Proving a set is a subspace of a given vector space question

Question

I'm familiar with proving subspaces but am unsure over how to approach this question. I don't understand what the notation is implying about $S$ so any help would be greatly appreciated. Cheers.

Decide if set $S$ is a subspace of the given vector space $V$.

$V=\mathbb{R}^2 \; and\;S=\{w=(x,y)\in \mathbb{R}^2 |\; x\ge0\}.$

Answer 1

HINT

Let consider

• $w_1=(1,0)\in S$
• $w_2=(2,0)\in S$

and then consider the combination

• $1\cdot w_1+(-1)\cdot w_2$