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What is the value of the determinant |{:...

What is the value of the determinant `|{:(1," "1," "1),(1,1+xyz," "1),(" "1," "1,1+xyz):}|`?

A

`1+x+y+z`

B

`2xyz`

C

`x^(2)y^(2)z^(2)`

D

`2x^(2)y^(2)z^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`|{:(1," "1," "1),(1,1+xyz," "1),(1," "1,1+xyz):}|" "{:(c_(2) rarr c_(2)-c_(1)),(c_(3) rarr c_(3)-c_(1)):}`
`=|{:(1,0,0),(1,xyz,0),(1,0,xyz):}|=1(x^(2)y^(2)z^(2)-0)=x^(2)y^(2)z^(2)`
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