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Math Help - Vector Space Axiom Proof

  1. #1
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    Vector Space Axiom Proof

    Hello,

    Is this right? I know this is trickier than it looks because you are only allowed to assume the axioms of vector spaces alone, nothing else.

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  2. #2
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    Quote Originally Posted by james121515 View Post
    Hello,

    Is this right? I know this is trickier than it looks because you are only allowed to assume the axioms of vector spaces alone, nothing else.



    It is right but, imo, ugly. I prefer the following (be sure you can write down the axiom on which each step relies):

    c\cdot 0=c(0+0)=c\cdot 0+c\cdot 0\Longrightarrow c\cdot 0+(-c\cdot 0)=c\cdot 0+c\cdot 0+(-c\cdot 0) \Longrightarrow 0 = c\cdot 0 +0=c\cdot 0 QED.

    Tonio
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  3. #3
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    only one quibble, tonio....i believe you should have written -(c0) rather than (-c)0.

    yes, these are in point of fact equal, but proving that uses the fact that 0v = 0, for any v, which is somewhat of a detour.

    (it's just a misplaced parenthesis, i'm sure you meant -(c0)).
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