JEE Advanced 2017 Paper 1 Mathematics Q10

Mathematics

Problem

For a real number α\alpha, if the system [1αα2α1αα2α1][xyz]=[1−11]\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} has infinitely many solutions, then 1+α+α21+\alpha+\alpha^2 is

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