Determine the values of `lambda` for which the following system of equations : `lambdax+3y-z=1` `x+2y+z=2` `-lambdax+y+2z=-1` has non-trival solutions.

Explanation

`Delta=0 `


`[[lambda , 1 , 1 ],
[-1 , lambda , 1 ],
[-1 , -1 , lambda]
=0 `


`lambda(lambda^{2}+1)-1(-lambda+1)+1(1+lambda)=0 `


`lambda^{3}+lambda+lambda-1+x+lambda=0 `


`lambda^{3}+3 lambda=0 lambda(lambda^{2}+3)=lambda=0`