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The system of equations
\[
\begin{array}{l}
(1+\lambda) x_{1}+x_{2}+x_{3}=1 \\
x_{1}+(1+\lambda) x_{2}+x_{3}=\lambda \\
x_{1}+x_{2}+(1+\lambda) x_{3}=\lambda^{2}
\end{array}
\]
(a) is inconsistent if \( \lambda=0 \) or \( \lambda=-3 \)
(b) has a unique solution if \( \lambda(\lambda+3) \neq 0 \)
(c) has infinite number of solution for \( \lambda=-3 \)
(d) has infinite number of solution for \( \lambda=0 \)
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