function x $=$ gaussJordan$($A$,$ B$)$

$\%$ Solve Ax $=$ B by Gauss$-$Jordan elimination algorithm.

$[$NA$,$ ~$]=$ size$($A$)$;

$[$~$,$ NB$]=$ size$($B$)$;

if NB ~$=$ NA

error$(\text{'}$A and B must have compatible dimensions'$)$;

end

N $=$ NA $+$ NB;

AB $=[$A$,$ B$]$;

for k $=1$:NA

$\%$ Scaled Partial Pivoting

$[$akx$,$ kx$]=$ max$($abs$($AB$($k:NA$,$ k$))./$ max$($abs$($AB$($k:NA$,$ k:NA$)),[],2))$;

if akx $<$ eps

error$(\text{'}$Singular matrix and No unique solution'$)$;

end

mx $=$ k $+$ kx $-1$;

if kx $>1$

tmp$\_$row $=$ AB$($k$,$ :$)$;

AB$($k$,$ :) $=$ AB$($mx$,$ :$)$;

AB$($mx$,$ :) $=$ tmp$\_$row;

end

$\%$ Gauss forward and backward elimination

pivot $=$ AB$($k$,$ k$)$;

AB$($k$,$ :) $=$ AB$($k$,$ :) $/$ pivot;

for m $=1$:NA

if m ~$=$ k

AB$($m$,$ :) $=$ AB$($m$,$ :) $-$ AB$($m$,$ k$)*$ AB$($k$,$ :$)$;

end

end

end

x $=$ AB$($:$,$ NA$+1$:N$)$;

end

modify the function gaus$()$ into gausj$()$ that implements GausJordan elimination algorithm and show that the function is indeed working.