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Exercise 1.4.11

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To prove it’s sufficient we can use Theorem 1.5 and then we know $W = span (W)$ is a subspace. To prove it’s necessary we can also use Theorem 1.5. Since $W$ is a subspace contains $W$ , we have $span (W) \subset W$ . On the other hand, it’s natural that $span (W) \supset W$ .

jephianlin

2011-06-27 00:00

Exercise 1.4.11

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