Write a script to create a matrix $\frac{?}{\text{b}\text{a}\text{r}}(\frac{?}{\text{b}\text{a}\text{r}}(A))in{R}^{nn}$ with ninN, where $\frac{?}{\text{b}\text{a}\text{r}}(\frac{?}{\text{b}\text{a}\text{r}}(A))$ is:

$\frac{?}{\text{b}\text{a}\text{r}}(\frac{?}{\text{b}\text{a}\text{r}}(A))=\left[\begin{array}{ccccccccc}4& -1& 0& 0& \text{d}\text{o}\text{t}\text{s}& 0& 0& 0& -1\\ -1& 4& -1& 0& \text{d}\text{o}\text{t}\text{s}& 0& 0& 0& 0\\ 0& -1& 4& -1& \text{d}\text{o}\text{t}\text{s}& 0& 0& 0& 0\\ \text{v}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}& \text{d}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}\\ 0& 0& 0& 0& \text{d}\text{o}\text{t}\text{s}& -1& 4& -1& 0\\ 0& 0& 0& 0& \text{d}\text{o}\text{t}\text{s}& 0& -1& 4& -1\\ -1& 0& 0& 0& \text{d}\text{o}\text{t}\text{s}& 0& 0& -1& 4\end{array}\right]$

Now, solve the system $\frac{?}{\text{b}\text{a}\text{r}}(\frac{?}{\text{b}\text{a}\text{r}}(A))vec(x)=$vec$(b),$ with vec$(b)=[111$dots$11{]}^T$ and vec$(b)in{R}^n,$ using the Jacobi Iteration, Gauss$-$Seidel,

and Successive Over$-$Relaxation methods for $n=25,50,100.$ Utilize the $p-$norm of the residual, $||vec(r)|{|}_p,$ as

the stopping criterion, with $p=2$ and $p=.$ Determine the number of iterations required for each

method to achieve with $lon={10}^{-2},{10}^{-4},{10}^{-6}.$ Compare your numerical solutions obtained

with the three iterative methods to the solutions obtained with the linear algebra solver of Python.

$****$Iterative Methods:

Your assignment is to develop a program that solves linear system of equations using various methods

as specified below. Test your implementation with matrix provided below. A Python example scripts are included below to demonstrate how to read the MatrixMarket matrix data files and construct the matrix A and the right$-$hand vector b$.$ You are expected to use this script to read a matrix A and a vector b and solve the equation Ax $=$ b with Python, ensuring consistency with the provided answers.