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      1 Matrix3f A(3,3);
      2 A << 1,2,3,  4,5,6,  7,8,10;
      3 PartialPivLU<Matrix3f> luOfA(A); // compute LU decomposition of A
      4 Vector3f b;
      5 b << 3,3,4;
      6 Vector3f x;
      7 x = luOfA.solve(b);
      8 cout << "The solution with right-hand side (3,3,4) is:" << endl;
      9 cout << x << endl;
     10 b << 1,1,1;
     11 x = luOfA.solve(b);
     12 cout << "The solution with right-hand side (1,1,1) is:" << endl;
     13 cout << x << endl;
     14