Given the following nonlinear system,

$x_1+2x_2+3x_3+4x_4=1+x_1{x}_2^4$

$2x_1+3x_2+4x_3+x_4=5+x_2{x}_3^4$

$3x_1+4x_2+x_3+2x_4=6+x_3^{***}{x}_4^4$

$4x_1+x_2+2x_3+3x_4=11+x_4{x}_1^4$

$($a$)$ Construct an algorithm and apply the Gauss$-$Seidel iterative method to the solve the system. Make your initial guess for the solution and set the absolute error limit to $0\mathrm{.}0001.$ Submit the code, the solution, and the number of iterations needed. Note that an underrelaxation factor of $0\mathrm{.}5$ or less may be needed for convergence.

$($b$)$ Use MATLAB fsolve to find the solution for this problem.