cout<< "The matrix v is:"<< endl;cout<< v<< endl;Vector3d v0(1, v(1, 0), v(2, 0));cout<< "The first Householder vector is: v_0 = "<< v0.transpose()<< endl;Vector3d v1(0, 1, v(2, 1));cout<< "The second Householder vector is: v_1 = "<< v1.transpose()<< endl;Vector3d v2(0, 0, 1);cout<< "The third Householder vector is: v_2 = "<< v2.transpose()<< endl;Vector3d h=Vector3d::Random();cout<< "The Householder coefficients are: h = "<< h.transpose()<< endl;Matrix3d H0=Matrix3d::Identity() - h(0) *v0 *v0.adjoint();cout<< "The first Householder reflection is represented by H_0 = "<< endl;cout<< H0<< endl;Matrix3d H1=Matrix3d::Identity() - h(1) *v1 *v1.adjoint();cout<< "The second Householder reflection is represented by H_1 = "<< endl;cout<< H1<< endl;Matrix3d H2=Matrix3d::Identity() - h(2) *v2 *v2.adjoint();cout<< "The third Householder reflection is represented by H_2 = "<< endl;cout<< H2<< endl;cout<< "Their product is H_0 H_1 H_2 = "<< endl;cout<< H0 *H1 *H2<< endl;HouseholderSequence< Matrix3d, Vector3d > hhSeq(v, h)