For a particular $4$x$4$ linear equations system explain Jacobi

and Gauss Siedel Methods and design a program of the Gauss Siedel

method for any $4$x$4$ equations system.

b$)(10$ p$)$Run the program for the same example and add your output.

c$)(10$ p$)$ Write the necessary theorem and proof for convergence of

successive methods$\mathrm{.}5x_1+2x_2-3x_3+4x_4=15$

$3x_1-4x_2+2x_3+2x_4=8$

$x_1+3x_2-2x_3+6x_4=10$

$2x_1+2x_2+4x_3-7x_4=5$