Let $$A = \left[\begin{array}{cc} -6 &17\cr 6 &-17\cr -18 &1\cr 18 &-1 \end{array}\right].$$ A singular value decomposition of $A$ is $$A = \left[\begin{array}{cccc} 0.5 &0.5 &0.5 &0.5\cr -0.5 &-0.5 &0.5 &0.5\cr -0.5 &0.5 &0.5 &-0.5\cr 0.5 &-0.5 &0.5 &-0.5 \end{array}\right] \left[\begin{array}{cc} 20 &0\cr 0 &30\cr 0 &0\cr 0 &0 \end{array}\right] \left[\begin{array}{cc} 0.6 &0.8\cr -0.8 &0.6 \end{array}\right].$$ Find the least-squares solution of the linear system $A\vec{x} = \vec{b}$ where $$\vec{b} = \left[\begin{array}{c} 3\cr 1\cr -3\cr -3 \end{array}\right].$$
$\vec{x}^* =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$