Math Is Fun Forum

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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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“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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scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Vector Spaces!

I think 123ronnie321 is looking for

– the direct sum, not the union.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Vector Spaces!

Ah, I am sorry, then.

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“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
The knowledge of some things as a function of age is a delta function.