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1) Let L be the line through the origin of R2 that makes an angle of π/4 with the positive x-axis, and let A be the standard matrix for the reflection of R2 about that line. Make a conjecture about the eigenvalues and eigenvectors of A and confirm your conjecture by computing them in the usual way
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I'm not sure what kind of conjecture to make about this I suppose it is reasonable to hypothesize that the eigenvectors will span \(\mathbb R^2\) anyway, finding them is not hard the line that intersects the x-axis at an angle of \(\frac\pi4\) is \(x=y\) what is the transformation for a point about that line?
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