Write a function x $=$ backSubst$($Z$,$ y$,$ k$)$ that performs back$-$substitution recursively to solve Zx $=$ y$.($ALLOW one loop$)$ here is example of forward substitution

function y $=$ fwdSubst$($L$,$b$,$k$)$

$\%$Foward substitution

$[$m$,$n$]=$size$($L$)$;

if ~exist$(\text{'}$k$\text{'})\%$ If first call no k param given, but k$=1$

k$=1$;

end

y$=$b$($k$)/$L$($k$,$k$)$;

if k $<$ n $\%$ Recursion step

l $=[$zeros$($k$,1)$;L$($k$+1$:m$,$k$)]$;

y $=[$y;fwdSubst$($L$,$b$-$y$*$l$,$k$+1)]$;

end

$2.$ here is already function:

function $[$A$,$ B$]=$ elimmat$($Ag$,$ g$)$

$\%$ Assuming Ag is a square matrix

n $=$ size$($Ag$,1)$;

$\%$ Initialize elimination matrices

A $=$ eye$($n$)$;

B $=$ eye$($n$)$;

$\%$ Perform elimination

A$($:$,$ g$)=-$Ag$($:$,$ g$)/$ Ag$($g$,$ g$)$;

B$($:$,$ g$)=$ Ag$($:$,$ g$)/$ Ag$($g$,$ g$)$;

end

Write function $[$L$,$ U$]=$ myLU$($A$)$ that reuses elimMat to give an LU factorization of A$.$

get matrix L and matrix U$.($allow one loop$)$

$3.$ write m$-$file script to execute program.