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#1 2013-02-25 04:13:58

123ronnie321
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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

#2 2013-02-26 17:11:54

anonimnystefy
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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 (2013-02-26 17:14:28)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-02-27 01:17:52

scientia
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Re: Vector Spaces!

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

#4 2013-02-27 05:22:24

anonimnystefy
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Re: Vector Spaces!

Ah, I am sorry, then.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment