# Holtlinalg1 61026nva consider the matrix a find the

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7.–/3 pointsholtlinalg1 6.1.026.nvaConsider the matrixAFind the characteristic polynomial for the matrixA. (Write your answer in terms ofλ=0 0 11 0 00 1 0..)(No Response)Find the real eigenvalues for the matrixA. (Enter your answers as a comma-separated list.)λ=(No Response)Find a basis for each eigenspace for the matrixA[1;1;1].A=0 0 11 0 00 1 0,11
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8.–/1 pointsHoltLinAlg1 6.1.037.Determine if the statement is true or false, and justify your answer.An eigenvalueλmust be nonzero, but an eigenvectorucan be equal to the zero vector.
9.–/1 pointsHoltLinAlg1 6.1.039.Determine if the statement is true or false, and justify your answer.Ifuis a nonzero eigenvector ofA, thenuandAupoint in the same direction.True. Sinceuis a nonzero eigenvector ofA, there existsλ> 0 such thatAu=True. Sinceuis a nonzero eigenvector ofA, there existsλ< 0 such thatAu=False.Auanduare perpendicular.False. Ifλ< 0, thenAuandupoint in opposite directions.False. Ifλ> 0, thenAuandupoint in opposite directions.λ< 0,A=1 00 0u=,10Au=uandλu.λu..

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