(本题满分 11 分) 设线性方程组 $$ \left\{ \begin{array}{l} x _ {1} + x _ {2} + x _ {3} = 0, \\ x _ {1} + 2 x _ {2} + a x _ {3} = 0, \\ x _ {1} + 4 x _ {2} + a ^ {2} x _ {3} = 0 \end{array} \right. \tag {①} $$ 与方程 $$ x _ {1} + 2 x _ {2} + x _ {3} = a - 1 \tag {②} $$ 有公共解, 求 $a$ 的值及所有公共解.