L=\left [\begin{array}{cccc} 1 & 0 & 0 & 0 \\ -1 & 1 & 0 & 0 \\ 2 & -1 & 1 & 0 \\ 1 & 2 & -1 & 1 \end{array} \right ], \quad U=\left [\begin{array}{cccc} 1 & -1 & 0 & 1 \\ 0 & 2 & -1 & 3 \\ 0 & 0 & -1 & 7 \\ 0 & 0 & 0 & 3 \end{array} \right ], \quad x=\left [\begin{array}{c} \frac{4}{3} \\ -\frac{1}{3} \\ -\frac{8}{3} \\ -\frac{2}{3} \end{array} \right ] .