Show that if θ is an element of Reals, then the operator R : Reals^2 -> Reals^2 given by R ( x , y ) = ( cosθ * x + sinθ * y , sinθ * x - cosθ * y ) always has an eigenvector in Reals^2.
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Show that if θ is an element of Reals, then the operator R : Reals^2 -> Reals^2 given by R ( x , y ) = ( cosθ * x + sinθ * y , sinθ * x - cosθ * y ) always has an eigenvector in Reals^2.
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This solution is comprised of a detailed explanation to answer show that if θ is an element of Reals, then the operator R : Reals^2 -> Reals^2 given by R ( x , y ) = ( cosθ * x + sinθ * y , sinθ * x - cosθ * y ) always has an eigenvector in Reals^2.
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