Exercise 28

Show that the inner product operation is linear: for $\vec{u},\vec{v},\vec{w}\in\mathbb{R}^{n}$ and $k,m\in\mathbb{R}$, $\vec{u}\mathbin{\smash{\bullet}}(k\vec{v}+m\vec{w})=k(\vec{u}\mathbin{\smash{\bullet}}\vec{v})+m(\vec{u}\mathbin{\smash{\bullet}}\vec{w})$.