Find the value of the `"determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|`

Options

A. x+y+z
B. 0
C. (x+y)(y+z)(z+x)
D. (x-y)(y-z)(z-x)

Answer

B

Explanation

`|{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|`
`=|{:(1,x,x+y+z),(1,y,x+y+z),(1,z,x+y+z):}|`
`(C_(3)toC_(3)+C_(2))`
`=(x+y+z)|{:(1,x,1),(1,y,1),(1,z,1):}|`
`=(x+y+z)xx0(therefore C_(1)" and "C_(3)" are idential")`
=0.