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If the value of the determinants |(a,1,1...

If the value of the determinants `|(a,1,1),(1,b,1),(1,1,c)|` is positive then:

A

cannot be less than 1

B

is greater than -8

C

is less than -8

D

must be greater than 8

Text Solution

Verified by Experts

The correct Answer is:
B
`|(a,1,1),(1,b,1),(1,1,c)|gt0`
`rArra(bc-1)-1(c-1)+1(1-b)gt0`
`rArr abc-a-c+1+1-bgt0`
`rArr abc+2-(a+b+c)gt0`
`rArr abcgt(a+b+c)-2`
Let, `a=-1,b=0 & c=1`
Then , `0gt-2` [which is correct]
Hence, abc = 0
`therefore` After considering all the option, (b) is correct option.
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