Problem $2.[40$ points$]$ Use Jupyter notebook for part $($b$)$ of this problem. Please complete part a$)$ on paper while write a relevant Python code for part b$)$ without using in$-$built function that's mentioned on the question.

Consider the following system of linear equations

$\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 8\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right]$

a$.[20$ points$]$ Find a solution of the system by hand using Gaussian elimination method.

b$.[20$ points$]$ Write Python code that finds a solution using LU method. $($Do not use Python's

built$-$in LU function. e$.$g$.,$

scipy.linalg.lu$.)$ Discuss how each line of your Python code

implementing LU algorithm corresponds to the calculations performed in part $($a$).$ Each and

every line of your code must be explained.