How to show something is a subspace

  • Thread starter HappyN
  • Start date
  • #1
16
0
How would you show that {(x,y,z) € R^3 :√11x - √13z=0} is a subspace of R^3?

I know you have to make sure it fits the definition of a subspace, i.e prove
u+v € W
and alpha(v) € W

but im not sure how you would do this using √11x - √13z=0 ?
 

Answers and Replies

  • #2
chiro
Science Advisor
4,790
132
How would you show that {(x,y,z) € R^3 :√11x - √13z=0} is a subspace of R^3?

I know you have to make sure it fits the definition of a subspace, i.e prove
u+v € W
and alpha(v) € W

but im not sure how you would do this using √11x - √13z=0 ?
What is the definition of addition and scalar multiplication in your vector space?
 
  • #3
16
0
What is the definition of addition and scalar multiplication in your vector space?
Do you mean the 7 axioms?
like: v+w=w+v for all v,w € V
(v+w)+z=v+(w+z) etc?
 
  • #4
313
1
I think that Chiro means think about the axioms and make sure the subspace satisfy them.
In particular check that the sum of two elements in the subspace yield another element in the subspace and that the scalar multiple of an element in the subspace yields another element in the subspace. The rest of the axioms will then follow automatically.
 
  • #5
chiro
Science Advisor
4,790
132
I think that Chiro means think about the axioms and make sure the subspace satisfy them.
In particular check that the sum of two elements in the subspace yield another element in the subspace and that the scalar multiple of an element in the subspace yields another element in the subspace. The rest of the axioms will then follow automatically.
Yep that's pretty much what I was trying to get the OP to think about.
 

Related Threads on How to show something is a subspace

Replies
3
Views
22K
Replies
12
Views
7K
Replies
6
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
7
Views
6K
Replies
5
Views
3K
Replies
3
Views
905
  • Last Post
Replies
7
Views
2K
Replies
4
Views
3K
Top