For a real number \(\alpha\), if the system \(\begin{bmatrix}1 & \alpha & \alpha^{2}\\&n...

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For a real number \(\alpha\), if the system \(\begin{bmatrix}1 & \alpha & \alpha^{2}\\ \alpha& 1 & \alpha \\\alpha^{2}& \alpha & 1\end{bmatrix} \begin{bmatrix}x\\ y\\ z\end{bmatrix} = \begin{bmatrix}1\\ -1\\ 1\end{bmatrix}\) of linear equations, has infinitely many solutions, then \(1 + \alpha + \alpha^{2} =\)
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