设 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \boldsymbol{\alpha}_3$ 均为 3 维列向量，记矩阵

$$
\boldsymbol{A}=\left(\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \boldsymbol{\alpha}_3\right), \boldsymbol{B}=\left(\boldsymbol{\alpha}_1+\boldsymbol{\alpha}_2+\boldsymbol{\alpha}_3, \boldsymbol{\alpha}_1+2 \boldsymbol{\alpha}_2+4 \boldsymbol{\alpha}_3, \boldsymbol{\alpha}_1+3 \boldsymbol{\alpha}_2+9 \boldsymbol{\alpha}_3\right),
$$


如果 $|\boldsymbol{A}|=1$ ，那么 $|\boldsymbol{B}|=$