With a state-space structure, prove that, by choosing (a_{11}=a_{22}=cos left(omega_{0} ight)) and (a_{21}=) (-a_{12}=-sin left(omega_{0} ight)), the

With a state-space structure, prove that, by choosing \(a_{11}=a_{22}=\cos \left(\omega_{0}\right)\) and \(a_{21}=\) \(-a_{12}=-\sin \left(\omega_{0}\right)\), the resulting oscillations in states \(x_{1}(n)\) and \(x_{2}(n)\) correspond to \(\cos \left(\omega_{0} n\right)\) and \(\sin \left(\omega_{0} n\right)\) respectively.