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6. Let A =   3 −12 4 −1 0 −2 −1 5 −1 ...

6. Let A =   3 −12 4 −1 0 −2 −1 5 −1   . 1 (a) Find all eigenvalues of A5 (Note: If λ is an eigenvalue of A, then λ n is an eigenvalue of A n for any integer n.). (b) Determine whether A is invertible (Check if the constant term of the characteristic polynomial χA(λ) is non-zero.). (c) If A is invertible, find (i) A−1 using the Cayley-Hamilton theorem (ii) All the eigenvalues of A−1

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