# Previous answers holtlinalg1 61026 consider the

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7. 3/3 points | Previous Answers HoltLinAlg1 6.1.026. Consider the matrix A Find the characteristic polynomial for the matrix A . (Write your answer in terms of λ Find the real eigenvalues for the matrix A . (Enter your answers as a comma-separated list.) λ = Find a basis for each eigenspace for the matrix A 1 1 1 [1;1;1] A = 0 0 1 1 0 0 0 1 0 . .) . , 1 1
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8. 1/1 points | Previous Answers HoltLinAlg1 6.1.037. Determine if the statement is true or false, and justify your answer. An eigenvalue λ must be nonzero, but an eigenvector u can be equal to the zero vector. Solution or Explanation False. An eigenvalue may be 0, as with the matrix which has eigenvalues and Moreover, by this definition , an eigenvector must be a nonzero vector. 9. 1/1 points | Previous Answers HoltLinAlg1 6.1.039. Determine if the statement is true or false, and justify your answer. If u is a nonzero eigenvector of A , then u and A u point in the same direction. and A = 1 0 0 0 λ = 0 λ = 1. True. Since u is a nonzero eigenvector of A , there exists λ > 0 such that A u = λ u . True. Since u is a nonzero eigenvector of A , there exists λ < 0 such that A u = λ u . False. A u and u are perpendicular. False. If λ > 0, then A u and u point in opposite directions. False. If λ < 0, then A u and u point in opposite directions. λ < 0, A = 1 0 0 0 u = , 1 0 A u = u .