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#1 2013-02-24 05:13:58

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Vector Spaces!

Let V be a vector space and A,B be subsets of V .

prove that:  span (A U B) = span (A) + span (B)

looks pretty obvious but dont know how to prove it using math

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#2 2013-02-25 18:11:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: Vector Spaces!

Hi 123ronnie321

I don't think that's true. Look at A={(1,0,0),(0,1,0)} and B={(1,0,0),(0,0,1)}, for example.

, on the other hand, is true.

Last edited by anonimnystefy (2013-02-25 18:14:28)


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#3 2013-02-26 02:17:52

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: Vector Spaces!

I think 123ronnie321 is looking for
– the direct sum, not the union.

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#4 2013-02-26 06:22:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: Vector Spaces!

Ah, I am sorry, then.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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