Suppose V V is a finite dimensional vector space. Suppose TE (0) TEL(V) is a linear...

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Suppose V V is a finite dimensional vector space. Suppose TE (0) TEL(V) is a linear operator with eigenvalue XX, and let v v be an eigenvector corresponding A. Let p(z)=3+2021z+2z2 p (z) = 3 + 2021 z + 2 z 2, and consider the linear operator p(T) p (T). Prove that p(2) p (A) is an eigenvalue of p(T) p (T) with corresponding eigenvector v v Suppose V V is a finite dimensional vector space. Suppose TE (0) TEL(V) is a linear operator with eigenvalue XX, and let v v be an eigenvector corresponding A. Let p(z)=3+2021z+2z2 p (z) = 3 + 2021 z + 2 z 2, and consider the linear operator p(T) p (T). Prove that p(2) p (A) is an eigenvalue of p(T) p (T) with corresponding eigenvector v v

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