True since det a ? 2 in ? 1 ? 2 ? 2 ? 2 ? n λ2 we

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True. Since det(AλIn) = (λ1λ)(λ2λ)(λnλ), we conclude that the product of the eigenvalues is equal tothe constant term of the characteristic polynomial.
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14.4/4 points |Previous AnswersHoltLinAlg2 6.1.047.Suppose thatAis a square matrix with characteristic polynomial(a) What are the dimensions ofA? (Givensuch that the dimensions are4, corresponding to(λ5)2(λ6)4(λ+ 1).n×n.)(b) What are the eigenvalues ofA? (Enter your answers as a comma­separated list.)(c) IsAinvertible?(d) What is the largest possible dimension for an eigenspace ofA?44
(d) The largest possible dimension of an eigenspace is4, corresponding to(λ5)2(λ6)4(λ+ 1).n×n.)

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