L=\left [\begin{array}{cccc} 1 & 0 & 0 & 0 \\ -1 & 1 & 0 & 0 \\ 2 & \frac{3}{2} & 1 & 0 \\ 1 & -\frac{5}{4} & \frac{5}{6} & 1 \end{array} \right ], \quad U=\left [\begin{array}{cccc} 2 & 0 & 2 & -1 \\ 0 & 0 & 1 & -2 \\ 0 & 0 & \frac{3}{2} & 3 \\ 0 & 0 & 0 & 2 \end{array} \right ],