Showing that U = {(x, y) | xy ≥ 0} is not a subspace of R^2

  • Thread starter pakkanen
  • Start date
  • #1
12
0

Homework Statement


Task: Show that U = {(x, y) | xy ≥ 0} is not a subspace of vector space R2

I wish you could help me to understand why U is not a subspace of R2x2.

I have actually found a vectors u and v such that it does not belong to U (e.g. (-3,-1) +(2,2) = (-1,1) ) but is that sufficient to show that U is not a subset of R2x2?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
956

Homework Statement


Task: Show that U = {(x, y) | xy ≥ 0} is not a subspace of vector space R2

I wish you could help me to understand why U is not a subspace of R2x2.

I have actually found a vectors u and v such that it does not belong to U (e.g. (-3,-1) +(2,2) = (-1,1) )
What does "it" refer to? are you trying to show that the sum of two vectors in the set may not be in the set? If so, yes, that is valid.

but is that sufficient to show that U is not a subset of R2x2?
Well, first, you are not trying to show U is not a subset. It is. But it is not a subspace. I suspect that was a typo. Yes, this is sufficient. To be a subspace, the subset must satisfy a number of properties. If it fails to satisfy any one of them it is not a subspace.

Homework Statement





Homework Equations





The Attempt at a Solution

 
  • #3
12
0
Sorry for being unclear. I meant the subspace and not subset as you mentioned. And now it became a clear for me. Thank you very much!
 

Related Threads on Showing that U = {(x, y) | xy ≥ 0} is not a subspace of R^2

Replies
9
Views
713
  • Last Post
Replies
4
Views
854
  • Last Post
Replies
16
Views
13K
Replies
2
Views
1K
Replies
4
Views
3K
  • Last Post
Replies
5
Views
2K
Top