Question: (a) Prove that every real 3 3 matrix has at least one real eigenvalue. (b) Find a real 4 4 matrix with no

(a) Prove that every real 3 × 3 matrix has at least one real eigenvalue.
(b) Find a real 4 × 4 matrix with no real eigenvalues.
(c) Can you find a real 5 × 5 matrix with no real eigenvalues?

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