Prove that if QA (t) is the characteristic polynomial of A, then pa(t) | PA(t). Prove...

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Prove that if QA (t) is the characteristic polynomial of A, then pa(t) | PA(t). Prove that if λ = C is an eigenvalue of A, then (t-λ) | PA(t). Prove that if 21, 22, ...,, E C are all the pairwise distinct eigenvalues of A and A is a diagonal- izable matrix, then (t-₁) (tλ₂) (t-λr) | PA(t). Prove that Par(t) = QA(t) and PÅr (t) = pa(t). Prove that if QA (t) is the characteristic polynomial of A, then pa(t) | PA(t). Prove that if λ = C is an eigenvalue of A, then (t-λ) | PA(t). Prove that if 21, 22, ...,, E C are all the pairwise distinct eigenvalues of A and A is a diagonal- izable matrix, then (t-₁) (tλ₂) (t-λr) | PA(t). Prove that Par(t) = QA(t) and PÅr (t) = pa(t).