Problem #$2(75\%)$:

Develop a computer program to solve the following system of equations $($employ initial guesses of $0\mathrm{.}0$ for all

unknowns$)$:

$-j-2k+4l-2m=97\mathrm{.}54$

$j-3k+2l-n=79\mathrm{.}75$

$2k-3l+6m=102\mathrm{.}28$

$3j+l-2m+7n=84\mathrm{.}49$

$-3j-k+m-2n=102\mathrm{.}37$

using the following two methods:

$($a$)$ Gauss$-$Seidel

$($b$)$ Jacobi

Perform iterations until the approximation error is $<mn\; id="EditorElement\_617306">0</mn><mn\; id="EditorElement\_617307">.</mn><mn\; id="EditorElement\_617308">0</mn><mn\; id="EditorElement\_617309">0</mn><mn\; id="EditorElement\_617310">0</mn><mn\; id="EditorElement\_617311">0</mn><mn\; id="EditorElement\_617312">1</mn>$ and then comment on the obtained results.

M$.$IMP Note:

For this problem, it is mandatory to use MatLab. However, you are not allowed to use any built$-$in functions in MatLab that are not available in the other compilers.