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the value of determinant |{:(1+alpha,1,1...

the value of determinant `|{:(1+alpha,1,1),(1, 1+beta,1),(1,1,1+gamma):}|` is

A

`2^(n)`

B

`2^(n-1)`

C

`2^(2n)`

D

`2^((n-1)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` For `S_(n),a_(11),a_(12),a_(13),….a_(1(n-1))` we have two options `'1'` or `'-1'`m but for `a_(1n)` we have only one way depending upon the product `(a_(11)*a_(12)*a_(13)*…..*a_(1(n-1)))`
`:.` For `R_(1)` we have `2^(n-1)` ways
Similarly for `R_(2),R_(3),R_(4),....R_(n-1)` we have `2^(n-1)` ways
For `R_(n)` we have only one way.
Hence total number of ways `(2^(n-1))^(n-1)=2^((n-1)^(2))`
For `S_(3)`, we have `2^((3-1)^(2))=1` elements.
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