已知 4 阶方阵 $\boldsymbol{A}=\left(\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \boldsymbol{\alpha}_{3}, \boldsymbol{\alpha}_{4}\right), \boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \boldsymbol{\alpha}_{3}, \boldsymbol{\alpha}_{4}$ 均为 4 维列向量,其中 $\boldsymbol{\alpha}_{2}, \boldsymbol{\alpha}_{3}, \boldsymbol{\alpha}_{4}$ 线性无关, $\boldsymbol{\alpha}_{1}=2 \boldsymbol{\alpha}_{2}-\boldsymbol{\alpha}_{3}$. 如果 $\boldsymbol{\beta}=\boldsymbol{\alpha}_{1}+\boldsymbol{\alpha}_{2}+\boldsymbol{\alpha}_{3}+\boldsymbol{\alpha}_{4}$, 求线性方程组 $\boldsymbol{A x}=\boldsymbol{\beta}$ 的通解.