Develop a computer program to solve the following system of equations

$($

employ initial guesses of

$0\mathrm{.}0$

$$

$$

for all

unknowns

$)$

:

$-$

j

$-$

$2$

k

$+$

$4$

l

$-$

$2$

m

$=$

$97\mathrm{.}54$

j

$-$

$3$

k

$+$

$2$

l

$-$

n

$=$

$79\mathrm{.}75$

$2$

k

$-$

$3$

l

$+$

$6$

m

$=$

$102\mathrm{.}28$

$3$

j

$+$

l

$-$

$2$

m

$+$

$7$

n

$=$

$84\mathrm{.}49$

$-$

$3$

j

$-$

k

$+$

m

$-$

$2$

n

$=$

$102\mathrm{.}37$

using the following two methods:

$($

a

$)$

$$

$$

Gauss

$-$

Seidel

$($

b

$)$

$$

$$

Jacobi

Perform iterations until the approximation error is

$<$

$0\mathrm{.}00001$

$$

$$

and then comment on the obtained results.

Please follow the below given details and i need the exact solution of the problem.

IMP Note:

For this problem, it is mandatory to use MatLab. However, you are not allowed to use any built in functions in MatLab that are not available in the other compilers.

Below is the code given to me but not getting the output. resolve it$.$

$\%$ Given system of equations

A $=[-1-24-20$;

$1-32-10$;

$02-360$;

$31-270$;

$-3-110-2]$;

b $=[97\mathrm{.}54$; $79\mathrm{.}75$; $102\mathrm{.}28$; $84\mathrm{.}49$; $102\mathrm{.}37]$;

$\%$ Initial guess

x$0=[0$; $0$; $0$; $0$; $0]$;

$\%$ Gauss$-$Seidel Method

disp$(\text{'}$Gauss$-$Seidel Method:$\text{'})$;

$[$x$\_$gs$,$ iterations$\_$gs$]=$ gaussSeidel$($A$,$ b$,$ x$0,0\mathrm{.}000001)$;

disp$([\text{'}$Solution after $\text{'},$ num$2$str$($iterations$\_$gs$),\text{'}$ iterations:$\text{'}])$;

disp$($x$\_$gs$)$;

$\%$ Jacobi Method

disp$(\text{'}$Jacobi Method:$\text{'})$;

$[$x$\_$jacobi, iterations$\_$jacobi$]=$ jacobi$($A$,$ b$,$ x$0,0\mathrm{.}000001)$;

disp$([\text{'}$Solution after $\text{'},$ num$2$str$($iterations$\_$jacobi$),\text{'}$ iterations:$\text{'}])$;

disp$($x$\_$jacobi$)$;

$\%$ Gauss$-$Seidel method function

function $[$x$,$ iterations$]=$ gaussSeidel$($A$,$ b$,$ x$0,$ tolerance$)$

n $=$ length$($b$)$;

x $=$ x$0$;

x$\_$prev $=$ x$0+2*$tolerance; $\%$ to enter the while loop

iterations $=0$;

while norm$($x $-$ x$\_$prev, inf$)>$ tolerance

x$\_$prev $=$ x;

for i $=1$:n

x$($i$)=($b$($i$)-$ A$($i$,1$:i$-1)*$x$(1$:i$-1)-$ A$($i$,$i$+1$:n$)*$x$\_$prev$($i$+1$:n$))/$ A$($i$,$i$)$;

end

iterations $=$ iterations $+1$;

end

end

$\%$ Jacobi method function

function $[$x$,$ iterations$]=$ jacobi$($A$,$ b$,$ x$0,$ tolerance$)$

n $=$ length$($b$)$;

x $=$ x$0$;

x$\_$prev $=$ x$0+2*$tolerance; $\%$ to enter the while loop

iterations $=0$;

while norm$($x $-$ x$\_$prev, inf$)>$ tolerance

x$\_$prev $=$ x;

for i $=1$:n

x$($i$)=($b$($i$)-$ A$($i$,$:$)*$ x$\_$prev $+$ A$($i$,$i$)*$ x$\_$prev$($i$))/$ A$($i$,$i$)$;

end

iterations $=$ iterations $+1$;

end

end.

MIMP : Gauss$-$Seidel Method:

Unrecognized function or variable 'gaussSeidel'. I want the solution of this error and give me proper code along eith proper iterations showing each and every steps.