Let be an eigenvalue of A with corresponding eigenvector x If a and is not an eigenvalue of A, show that 1 ( ) is an eigenvalue of (A al) 1 with corresponding eigenvector x (Why must A I be invertible

Question: Let be an eigenvalue of A with corresponding eigenvector x. If a and is not an eigenvalue of A, show that

Let λ be an eigenvalue of A with corresponding eigenvector x. If a ≠ λ and α is not an eigenvalue of A, show that 1 / (λ - α) is an eigenvalue of (A - al)-1 with corresponding eigenvector x. (Why must A = αI be invertible??

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