Solution VO.T06 Chris Black

\begin{align*} \zerovector &= 0\vect{u} +(-0\vect{u})&&\knowl{./knowls/property.AIC.knowl}{\text{Property AIC}}\\ &= (0+0)\vect{u} + (-0\vect{u})&&\knowl{./knowls/property.ZCN.knowl}{\text{Property ZCN}}\\ &= (0\vect{u}+0\vect{u}) + (-0\vect{u})&&\knowl{./knowls/property.DSAC.knowl}{\text{Property DSAC}}\\ &= 0\vect{u} + (0\vect{u} + (-0\vect{u}))&&\knowl{./knowls/property.AAC.knowl}{\text{Property AAC}}\\ &= 0\vect{u} + \zerovector&&\knowl{./knowls/property.AIC.knowl}{\text{Property AIC}}\\ &= 0\vect{u}&&\knowl{./knowls/property.ZC.knowl}{\text{Property ZC}} \end{align*}