# 13 11 points previous answers holtlinalg1 61046

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13.1/1 points |Previous AnswersHoltLinAlg1 6.1.046.Determine if the statement is true or false, and justify your answer.The product of the eigenvalues (counting multiplicities) ofAis equal to the constant term of thecharacteristic polynomial ofA.Solution or ExplanationFalse. Consider.1001det(AλIn) = (λ1λ)(λ2λ)(λnλ),
14.4/4 points |Previous AnswersHoltLinAlg1 6.1.047.Suppose thatAis a square matrix with characteristic polynomial(a) What are the dimensions ofA? (Givensuch that the dimensions are(λ3)2(λ4)4(λ+ 1).7
(b) What are the eigenvalues ofA? (Enter your answers as a comma-separated list.)
(c) IsAinvertible?
(d) What is the largest possible dimension for an eigenspace ofA?44Solution or Explanation(c)Ais invertible, since 0 is not an eigenvalue.(d) The largest possible dimension of an eigenspace is4, corresponding to.1..
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