Question: Suppose that is an eigenvalue of A. (a) Prove that c is an eigenvalue of the scalar multiple c A. (b) Prove that

Suppose that λ is an eigenvalue of A.

(a) Prove that c λ is an eigenvalue of the scalar multiple c A. 

(b) Prove that λ + d is an eigenvalue of A + d I.

(c) More generally, c λ + d is an eigenvalue of B = c A + d I for scalars c, d.

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