Exercise 5.A.1

Answers

Proof. (a) Suppose $u \in U$ . Because $Tu = 0$ and $0 \in U$ , it follows that $U$ is invariant under $T$ .

(b) Suppose $u \in U$ . By definition $Tu \in range T$ . But $range T \subset U$ , hence $Tu \in U$ . □

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2017-10-06 00:00