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      1 Matrix3d m;
      2 m << 1,1,0,
      3      1,3,2,
      4      0,1,1;
      5 cout << "Here is the matrix m:" << endl << m << endl;
      6 cout << "Notice that the middle column is the sum of the two others, so the "
      7      << "columns are linearly dependent." << endl;
      8 cout << "Here is a matrix whose columns have the same span but are linearly independent:"
      9      << endl << m.fullPivLu().image(m) << endl;
     10