,R2→R2−R1 1000b2c−bab−ac−b=0 b(c−b)−(b−a)(2c−b)=0 On simplification, b2=a1+c1 ∴a,b,c are in Harmonic Progression.
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
Held on 30 Apr 2003 · Verified 6 Jul 2026.
satisfy a+2b+3c=0
are in A.P.
are in G.P.
are in H.P.
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