A=[1 2; 0.499 1.001];
b=[3; 1.5];

A1=[1 2; 0.5 1.0015];
b1=[3; 1.4985];

x=A\b
x1=A\b1
res=A*x1-b1
x2=A1\b
res=A1*x2-b
x3=A1\b1
res=A1*x3-b1

k=cond(A);


dA=A1-A;

db=b1-b;
dx=x3-x;
fprintf('\n \t k: %1.5e',k);
fprintf('\n \t term 1: %1.5e',norm(dx)/norm(x));
fprintf('\n \t term 2: %1.5e',norm(dA)/norm(A));
fprintf('\n \t term 3: %1.5e',norm(db)/norm(b));
fprintf('\n \t test hyp: %1.5e < 1',k*norm(dA)/norm(A));
fprintf('\n \t coeff: %1.5e',k/(1-k*norm(dA)/norm(A)));

det(A)
det(A1)