Do not copy existing chegg solutions, I will down vote if its copied. Please provide detailed and clear steps.

2.3-22. Unknown-Input Observability We know that given the input and output (and their necessary derivatives) for an observable system we can determine its state. Prove that for an obsery- able system we can determine the state without knowledge of the input if and only if the first n - 1 Markov parameters, h: to h -1, are zero. Show that this is equivalent to the fact that the transfer function has no (finite) zeros