设矩阵 $A=\left(\begin{array}{cccc}2 & -3 & 3 & 1 \\ 3 & -5 & 2 & 2 \\ 9 & -16 & 1 & 7\end{array}\right), X=\left(\begin{array}{c}x_1 \\ x_2 \\ x_3 \\ x_4\end{array}\right), \beta=\left(\begin{array}{l}6 \\ 4 \\ 2\end{array}\right)$ ，求方程组 $A X=\beta$ 通解．