# Solution or explanation true since we conclude that

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we conclude that the product of theeigenvalues is equal to the constant term of the characteristic polynomial.
Aλ2In) = (λ1λ2)(λ2λ2) (λnλ2), we conclude that the product of theeigenvalues is equal to the constant term of the characteristic polynomial.
AλIn) = (λ1λ)(λ2λ) (λnλ), we conclude that the product of theeigenvalues is equal to the constant term of the characteristic polynomial.False. Consider.1001
AλIn) = (λ1λ)(λ2λ) (λnλ), we conclude that the product of theeigenvalues is equal to the leading coefficient of the characteristic polynomial.
14.–/4 pointsHoltLinAlg1 6.1.047.Suppose that Ais a square matrix with characteristic polynomial (a) What are the dimensions of A? (Give nsuch that the dimensions are 4, corresponding to (λ5)3(λ4)4(λ+ 1).n×n.)(b) What are the eigenvalues of A? (Enter your answers as a comma-separated list.)(c) Is Ainvertible?
(d) What is the largest possible dimension for an eigenspace of A?(No Response)4Solution or Explanation
(d) The largest possible dimension of an eigenspace is 4, corresponding to (λ5)3(λ4)4(λ+ 1).n×n.)
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