(a) Find an $L U$ factorisation of the matrix

$$A=\left[\begin{array}{cccc} 1 & 1 & 0 & 3 \\ 0 & 2 & 2 & 12 \\ 0 & 5 & 7 & 32 \\ 3 & -1 & -1 & -10 \end{array}\right]$$

where the diagonal elements of $L$ are $L_{11}=L_{44}=1, L_{22}=L_{33}=2$.

(b) Use this factorisation to solve the linear system $A \mathbf{x}=\mathbf{b}$, where

$$\mathbf{b}=\left[\begin{array}{c} -3 \\ -12 \\ -30 \\ 13 \end{array}\right]$$