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If the system of linear equations ax ...

If the system of linear equations
`ax +by+ cz =0`
`cx + ay + bz =0`
` bx + cy +az =0` where a,b,c,` in` R are non-zero and distinct, has a non-zero solution, then:

A

a+b+c=0

B

a,b,c are in A.P.

C

`1/a,1/b,1/c` are in A.P.

D

a,b,c are in G.P.

Text Solution

Verified by Experts

The correct Answer is:
A
`|(a,b,c),(c,a,b),(b,c,a)|=0`
`rArr (a^2-bc)-b(ac-b^2)+c(c^2-ab)=0 rArr a^3 -abc-abc+b^3+c^3-abc=0`
`rArr a^3+b^3+c^3-3abc=0 rArr (a+b+c)(a^2+b^2+c^2-ab-b-ca)=0`
`rArr` a+b+c=0
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