% Solves AX=B by Gaussian Elimination (naive)
% Input: A-nxn matrix, B-nx1 vector,and dimension n.
% Output: X-solution of the AX=B.

function[X]=gaussnaive(A,B,n)
X=zeros(n,1); m=1;
%Step1. Forward Elimination
for j=1:n-1
    for k=j+1:n
  m=A(k,j)/A(j,j);
  for s=j:n
      A(k,s)=A(k,s)-m*A(j,s);
  end
  B(k)=B(k)-m*B(j);
    end
end
% Step2. Bacward substitution
X(n)=B(n)/A(n,n);
for p=1:n-1
    k=n-p;
    for j=k+1:n
        B(k)=B(k)-A(k,j)*X(j);
    end
    X(k)=B(k)/A(k,k);
end
___________________________________________________________________________
%Problem 2.1.2 (a)
A=[2 -2 -1; 4 1 -2; -2 1 -1];
B=[-2;1;-3];
n=3;
[X]=gaussnaive(A,B,n)

X =

     1
     1
     2
%Problem 2.1.2 (b)
clear;
A=[1 2 -1; 0 3 1; 2 -1 1];
B=[2;4;2];
n=3;
[X]=gaussnaive(A,B,n)
X =
     1
     1
     1
% Problem 2.1.2 (c)
A=[2 1 -4; 1 -1 1; -1 3 -2];
B=[-7; -2; 6];
n=3;
[X]=gaussnaive(A,B,n)
X =

    -1
     3
     2