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Question

If the system of linear equations
2x+2ay+az=02x+3by+bz=02x+4cy+cz=0,

where a,b,cR are non-zero and distinct; has non-zero solution, then


Your Answer
A
a+b+c=0
Your Answer
B
a,b,c are in A.P.
Correct Answer
C
1a,1b,1c are in A.P.
Your Answer
D
a,b,c are in G.P.

Solution

The correct option is C 1a,1b,1c are in A.P.
∣ ∣22aa23bb24cc∣ ∣=0

R2R2R1,R3R1∣ ∣22aa03b2aba04c2aca∣ ∣=0

3bc2ac3ab+2a2[4bc4ac2ab+2a2]=0bc+2acab=0ab+bc=2ac1c+1a=2b
1a,1b,1c are in A.P.

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