(Solved): Let \( V=\mathbb{R} \). For \( u, v \in V \) and \( a \in \mathbb{R} \) define vector addition by \ ...

Let \( V=\mathbb{R} \). For \( u, v \in V \) and \( a \in \mathbb{R} \) define vector addition by \( u \) ? \( v:=u+v-2 \) and scalar multiplication by \( a \quad u:=a u-2 a+2 \). It can be shown that \( (V, \boxplus, \square) \) is a vector space over the scalar field \( \mathbb{R} \). Find the following: the sum: \( 9-6= \) the scalar multiple: \( -7 \cdot 9= \) the zero vector: \( \underline{0}_{V}= \) the additive inverse of \( x \) : Note: You can earn partial credit on this problem.