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If a ,b and c are all non-zero and |1...

If `a ,b` and `c` are all non-zero and `|1+a1 1 1a+b1 1 1a+c|=0,` then prove that `1/a+1/b+1/c+1=0`

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2

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1

C

-1

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Text Solution

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The correct Answer is:
C
Given `|{:(1+a," "1," "1),(" "1,1+b," "1),(" "1," "1,1+c):}|=0`
Applying `C_(2) rarr C_(2)-C_(1)and C_(3)rarr C_(3)-C_(1)`
`rArr |{:(1+a,-a,-a),(" "1,b,0),(" "1,0,c):}|=0`
`rArr` Expanding along `R_(3), 1(ab)+c(b+ab+a)=0`
`rArr ab + bc + ca + abc = 0`
`rArr (1)/(a)+(1)/(b)+(1)/(c)=-1`
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NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
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