Calculate the $L U$ factorization of the matrix

$$A=\left(\begin{array}{rrrr} 3 & 2 & -3 & -3 \\ 6 & 3 & -7 & -8 \\ 3 & 1 & -6 & -4 \\ -6 & -3 & 9 & 6 \end{array}\right)$$

Use this to evaluate $\operatorname{det}(A)$ and to solve the equation

$$A \mathbf{x}=\mathbf{b}$$

with

$$\mathbf{b}=\left(\begin{array}{r} 3 \\ 3 \\ -1 \\ -3 \end{array}\right)$$