I have some technical questions about spans and bases which my textbook really does not cover very well. I would appreciate answers to them. They are not textbook problems, merely specific quesitons relating to the definitions of "span" and "basis".(adsbygoogle = window.adsbygoogle || []).push({});

1) If span(S) = V, need the elements of S be in V?

2) If S is a basis for V, need the elements of S be in V?

3) If S spans V, does S span every subspace of V?

4) If S is a basis for V, is S a basis for every subspace of V?

5) If S is linearly independent, is every subset of S also linearly independent?

6) If S is linearly dependent, is every superset of S also linearly dependent?

If I am not wrong, the answers to the questions are:

1) Yes

2) Yes

3) Yes

4) No

5) Yes

6) Yes

But I would like explicit confirmation.

All help is appreciated. Thanks.

BiP

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# Some technical questions about spans and bases

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