Find the least-squares solution $\vec{x}^*$ of the system $$\left[\begin{array}{ccc} 1 &-1 &-1\cr 1 &1 &-1\cr 1 &1 &1\cr 1 &-1 &1 \end{array}\right] \vec{x} = \left[\begin{array}{c} 2\cr -2\cr -2\cr -10 \end{array}\right].$$
$\vec{x}^* =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$