doc/examples/Tutorial_PartialLU_solve.cpp

#include <Eigen/Core>
#include <Eigen/LU>
#include <iostream>

int main()
{
   Eigen::Matrix3f A;
   Eigen::Vector3f b;
   A << 1,2,3,  4,5,6,  7,8,10;
   b << 3, 3, 4;
   std::cout << "Here is the matrix A:" << std::endl << A << std::endl;
   std::cout << "Here is the vector b:" << std::endl << b << std::endl;
   Eigen::Vector3f x = A.lu().solve(b);
   std::cout << "The solution is:" << std::endl << x << std::endl;
}