Solve the following system of equations

$2x_1-6x_2-x_3=-38$

$-3x_1-x_2+7x_3=-34$

$-8x_1+x_2-2x_3=-20$

using

i$)$ Gauss Seidel, writing only the first two iterations solved by hand $($no code required$).$ Start

with a guess of zeros. If necessary, rearrange the equations to achieve convergence. Find the

error at each iteration.

ii$)$ LU decomposition by hand and python builtin method.

iii$)$ Python linalg.solve method.