simplifications in the ei_solve_impl system, factor out some boilerplate code

doc/snippets/FullPivLU_kernel.cpp

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