What is matrix factorization? Factorize the given matrix A into LU using Doolittle algorithm and also solve Ax = b for given b using L and U matrices.

A = \(\begin{bmatrix}2 & 4 & -4 & 0\\ 1 & 5 & -5 & -3\\ 2 & 3 & 1 & 3\\ 1 & 4 & -2 & 2\end{bmatrix}\) and b = \(\begin{bmatrix}12\\ 18\\ 8\\ 8\end{bmatrix}\)