simplifications in the ei_solve_impl system, factor out some boilerplate code

doc/snippets/FullPivLU_image.cpp

@@ -6,4 +6,4 @@ 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.lu().image(m) << endl;
+     << endl << m.fullPivLu().image(m) << endl;

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:"

doc/snippets/FullPivLU_solve.cpp

@@ -2,7 +2,7 @@ Matrix<float,2,3> m = Matrix<float,2,3>::Random();
 Matrix2f y = Matrix2f::Random();
 cout << "Here is the matrix m:" << endl << m << endl;
 cout << "Here is the matrix y:" << endl << y << endl;
-Matrix<float,3,2> x = m.lu().solve(y);
+Matrix<float,3,2> x = m.fillPivLu().solve(y);
 if((m*x).isApprox(y))
 {
   cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;

doc/snippets/HouseholderQR_solve.cpp

@@ -4,6 +4,6 @@ Matrix3f y = Matrix3f::Random();
 cout << "Here is the matrix m:" << endl << m << endl;
 cout << "Here is the matrix y:" << endl << y << endl;
 Matrix3f x;
-m.householderQr().solve(y, &x);
+x = m.householderQr().solve(y);
 assert(y.isApprox(m*x));
 cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;