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Math Help - Axioms of a vector space

  1. #1
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    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?
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  2. #2
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    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?
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    Quote Originally Posted by Ackbeet View Post
    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
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  4. #4
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    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?
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  5. #5
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    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
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  7. #7
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    I take it axioms 1 and 2 you can just assume are true.
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    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.
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  10. #10
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    Quote Originally Posted by Plato View Post
    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.
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  11. #11
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    Looks good to me.
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  12. #12
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    Quote Originally Posted by Ackbeet View Post
    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
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  13. #13
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    Just the bottom one. Your top one doesn't work for Axiom 3. Axiom 4 works fine, actually.
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  14. #14
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    Quote Originally Posted by Ackbeet View Post
    Just the bottom one. Your top one doesn't work for Axiom 3. Axiom 4 works fine, actually.
    Yeah i see the 2's and the 1's are the wrong way round for what i did for 3 so it doesn't work.
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  15. #15
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    Right. Is there anything else that is confusing you?
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