(本题满分 11 分) 设向量组 $\pmb{\alpha}_{1} = (1,0,1)^{\mathrm{T}},\pmb{\alpha}_{2} = (0,1,1)^{\mathrm{T}},\pmb{\alpha}_{3} = (1,3,5)^{\mathrm{T}}$ 不能由向量组 $\pmb{\beta}_{1} = (1,1,1)^{\mathrm{T}},$ $\pmb {\beta}_2 = (1,2,3)^{\mathrm{T}},\pmb {\beta}_3 = (3,4,a)^{\mathrm{T}}$ 线性表示. (I)求 $a$ 的值； （Ⅱ）将 $\beta_{1},\beta_{2},\beta_{3}$ 用 $\alpha_{1},\alpha_{2},\alpha_{3}$ 线性表示