Exercise 19

Prove these.

• For any $\vec{v}\in V$, if $\vec{w}\in V$ is an additive inverse of $\vec{v}$, then $\vec{v}$ is an additive inverse of $\vec{w}$. So a vector is an additive inverse of any additive inverse of itself.

• Vector addition left-cancels: if $\vec{v},\vec{s},\vec{t}\in V$ then $\vec{v}+\vec{s}=\vec{v}+\vec{t}\,$ implies that $\vec{s}=\vec{t}$.