Q7rs2 - 2 Solution: The characteristic polynomial det has...

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2 Solution: The characteristic polynomial det ± 3 λ 2 15 λ ² = λ 2 8 λ +17 has the roots λ =4 ± i ,and ± 3 (4 + i )2 11 (4 + i ) ² ~v = ~ 0 has the solution ~v = ± 2 1+ i ² . [It actually has the solution ~v = ± 2 z (1 + i ) z ² , but z = 1 is the simplest choice.] Writing = ~u + i~w where ~u and ~w have real components, we have T ( ~u )+ iT ( )= T ( ~v )=(4+ i ) =(4+ i )( ~u + )=4 ~u
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This note was uploaded on 04/12/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

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