The system of equations kx+y+z=1,x+ky+z=k and x+y+zk=k2 has no solution if k is

The augmented matrix of the system of equations is k1111k1k11kk2R2→kR2−R1,R3→kR3−R1                                                                               ≈k1110k2−1k−1k2−11k−1k2−1k3−1                                                                              ≈k−12k1110k+11k+101k+1k2+k+1R3→k+1R3−R2                                                                              ≈k−12k1110k+11k+100k2+2kkk2+2k+1                                                                               ≈kk−12k1110k+11k+100k+2k2+2k+1Third equation of the system of equations is k+2z=k+12   z=k+12k+2If k+2=0, system has no solution,  it means for k = -2 , system has no solution.