Question: Suppose that T is n n and c, d are scalars. (a) Prove that if T has the eigenvalue with an associated eigenvector

Suppose that T is n × n and c, d are scalars.
(a) Prove that if T has the eigenvalue λ with an associated eigenvector →v then →v is an eigenvector of cT + dI associated with eigenvalue cλ + d.
(b) Prove that if T is diagonalizable then so is cT + dI.

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