Matlab 'Function Unset/Unused' - matlab

Question

I am new to Matlab, so there is a lot I do not understand; I have three questions, as followed:
The biggest issue I have revolves around function B= upper_triang(A) where it states that it is 'a function unused'. Reading through the Matlab tooltip, and I am guessing that it has to do with a value that has not been defined? ANd B of course being unset, but I thought I defined B as a function, so why is it unset? I am assuming that B is U, but in the math part that is ahh, so I am not sure what it would be.
To give context to my code I sent the part of the homework code I have a question on.
%%%This is for part a for problem 1.
A=zeros(8,8);%%%For the size column and row size of matrix A.
for j=1:8
for k=1:8
if j==k
A(j,k)=-2;
end
if abs(j-k)==1
A(j,k)=1;
end
end
end
[L,U]=lu(A); %%%Proving L and U.
L*U; %%%Proving that L*U=A, thus it is correct.
%%%This is for part b for problem 1
function B= upper_triang(A)
%%%Input A--> Matrix for m*n for the size
%%%Output B--> Is the upper triangular matrix of the same size
[m,n]=size(A);
for k=1:m-1
for i=k+1:m
u=A(i,k)/A(k,k);
for j=(k):n
A(i,j)=A(i,j)-u*A(k,j);
end
end
end
B-A;
end

Answer 1

Function being unused
The problem here is that you've only created a function, but you've never used it. Everything after the function B = upper_triang(A) just tells Matlab what to do in case that function is ever called, but your never do.
I'm guessing that, after your LU decomposition but before the declaration of your function, you should add a line
B = upper_triang(A);
Output unset
There is a second problem which is that, while you declared that B should be the output of your function upper_triang(), it it not "created" anywhere in the function itself.
There should be a line somewhere with
B = something;
Now, my linear algebra is quite rusty but I think that what you're trying to do should rather be:
%%%This is for part b for problem 1
function B= upper_triang(A)
%%%Input A--> Matrix for m*n for the size
%%%Output B--> Is the upper triangular matrix of the same size
[m,n]=size(A);
B = A; % copy the input matrix in B, and work with it from now on
for k=1:m-1
for i=k+1:m
u=B(i,k)/B(k,k);
for j=(k):n
B(i,j)=B(i,j)-u*B(k,j);
end
end
end
B = B - A; % not really sure about this
end