Task $1$: Given the following linear system of equations,

$\left[\begin{array}{ccc}-2& 1& -2\\ -4& 3& -3\\ 2& 2& 4\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}1\\ 4\\ 4\end{array}\right]$

a$)(10$ pts$)$ Find the LU decomposition of the coefficient matrix

b$)(10$ pts$)$ Find the solution to the linear system based on the computed LU decomposition. Please also provide the steps on how to get the answers.