Matrix3f A;
Vector3f b;
A << 1,2,3,  4,5,6,  7,8,9;
b << 3, 3, 4;
cout << "Here is the matrix A:" << endl << A << endl;
cout << "Here is the vector b:" << endl << b << endl;
Vector3f x;
A.partialLu().solve(b, &x);
cout << "The solution is:" << endl << x << endl;