For a real number α, if the system⎡⎢⎣1αα2α1αα2α1⎤⎥⎦ – InterviewSolution

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1.	For a real number α, if the system⎡⎢⎣1αα2α1αα2α1⎤⎥⎦⎡⎢⎣xyz⎤⎥⎦=⎡⎢⎣1−11⎤⎥⎦of linear equations, has infinitely many solutions, then 1+α+α2=
Answer» For a real number $α$ , if the system $⎡ ⎢ ⎣ \begin{matrix} 1 & α & α^{2} α & 1 & α α^{2} & α & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 1 \end{matrix} ⎤ ⎥ ⎦$ of linear equations, has infinitely many solutions, then $1 + α + α^{2} =$

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