Q7ts2 - 2 Solution The characteristic polynomial det has...

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2 Solution: The characteristic polynomial det ± 3 λ 2 11 λ ² = λ 2 4 λ +5 has the roots λ =2 ± i ,and ± 3 (2 + i )2 (2 + i ) ² ~v = ~ 0 has the solution ~v = ± 2 1+ i ² . [It actually has the solution ~v = ± 2 z ( i ) z ² , but z = 1 is the simplest choice.] Writing ~v = ~u + i~w where ~u and ~w have real components, we have T ( ~u )+ iT ( )= T ( ~v )=(2+ i ) =(2+ i )( ~u + )=2 ~u +
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