I am trying to write a program in Matlab to solve a system of linear equations using LU decomposition which employs the use of gauss elimination and hence a lot of arithmetic steps.

The answers are close to the right solution but the round-off errors are pretty high as compared to other languages like Python etc.

For instance, one of the solutions is exactly 3 but I get 2.9877.

I know in-built functions should be used for such trivial things since Matlab is a high-computing language but if I still wanted to do it with loops etc would I always get round-off errors or is there a way to reduce those while doing numerical calculations?

I am attaching the code but it's big and not worth reading. I have still attached it for the sake of completion. One can just note the use of many arithmetic operations which introduce a lot of round-off errors.

Are these round-off errors intrinsic to Matlab and unavoidable?

clc
clear
%No of equations is n
n=3;
%WRITING THE Coefficients
A(1,1)=3;
A(1,2)=-0.1;
A(1,3)=-0.2;
B(1)=7.85;

A(2,1)=0.1;
A(2,2)=7;
A(2,3)=-0.3;
B(2)=-19.3;

A(3,1)=0.3;
A(3,2)=-0.2;
A(3,3)=10;
B(3)=71.4;
%Forward Elimination
for i=1:n-1
  for j=i 1:n
    fact=A(j,i)/A(i,i);
    A(j,i)=fact;
    
    A(j,j:n)=A(j,j:n)-fact*A(i,j:n);
    B(j)=B(j)-fact*B(i);
  end
end
disp(A)
% Calculating d matrix
sum=0;
D(1)=B(1);
for i=2:n
  for j=1:i-1
    sum=sum A(i,j)*B(j);
    D(i)=B(i)-sum;
  end
end
disp("D =")
disp(transpose(D))