Let F be a field with elements and let V be a vector space above F with dimension of .

1. How many different basis do V have?

2. How many subspaces of dimension of do V have?

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- December 2nd 2009, 03:44 PMAlso sprach ZarathustraField and vector space
Let F be a field with elements and let V be a vector space above F with dimension of .

1. How many different basis do V have?

2. How many subspaces of dimension of do V have? - December 2nd 2009, 04:13 PMtonio

It is not "who" but "how"...!נו באמת

Anyway: how many elements in V can be the first element in the basis? (all but the zero vector): how many elements can be the second element in a basis? (all but the scalar multiples of the first one, and there are q multiples like these), etc.

Try now to do the second part by yourself.

Tonio - December 2nd 2009, 04:28 PMAlso sprach Zarathustra
Shalom! I am mitbaesh beatzmi...

Can you please write the whole answer for the question.

1. q^n-1 ?

2.? - December 2nd 2009, 04:32 PMAlso sprach Zarathustra
p.s:

What is MHF expert mean? - December 2nd 2009, 08:15 PMtonio
- December 2nd 2009, 08:21 PMtonio

No, not the whole answer but some highlights: there are choices for the first vector (since zero cannot be part of a basis), then there are choices for the second vector (all the available vectors minus those that are a scalar multiple of the first one), then there are choices for the third one (all the possible vectors minus all the scalar multiples of the first two), etc.

All in, there are ...try to end the argument by yourself now.

Tonio

Ps ...הרבה יותר כיף לגלות את הפתרון בעצמך, אפילו אם זה קשה, מאשר לקבל את הכל מוכן - December 3rd 2009, 01:47 AMAlso sprach Zarathustra
And what about 2?

- December 3rd 2009, 04:04 AMDefunkt
- December 3rd 2009, 04:59 PMtonio
- December 3rd 2009, 05:09 PMDefunkt
יפה יפה... אני מניח שכבר סיימת תואר ראשון?