Write matrix factorization? How can be used to solve a system of linear equations? Factorize the given matrix A and solve the system of equations Ax = b for given b using L and U matrices.

A = \(\begin{bmatrix}1 & 2 & 3\\ 2 & 8 & 11\\ 3 & 22 & 36\end{bmatrix}\) and b = \(\begin{bmatrix}4\\ 12 \\28\end{bmatrix}\)