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      1 MatrixXf m = MatrixXf::Random(3,5);
      2 cout << "Here is the matrix m:" << endl << m << endl;
      3 MatrixXf ker = m.fullPivLu().kernel();
      4 cout << "Here is a matrix whose columns form a basis of the kernel of m:"
      5      << endl << ker << endl;
      6 cout << "By definition of the kernel, m*ker is zero:"
      7      << endl << m*ker << endl;
      8