Question

Supppose A is an invertible n\times n matrix and v is an eigenvector of A with associated eigenvalue -3. Convince yourself that v is an eigenvalue of the following matrices, and find the associated eigenvalues:
1. \ A^6, \ eigenvalue = ,
2. \ A^{-1}, \ eigenvalue = ,
3. \ A + 5 I_n, \ eigenvalue = ,
4. \ 6 A, \ eigenvalue = .

Answer 1

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