Problem $1$

MATLAB or Python

$\left[\begin{array}{cccc}-7& 3& -2& 1\\ -2& 9& -2& -1\\ 1& 3& -11& -5\\ -1& -6& 1& 12\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]=\left[\begin{array}{c}7\\ 10\\ -4\\ -16\end{array}\right]$

$($i$)$ Find the solution to the above problem using $($numpy$.$linalg.solve in

Pythonor linsolve in MATLAB $)$

$($ii$)$ Use MATLAB or Python to construct the Jacobi iteration

$($iii$)$ Use MATLAB or Python to construct the Gauss$-$Seidel algorithm