Question: (a) Find the explicit formula for the characteristic polynomial det(A - I) = -3 + a2 - b + c of a general 3

(a) Find the explicit formula for the characteristic polynomial det(A - λI) = -λ3 + aλ2 - bλ + c of a general 3 × 3 matrix. Verify that a = tr A, c = det A. What is the formula for b?
(b) Prove that if A has eigenvalues λ1, λ2, λ3, then a = tr A = λ1 + λ2 + λ3, b = λ1 λ2 + λ1 λ3 + λ2 λ3, c = det A = λ1 λ2 λ3.

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