设 $\pmb{\alpha}_{1} = (1,2, - 1,0)^{\mathrm{T}},\pmb{\alpha}_{2} = (1,1,0,2)^{\mathrm{T}},\pmb{\alpha}_{3} = (2,1,1,a)^{\mathrm{T}}$ 若由 $\pmb{\alpha}_{1},\pmb{\alpha}_{2},\pmb{\alpha}_{3}$ 生成的向量空间的维数为2，则 $a =$