If \( a, b, c \) are non-zeros, then the system of equations
\[
\begin{array}{l}
(\alpha+a) x+\a... VIDEO
If \( a, b, c \) are non-zeros, then the system of equations
\[
\begin{array}{l}
(\alpha+a) x+\alpha y+\alpha z=0 \\
\alpha x+(\alpha+b) y+\alpha z=0 \\
\alpha x+\alpha y+(\alpha+c) z=0
\end{array}
\]
has a non-trivial solution if
(a) \( \alpha^{-1}=-\left(a^{-1}+b^{-1}+c^{-1}\right) \)
(b) \( \alpha^{-1}=a+b+c \)
(c) \( \alpha+a+b+c=1 \)
(d) None of these
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