I just can't completely answer this question, does it want me to prove it using all 10 axioms? Or is there another way

http://i89.photobucket.com/albums/k2...atrixHelp2.jpg

Thanks

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- Oct 29th 2007, 05:25 PMAdrianProving a Vector Space
I just can't completely answer this question, does it want me to prove it using all 10 axioms? Or is there another way

http://i89.photobucket.com/albums/k2...atrixHelp2.jpg

Thanks - Oct 29th 2007, 07:52 PMThePerfectHacker
Here is an easier way to do this without using all 10 properties of a vector space.

**Theorem:**Let be a vector space over a field (you probably learned it over ). Let be a subset of so that for all and for all and . Then is a vector space over the field ( ).

So you only need to check closure of vector addition and scalar multiplication. - Oct 29th 2007, 08:00 PMAdrian
I'm not sure if I'm correct but, the closure under addition wouldn't be true because the final matrix has to end up as

[a+c 2]

[ 2 b+d]

???

I'm almost positive axiom 6 for scalar multiplication holds, but I'm not sure about axiom 1, if you could tell me whether my above theory is correct or not that would be great. I am not very good at proving axioms at least 1 and 6, because there is no left and right hand side of the equation to compare, so I get really lost. - Oct 30th 2007, 12:32 AMkalagota