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The system of equations
\[
\begin{array}{l}
6 x+5 y+\lambda z=0 \\
3 x-y+4 z=0 \\
x+2 y-3 z=0
\end{array}
\]
has
(a) only a trivial solution for \( \lambda \in \mathrm{R} \)
(b) exactly one nontrivial solution for some real \( \lambda \)
(c) infinite number of nontrivial solutions for one value of \( \lambda \)
(d) only one solution for \( \lambda \neq-5 \)
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