anonymous
  • anonymous
can someone help explain how to determine if something is a vector space or not
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Zarkon
  • Zarkon
http://en.wikipedia.org/wiki/Vector_space#Definition
anonymous
  • anonymous
you have to check it for the axioms and see if they are true or not
anonymous
  • anonymous
how 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Zarkon
  • Zarkon
Is that space closed under addition
anonymous
  • anonymous
i 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
  • Zarkon
right...as stated it is not a vector space...no zero vector and no closure of addition
anonymous
  • anonymous
that is the very thing that Im confused about how do you determine that there is no zero vector and no closure of addition
Zarkon
  • Zarkon
the zero vector has to be just the number 0 0 is not a 5th degree polynomial
Zarkon
  • Zarkon
\[(x^5+3x)+(-x^5+x^2)=3x-x^2\] which is not a 5th degree polly
anonymous
  • anonymous
is 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
  • anonymous
further more, \[x^5-2x+(-x^5)\] does not have degree 5, so it is not closed under addition
anonymous
  • anonymous
what zarkon said
anonymous
  • anonymous
ok that makes sense so what is the differance in saying it has fifth degree and fifth degree or less
anonymous
  • anonymous
is one a vector and one is not and why
Zarkon
  • Zarkon
5th degree or less is a vector space
anonymous
  • anonymous
so 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
  • Zarkon
use the difinition I provided in my first post
anonymous
  • anonymous
i know it has to adhere to the list of axioms but can you explain it a little.

Looking for something else?

Not the answer you are looking for? Search for more explanations.