(Solved) Find all real numbers λ such that the homogenous system (λ I_n-A)x=0 has a non-trivial solution.


Question: Find all real numbers \(\lambda \) such that the homogenous system \(\left( \lambda {{I}_{n}}-A \right)x=0\) has a non-trivial solution.

\[A=\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 1 & -1 \\ 1 & 0 & 0 \\ \end{matrix} \right]\]

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