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Let T : P(R) → P(R) be the linear map defined by T(p(x)) = xp′(x) (you...

Let T : P(R) → P(R) be the linear map defined by T(p(x)) = xp′(x) (you may take it for granted that T is linear). Show that for each λ ∈ Z with λ ≥ 0, λ is an eigenvalue of T , and xλ is a corresponding eigenvector.
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