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Exercise 8.A.16

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Proof. Obviously $V = range T^{0} = range I$ . Let $k$ be a nonnegative integer. Suppose $v \in range T^{k + 1}$ . Then $v = T^{k + 1} u$ for some $u \in V$ . But then $v = T^{k} (Tu)$ . This implies that $v \in range T^{k}$ . □

celiopassos

2017-10-06 00:00

Exercise 8.A.16

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