Find an LU factorization of the matrix

$$A=\left(\begin{array}{rrrr} 2 & -1 & 3 & 2 \\ -4 & 3 & -4 & -2 \\ 4 & -2 & 3 & 6 \\ -6 & 5 & -8 & 1 \end{array}\right)$$

and use it to solve the linear system $A \mathbf{x}=\mathbf{b}$, where

$$\mathbf{b}=\left(\begin{array}{r} -2 \\ 2 \\ 4 \\ 11 \end{array}\right)$$