Vector space

  • Thread starter eyehategod
  • Start date
  • #1
82
0
15. Determine wheter the set is a vector space.
The set of all fifth-degree polynomials with the standard operations.
AXIOMS
1.u+v is in V
2.u+v=v+u
3.u+(v+w)=(u+v)+w
4.u+0=u
5.u+(-u)=0
6. cu is in V
7.c(u+v)=cu+cv
8.(c+d)u=cu+cd
9.c(du)=(cd)u
10.1(u)=u

the axioms that fail are 1,4,5, and 6. I dont know why 4,5,and 6 fail. Can anyone help me?
 

Answers and Replies

  • #2
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
7,051
18
How is the degree of a polynomial defined? Now, what is the additive identity, and is it a fifth-degree polynomial?
 

Related Threads on Vector space

  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
14
Views
6K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
2
Views
27K
  • Last Post
Replies
2
Views
13K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
13
Views
10K
  • Last Post
Replies
2
Views
2K
Replies
9
Views
1K
Top