\left\{ \begin{array} { l } { \lambda x _ { 1 } + x _ { 2 } + x _ { 3 } = 0 } \\ { x _ { 1 } + \lambda x _ { 2 } + x _ { 3 } = 0 } \\ { x _ { 1 } + x _ { 2 } + 2 x _ { 3 } = 0 } \end{array} \right.
Solve for x_1, x_2, x_3 (complex solution)
\left\{\begin{matrix}\\x_{1}=0\text{, }x_{2}=0\text{, }x_{3}=0\text{, }&\text{unconditionally}\\x_{1}\in \mathrm{C}\text{, }x_{2}=x_{1}\left(1-2\lambda \right)\text{, }x_{3}=x_{1}\left(\lambda -1\right)\text{, }&\lambda =1\text{ or }\lambda =0\end{matrix}\right.
Solve for x_1, x_2, x_3
\left\{\begin{matrix}x_{1}=0\text{, }x_{2}=0\text{, }x_{3}=0\text{, }&\lambda \neq 1\\x_{1}\in \mathrm{R}\text{, }x_{2}=x_{1}\left(1-2\lambda \right)\text{, }x_{3}=x_{1}\left(\lambda -1\right)\text{, }&\lambda =0\text{ or }\lambda =1\end{matrix}\right.
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