$A=$ np$.$random.normal $,$ size $=(n,n)$ np$.$identity $(n)$

$b=np.$ random.normal $,$ size $=(n,1)$

Two cases: $(1)n=150,(2)n=250($here $np$ means numpy$)$

$Ax=b$

A and $b$ : We use the same A and $b$ as in Problem $)=150,n=(250$

$($i$)$ Use Python or MATLAB to construct the Jacobi algorithm and find the solution

$($ii$)$ Use Python or MATLAB to construct the Gauss$-$Seidel algoroithm and find the solution

$($iii$)$ For both algorithms, you obtain the convergence plot of the solution $($as I provided in the slides$)$

$($iv$)$ Plot $||x-x_k|{|}^2$ for each $k$ where $x$ is the true solution $($you can use "numpy.linalg.solve" in Python or "linprog" in MATLAB to obtain the true solution$)$ and $x_{-}k$ is the solutions obtained from the two algorithms $(($i$)$ and $($ii$))$ in each step.

compare the computation time and accuracy of

Jacobi Algorithm

Gauss$-$Seidel algorithm

numpy.linalg.solve in Python or linprog in MATLAB