Question: Consider a real nn matrix A. Let 1; 2::::::::k:::::::n be its eigenval- ues. Let 2 R be such that = i; 8i = 1; 2::::::n.

Consider a real nn matrix A. Let 1; 2::::::::k:::::::n be its eigenval-

ues. Let 2 R be such that = i; 8i = 1; 2::::::n. Also let (k; v) be an eigen

pair of A, i.e Av = kv. Prove that (A I) is an invertible matrix and then

using that show that v is an eigenvector of (A I)1. Is it possible to nd

the corresponding eigenvalue? If so, determine that.

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