If system of equations2x+2ay+az=02x+3by+bz=02x+4cy+cz=0 has a non-trival solution, then

If system of equations2x+2ay+az=02x+3by+bz=02x+4cy+cz=0 has a non-trival solution, then

  1. A

    a+b+c=0

  2. B

    a,b,c are in A.P. 

  3. C

    1a,1b,1c are in A.P.

  4. D

    a,b,c are in G.P. 

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    Solution:

    If the given system of equations have a non-trivial 

    solution, then 

    22aa23bb24cc=0212aa13bb14cc=0                                    Applying R2R2R1,R3R3R1=212aa03b2aba04c2aca=0

    =23b2aba4c2aca=0=(3b2a)(ca)(4c2a)(ba)=0=3bc3ab2ac+2a24bc4ca2ab+2a2=0=bcab+2ca=0=1a+1c=2b1a,1b,1c are in A.P. 

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