$(10$ points$)$ The Gaussian elimination algorithm is implemented in MATLAB, and

subsequently a function $($or subroutine$)$ is stored as my$\_$linsolver.m$,$ which utilizes

Gaussian elimination and backward substitution to solve a system consisting of $n$

linear equations written in the form of

$Ax=b$

where $A$ is an $nn($non$-$singular$)$ matrix, $b$ a given $n-$dimensional column vector,

and $x$ the $(n-$dimensional$)$ solution vector.

Using the $m-$file my$\_$linsolver.m$,$ solve the linear system:

$3x_1+x_2+4x_3=6,$

$x_2-2x_3=-3,$

$x_1+2x_2-x_3=-2.$

The exact solution is $x=[1,-1,1{]}^T.$ Then, use the $m-$file in order to solve the $44$

system:

$x_1+x_2+x_4=2,$

$2x_1+x_2-x_3+x_4=1,$

$4x_1-x_2-2x_3+2x_4=0,$

$3x_1-x_2-x_3+x_4=-3.$

Compute the $l_2-$norm of the residual $||b-$Ahat$(x)|{|}_2$ where hat$(x)$ is the approximate solution

computed for the $44$ system. Provide the MATLAB output.