function x = gauss_elim_scalar(A,b)

% A should be square
% size(A) = [length(x) length(x)]

n = size(A,1);

for k = 1:(n-1)
    for i = (k+1):n
        mult = A(i,k) / A(k,k);
        A(i,k) = 0;
        for j = (k+1):n
            A(i,j) = A(i,j) - mult * A(k,j);
        end
        b(i) = b(i) - mult * b(k);
    end
end

x = zeros(n,1);
for k = n:-1:1
    sum = b(k);
    for j = (k+1):n
        sum = sum - A(k,j) * x(j);
    end
    x(k) = sum / A(k,k);
end