In example and homework $6$C$,$ the Newton$-$Raphson method for $2\backslash$times $2$ and $3\backslash$times $3$ non$-$linear

systems of equations were considered. This problem is associated with the development of an

m$-$file implementing the Newton$-$Raphson method for an $\backslash$times $$ non$-$linear system of equations

$(3)$ using Gauss elimination $($rather than Cramer$$s method$).$ To this end, consider the

following $\backslash$times $$ non$-$linear system:

$1(1,2,...,)=211$

$+2+500=0,$

$(1,2,...,)=12$

$++1=0$ for $=2,3,,1,$

$(1,2,...,)=12$

$+100=0.$

Where $$ and $$ are constants and $>1.($Note that $=1$ corresponds to a linear system of

equations$).$

Download and modify script draft$\_6$D$.$m$.$ The modifications that must be implemented are

indicated as commented statements in green with the $\%$ symbol. More specifically, the

following modifications must be implemented in the script:

$1.$ Definition of functions $,,.$

$2.$ Definition of the $\backslash$times $$ matrix elements of the Jacobian.

$3.$ Addition of the MATLAB code associated with Gauss elimination with partial pivoting.

Evaluation of the determinant is not necessary. These statements should, therefore, be removed.

Furthermore, the consistency checks of the dimensions are not required and should also be

removed.

The required input file, s$.$txt$,$ is also provided in canvas. Note that the number of equations to

be solved simultaneously at each iteration is ~ $1000.$

The computation should involve the minimum possible number of arithmetic operations. Execute

the script using the $$Run and Time$$ option of MATLAB