function x $=$ ConjugateGradientMethod$($A$,$ b$,$ x$0,$ tol, max$\_$iter$)$

$\%$ Conjugate Gradient Method to solve Ax $=$ b

if nargin $<4$

tol $=1$e$-10$;

end

if nargin $<5$

max$\_$iter $=$ length$($b$)$;

end

$\%$ Initial Setup

r $=$ b $-$ A $*$ x$0$;

p $=$ r;

rs$\_$old $=$ r$\text{'}*$ r;

x $=$ x$0$;

$\%$ Iterate

for k $=1$:max$\_$iter

Ap $=$ A $*$ p;

alpha $=$ rs$\_$old $/($p$\text{'}*$ Ap$)$;

x $=$ x $+$ alpha $*$ p;

r $=$ r $-$ alpha $*$ Ap;

rs$\_$new $=$ r$\text{'}*$ r;

if sqrt$($rs$\_$new$)<$ tol

break;

end

p $=$ r $+($rs$\_$new $/$ rs$\_$old$)*$ p;

rs$\_$old $=$ rs$\_$new;

end

end

$\%$ My student ID is $723113010001$

student$\_$id $=723113010001$;

last$\_$two$\_$digits $=$ mod$($student$\_$id$,100)$;

$\%$ Size of the problem

n$1=200+$ last$\_$two$\_$digits; $\%$ For the first problem

n$2=400+$ last$\_$two$\_$digits; $\%$ For the second problem

$\%$ Create matrix A and vector b for the first problem

A$1=$ diag$(-2*$ ones$($n$1,1))+$ diag$($ones$($n$1-1,1),1)+$ diag$($ones$($n$1-1,1),-1)$;

b$1=$ zeros$($n$1,1)$;

b$1(1)=-1$;

b$1($end$)=-1$;

$\%$ Create matrix A and vector b for the second problem

A$2=$ diag$(-2*$ ones$($n$2,1))+$ diag$($ones$($n$2-1,1),1)+$ diag$($ones$($n$2-1,1),-1)$;

b$2=$ zeros$($n$2,1)$;

b$2(1)=-1$;

b$2($end$)=-1$;

$\%$ Initial guess

x$0\_1=$ zeros$($n$1,1)$;

x$0\_2=$ zeros$($n$2,1)$;

$\%$ Solve using conjugate gradient method

x$1=$ ConjugateGradientMethod$($A$1,$ b$1,$ x$0\_1)$;

x$2=$ ConjugateGradientMethod$($A$2,$ b$2,$ x$0\_2)$;

$\%$ Display solutions

disp$(\text{'}$Solution for the first problem $($n $=201)$:$\text{'})$;

disp$($x$1)$;

disp$(\text{'}$Solution for the second problem $($n $=401)$:$\text{'})$;

disp$($x$2)$;

correct the code to remove parse errors