please help with this QM question, thank you

So far in this class we have been focusing on innite dimensional vector spaces (i.e.1 the spaces of functions). However, as we go beyond 1D the importance of nite dimensional vector spaces will grow. This is because beyond 1D we encounter the concept of spin, and spin systems are described by finite dimensional vector spaces (e.g.., spin up or spin down being the two possibilities). Suppose the Hamiltonian for a twolevel (i.e.., twodimensional) system is H: e(|1>(2| +l2> 0