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      1 Matrix3f A;
      2 Vector3f b;
      3 A << 1,2,3,  4,5,6,  7,8,9;
      4 b << 3, 3, 4;
      5 cout << "Here is the matrix A:" << endl << A << endl;
      6 cout << "Here is the vector b:" << endl << b << endl;
      7 Vector3f x;
      8 x = A.lu().solve(b);
      9 cout << "The solution is:" << endl << x << endl;
     10