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If the system of linear equations x + 2a...

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`

A

`A.P.`

B

`G.P.`

C

`H.P.`

D

satisfies `a+2b+3c=0`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` The system of linear equation has a non zero solution.
`Delta=|{:(1,2a,a),(1,3b,b),(1,4c,c):}|=0`
`:.(3bc-4bc)-(2ac-4ac)+(2ab-3ab)=0`
`:.bc+ab=2ac`
`:. (1)/(a)+(1)/(c )=(2)/(b)`
`impliesa,b,c` are in `H.P.`
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