[Solved] 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 = - - JEE (Advanced) 2017 Paper-1