The Gauss$-$Seidel method is an iterative method that is commonly used to solve systems of linear equations in engincering applications. Such a system is often presented as follows:

$\{\begin{array}{cc}\text{:}{a}_{n\text{:}-1}{x}_1^{(x-1)}+a_{n2}{x}^{(n+1)}+\text{c}\text{d}\text{o}\text{t}\text{s}& =a_n{x}_{n-1}^{(n+3)}=b_n\end{array}$

The system may be written as:

That is:

$(L+D)x^{(k+1)}+U{x}^{(k)}=b$

So that:

$x^{(k+1)}=(L+D{)}^{-1}[-U{x}^{(k)}+b]$

Write Matlab code that takes a square $44$ matrix, $A,$ as input and uses the Gauss$-$Seidel method outlined above to solve for values of $x_n.$

You do not need to carry out validity or verification checks on the user input.

Use a tolerance of: to $=1c-5$ and initial values of $x_n=0$

Your code should output the values of $x_n$ you obtain, and the number of iterations taken,

$(30$ marks$)$ itr. Please use matlab.