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Linear Algebra

Exercise 5.1.10

Answers

1.: What did the author want to ask? Just calculate it!
2.: Just calculate it and get the answer ${(λ - t)}^{n}$ , where $n$ is the dimension of $V$ .
3.: We already have that for any ordered basis $β$ , ${[λ I_{V}]}_{β} = λI$ , a diagonal matrix. So it’s diagonalizable. By the previous exercise, we also have that the only eigenvalue is the zero of the characteristic polynomial, $λ$ .

jephianlin

2011-06-27 00:00

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