\alpha _1 = \alpha _2 = 1,\beta _1 = - 1 \Rightarrow \alpha _1 a_1 + \alpha _2 a_2 = \left( {{\rm 1}{\rm ,0}{\rm ,1}{\rm , - 2}} \right) + \left( {0,1,0,1} \right) = \left( {1,1,1, - 1} \right)