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# Can anybody help me with vector spaces? watch

1. 1ST QUESTION: Is this statement true or false (and why)...

Every non-zero vector space has finitely many different bases.

2ND QUESTION: Does the set of all 2x2 matrices of determinant bigger than or equal to zero form a vector space?
2. For #1, does have finitely many bases?

For #2, if have determinant then must ? If then what is ? Is this ?
3. This is getting a bit ridiculous. Can you put all future vector spaces questions into this thread, rather than creating new ones? Thanks.

I'll also add that you are not going to learn much if you just keep asking for help instead of thinking about the questions yourself.
4. (Original post by nuodai)
For #1, does have finitely many bases?

For #2, if have determinant then must ? If then what is ? Is this ?
The first one is false, because R^2 has infinitely many different bases.

For the second one...A does not does not always have a determinent that is greater than or equal to zero...but how does this answer the quesetion?
5. (Original post by Artus)
The first one is false, because R^2 has infinitely many different bases.
Indeed; can you demonstrate that?

(Original post by Artus)
For the second one...A does not does not always have a determinent that is greater than or equal to zero...but how does this answer the quesetion?
Well if it were true that didn't have a determinant then it couldn't be a vector space, since it wouldn't be closed under scalar multiplication (which it should be, by definition of a vector space).

But first, are you sure that doesn't always have determinant (when is a 2x2 matrix with non-negative determinant).
6. (Original post by DFranklin)
This is getting a bit ridiculous. Can you put all future vector spaces questions into this thread, rather than creating new ones? Thanks.

I'll also add that you are not going to learn much if you just keep asking for help instead of thinking about the questions yourself.
Actually, I do try to do it by myself...but I have a huge exam tomorrow, so I'm doing all the questions in the homework (the homework of 10 sections) again and asking the ones that confuse me...

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