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Math / Linear Algebra 4 / Chapter 1.4 / Problem 17

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

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Let W be a subspace of a vector space V. Under what conditions are there only a finite

Chapter 1, Problem 17

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QUESTION:

Let W be a subspace of a vector space V. Under what conditions are there only a finite number of distinct subsets S of W such that S generates W?

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QUESTION:

Let W be a subspace of a vector space V. Under what conditions are there only a finite number of distinct subsets S of W such that S generates W?

ANSWER:

Step 1 of 2

Let W be a subspace of a vector space V.

Then, a finite number of distinct subsets of W such that S generates W under the condition that W is finite.

If W is infinite. Suppose S is a distinct subset of W. Then, we can consider

Here, be an arbitrary element.

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