JEE-Mains 2015 (5/30)

Algebra Level 4

\[\begin{cases} 2x_1-2x_2+x_3=\lambda x_1 \\ 2x_1-3x_2+2x_3=\lambda x_2 \\ -x_1+2x_2=\lambda x_3 \end{cases}\] Find the set of all values of \(\lambda\) for which the above system of linear equations has a non-trivial solution.

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