Answer
See below
Work Step by Step
Given:
$v=(1,2)\\
w=(1,1) \in R^2$
1. $=1.1-2.2=-3\lt 0\\
=1.1-1.1=0$
Hence, the property does not hold.
2. $=v_1w_1-v_2w_2\\
=w_1v_1-w_2v_2\\
=$
3. With scalar $k$, we have $kv=(kv_1,kv_2)$
and $=(kv_1)w_1-(kv_2)w_2\\
=kv_1w_1-kv_2w_2\\
=k(v_1w_1-v_2w_2)\\
=k$
4. Let $u=(u_1,u_2)$ in $R^2$
$u+v=(u_1,u_2)+(v_1,v_2)\\
=(u_1+v_1,u_2+v_2)\\
\rightarrow =(u_1+v_1)w_1-(u_2+v_2)w_2\\
=u_1w_1+v_1w_1-u_2w_2-v_2w_2\\
=(u_1w_1-u_2w_2)+(v_1w_1-v_2w_2)\\
=+$
