The values of k for which the system of ...

The values of `k` for which the system of equations `kx+y+z=0,x-ky+z=0` and `x+y+z=0` possesses non-trivial solution. Are

A

`1,2`

B

`-1,1`

C

`1,-2`

D

`-1,-2`

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The correct Answer is:

B

`Delta=0`
`implies|{:(k,1,1),(1,-k,1),(1,1,1):}|=0`
`impliesk(-k-1)-1(1-1)+1(1+k)=0`
`implies-k^(2)-k+1+k=0`
`k=+-1`

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