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