Quiz3.EGM4313.Fall2011.solution

Quiz3.EGM4313.Fall2011.solution - EGM 4313 - Mikolaitis...

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EGM 4313 - Mikolaitis NAME:_____________________________ Fall 2011 Sorting Number:______________________ Quiz 3 Open book/Closed notes/No calculators or computers 30 minute time limit Find the eigenvalues and as many linearly independent eigenvectors as possible for the matrix 1 1 1 0 2 0 2 2 1 A Solution: First we need to find the eigenvalues by solving 1 1 1 0 2 0 0 2 2 1 . This is most easily accomplished by expanding about the middle row: 2 1 1 1 11 0 2 0 (2 ) (2 )((1 ) 2) 0 21 2 2 1 2, 1 2 i Expanding about the first column is also not too bad: 2 2 1 1 1 2 0 1 1 0 2 0 (1 ) 2 (2 )(1 ) 2(2 ) 2 1 2 0 2 2 1 (2 )((1 ) 2) 0 2,1 2 i It is similarly easy even if expanding about the first row. 2 2 1 1 1 2 0 0 2 0 2 0 ) 1 (2 )(1 ) 2(2 ) 2 1 2 2 2 2 1 (2 )((1 ) 2) 0 2 i
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There are three distinct eigenvalues so there must be three linearly independent eigenvectors.
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Quiz3.EGM4313.Fall2011.solution - EGM 4313 - Mikolaitis...

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