All the values of \( \lambda \) for which the system of equations \...

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All the values of \( \lambda \) for which the system of equations
\[
\begin{array}{r}
(\lambda+5) x+(\lambda-4) y+z=0 \\
(\lambda-2) x+(\lambda+3) y+z=0 \\
\lambda x+\lambda y+z=0
\end{array}
\]
has a non-trivial solution lie in the set
(a) \( \{-1,2\} \)
(b) \( \{0,-1\} \)
(c) \( \{0\} \)
(d) \( \mathbf{R} \)
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