设矩阵 $\boldsymbol{A}=\left(\begin{array}{lll}1 & 0 & 1 \\ 1 & 1 & 2 \\ 0 & 1 & 1\end{array}\right), \boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \boldsymbol{\alpha}_3$ 为线性无关的 3 维列向量组, 则向量组 $\boldsymbol{A} \boldsymbol{\alpha}_1, \boldsymbol{A} \boldsymbol{\alpha}_2, \boldsymbol{A} \boldsymbol{\alpha}_3$ 的秩 为