The sum of distinct values of λ for which the system of equations : λ - 1   x + 3 λ + 1…

The sum of distinct values of $\lambda$ for which the system of equations :

$\left(\lambda -1\right) x+\left(3\lambda +1\right) y+2\lambda z=0$

$\left(\mathrm{\lambda }-1\right) \mathrm{x}+\left(4\mathrm{\lambda }-2\right) \mathrm{y}+\left(\mathrm{\lambda }+3\right) \mathrm{z}=0$

$2\mathrm{x}+\left(3\mathrm{\lambda }+1\right) \mathrm{y}+3 \left(\mathrm{\lambda }-1\right) \mathrm{z}=0$,

Has non-zero solutions, is ....... .