If the system of linear equations `x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0` has a non-zero solution, then `a, b, c`

Question

If the system of linear equations `x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0` has a non-zero solution, then `a, b, c`

If the system of linear equations `x+2ay +az =0,x+3by+bz =0 and 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`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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.`

5 views Answered 2023-02-05 15:29