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Exercise 5.C.8

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Proof. Assume $T$ has other eigenvalues besides $8$ (otherwise there is nothing to prove). Then, since $\dim E (8, T) + 1 = \dim F^{5}$ and by part (d) of 5.41, $T$ has only one eigenvalue besides $8$ . Therefore at least between $T - 2 I$ and $T - 6 I$ is invertible. □

celiopassos

2017-10-06 00:00

Exercise 5.C.8

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