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Suppose that a 4 × 4 matrix A has eigenvalues ?1 = 1, ?2 = ?...

Suppose that a 4 × 4 matrix A has eigenvalues ?1 = 1, ?2 = ? 2, ?3 = 4, and ?4 = ? 4. Use the following method to find det (A).

If

p(?) = det (?I ? A) = ?n + c1?n ? 1 + ? + cn

So, on setting ? = 0, we obtain that

det (? A) = cn or det (A) = (? 1)ncn

det (A) =

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