For a real number ????, if the system
![\left[\begin{array}{ccc}1&\alpha &\alpha^{2} \\\alpha &1&\alpha \\\alpha^{2}&\alpha &1\end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1\\-1\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B%5Calpha+%26amp%3B%5Calpha%5E%7B2%7D+%5C%5C%5Calpha+%26amp%3B1%26amp%3B%5Calpha+%5C%5C%5Calpha%5E%7B2%7D%26amp%3B%5Calpha+%26amp%3B1%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C-1%5C%5C1%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}1&\alpha &\alpha^{2} \\\alpha &1&\alpha \\\alpha^{2}&\alpha &1\end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1\\-1\\1\end{array}\right]")
of linear equations, has infinitely many solutions, then 1 + ???? + ????² =
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