(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Closed real vector spaces

1. The problem statement, all variables and given/known data

Determine whether the given set V is closed under the operations (+) and (.):

V is the set of all ordered pairs of real numbers (x,y) where x>0 and y>0:

(x,y)(+)(x',y') = (x+x',y+y')

and

c(.)(x,y) = (cx,cy), where c is a scalar, (.) = multiplication

2. Relevant equations

To show if they are closed or not, i know that i must satisfy a set of conditions such as:

u(+)v = v(+)u

u(+)0 = u

c(.)(u+v) = c(.)u(+)c(.)(v)

et...

I also know that (x,y)(+)(x',y') = (x+x',y+y') is closed but c(.)(x,y) = (cx,cy) is not. So how do i show this? Just use arbitrary numbers?

3. The attempt at a solution

I tried plugging in x = y = c = 1 for simplicity, but if i do that, it shows that both are closed

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Closed real vector spaces

**Physics Forums | Science Articles, Homework Help, Discussion**