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Unformatted text preview: ˚ J 2 .1/ . We obtain cyclic vectors for two invariant subspaces using the last two columns of the matrix P ± 1 , which are 2 6 6 4 1 ± 1=2 1 3 7 7 5 : Since the entries of these columns are constant polynomials, these two columnn are already the cyclic vectors we are looking for. A second basis vector for each for the two invariant subspaces is obtained by applying A ± E to the cyclic vector. The result is the basis v 1 D 2 6 6 4 1 ± 1=2 3 7 7 5 , v 2 D .A ± E/v 1 D 2 6 6 4 2 1 3 7 7 5 , w 1 D 2 6 6 4 1 3 7 7 5 , and...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Vectors

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