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anonymous
 4 years ago
can someone help explain how to determine if something is a vector space or not
anonymous
 4 years ago
can someone help explain how to determine if something is a vector space or not

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you have to check it for the axioms and see if they are true or not

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how do you use the axioms to determine for instance if the set of all fifth degree polynomials with the standard operations is a vestor space

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1Is that space closed under addition

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i guess there is a subtlety here. if it means the polynomial must have degree 5, then there is no zero vector. if it means degree 5 or less, then yes

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1right...as stated it is not a vector space...no zero vector and no closure of addition

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that is the very thing that Im confused about how do you determine that there is no zero vector and no closure of addition

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1the zero vector has to be just the number 0 0 is not a 5th degree polynomial

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1\[(x^5+3x)+(x^5+x^2)=3xx^2\] which is not a 5th degree polly

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is there a vector (fifth degree polynomial in this case) say \[p(x)\] with \[p(x)+v(x)=v(x)\] for all fifth degree polynomials v the answer is no, because the only polynomial that would work would be the zero polynomial, which does not have degree 5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0further more, \[x^52x+(x^5)\] does not have degree 5, so it is not closed under addition

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok that makes sense so what is the differance in saying it has fifth degree and fifth degree or less

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is one a vector and one is not and why

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.15th degree or less is a vector space

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so what is the step by step method to determing the answer to these types of problems. I mean when talking about continuous functions and things like that wouldnt get a little tricky

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1use the difinition I provided in my first post

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i know it has to adhere to the list of axioms but can you explain it a little.
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