Let the system of linear equations \[ \begin{array}{l} x+y+\alpha z=2 \\ 3 x+y+z=4 \\ x+2 z=1 \e...

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Let the system of linear equations
\[
\begin{array}{l}
x+y+\alpha z=2 \\
3 x+y+z=4 \\
x+2 z=1
\end{array}
\]
have a unique solution \( \left(x^{*}, y^{*}, z^{*}\right) \). If \( \left(\alpha, x^{*}\right),\left(y^{*}, \alpha\right) \) and \( \left(x^{*},-y^{*}\right) \) are collinear points, then the sum of absolute values of all possible values of \( \alpha \) is
(a) 4
(b) 3
(c) 2
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