eigen/doc/snippets/FullPivLU_solve.cpp

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.fullPivLu().solve(y);
if ((m * x).isApprox(y)) {
  cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
} else
  cout << "The equation mx=y does not have any solution." << endl;