- #1

steelphantom

- 159

- 0

## Homework Statement

Give an example of a nonempty subset U of R

^{2}such that U is closed under scalar multiplication, but U is not a subspace of R

^{2}.

## Homework Equations

## The Attempt at a Solution

I think I have it, but I just want to make sure it's right:

Let U = {(x, x + 2)} | x is in R}. Let u be in U. Then au = a(x, x + 2) = (ax, a(x + 2)), which is still in U (i.e. still on the same line). But this is not a subspace of R

^{2}because 0 is not in this subset.

Thanks!