$L$ $U$ Decomposition Not Working (not Sure what I'm doing wrong: Matlab)

Question

I'm given this question 14a. The question gives me the pseudocode and I'm supposed to code it up on the algorithm or procedure in Matlab. I use this matrix for my A in my Matlab code:

I run my Matlab code but yet I keep getting incorrect results. My L*U ends up not being equal to A. I'm really confused as I follow the pseudocode pretty much exactly.

Here's my Matlab code:

A=[1 4 0 0; 3 4 1 0; 0 2 3 4; 0 0 1 3];

$n=4$;

$L=zeros(n,n)$;

$U=zeros(n,n)$;

$L(1,1)=A(1,1)$;

for $i=2:4$

$L(i,i-1)=A(i,i-1)$;

$U(i-1,i)=A(i-1,i)/L(i-1,i-1)$;

$L(i,i)=A(i,i)-(L(i,i-1)*U(i-1,i))$; end

$Z=L*U$;

If someone could help me debug my code, I would really appreciate it as my L*U (which I store as Z) ends up not being equal to A and I have no idea what I'm doing wrong).

Answer 1

ReplaceU=zeros(n,n); by U=eye(n);

$U$ is an upper bidiagonal matrix, we know that the diagonal entries are $1$.