# Axioms of a vector space

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• Aug 17th 2010, 04:26 AM
Axioms of a vector space
In my notes that i've took. We don't seem to do all 10 for each question to prove it. But from some questions we do associaitivity and communativity and that proves it. Sometimes we find if the zero vector exists.I don't understand it at all, help please?
• Aug 17th 2010, 04:35 AM
Ackbeet
What you have to show depends on the context. Some things are usually taken for granted, such as the field axioms for real numbers. Often, you can get quite a bit of mileage out of those.

But another very important case is subspaces. For subspaces, you usually just need to show closure, and everything else comes along for the ride. Is that what you're thinking of?
• Aug 17th 2010, 05:12 AM
Quote:

Originally Posted by Ackbeet
What you have to show depends on the context. Some things are usually taken for granted, such as the field axioms for real numbers. Often, you can get quite a bit of mileage out of those.

But another very important case is subspaces. For subspaces, you usually just need to show closure, and everything else comes along for the ride. Is that what you're thinking of?

It's for real numbers

It says u + v = ( u1 + v2 )
......................(u2 + v1 +2)

do i take u as u1 and u2 and v as v1 nd v2 if its in R^2
• Aug 17th 2010, 05:46 AM
Ackbeet
So you want to show that the real numbers constitute a vector space? If so, I'm looking down the axiom list for vector spaces, and I'm thinking that all of those follow quite readily from the field axioms of the real numbers. Is there one of which you're not sure?
• Aug 17th 2010, 05:59 AM
Can i put the question up, the axioms i have. Then my workings by hand. And anyone can see if i've done it right please
• Aug 17th 2010, 06:03 AM
• Aug 17th 2010, 06:14 AM
I take it axioms 1 and 2 you can just assume are true.
• Aug 17th 2010, 06:17 AM
• Aug 17th 2010, 06:22 AM
Plato
If I were you, I would start with axiom #5 finding a ‘zero vector’ and then look to see if axiom #3 holds for that vector.
• Aug 17th 2010, 06:32 AM
Quote:

Originally Posted by Plato
If I were you, I would start with axiom #5 finding a ‘zero vector’ and then look to see if axiom #3 holds for that vector.

http://i33.tinypic.com/1zb5ovm.jpg
• Aug 17th 2010, 06:33 AM
Ackbeet
Looks good to me.
• Aug 17th 2010, 06:44 AM
Quote:

Originally Posted by Ackbeet
Looks good to me.

Both of them or just the bottom one. I think the bottom one is right but not the top one for axiom 4
• Aug 17th 2010, 06:48 AM
Ackbeet
Just the bottom one. Your top one doesn't work for Axiom 3. Axiom 4 works fine, actually.
• Aug 17th 2010, 06:51 AM