Is dead state only linked with the final state in any automata?

Question

I am very much new to this subject and as far as I have tried the small research I found this most meaningful at this link

Dead State - A rejecting state that is essentially a dead end. Once the machine enters a dead state, there is no way for it to reach an accepting state, so we already know that the string is going to be rejected. Graphically, the dead state is often omitted and assumed for any input that the machine does not have explicit instructions on what to do with. A machine may have multiple dead states, but at most only one dead state is needed per machine.

Now I am designing a what is very simple machine for my homework and the question is that part in the definition

......that string is often omitted....

so what should I do for a machine that says that

L1 = {Strings starting with “a” over ∑ = {a,b} }

Now I know that this will be a very simple machine that will move towards final state if it starts with a and stays in final state over any new comer so the real question should I add the Dead State here, because the definition is saying that

dead state is often omitted and assumed for any input that the machine doesn't have explicit instructions on what to do with

, that can move the automaton to the dead state in case the first letter is not a and so that dead stays lock the machine to that dead state. Considering my question L1 should I mention dead state or just leave it assumed.

Sorry for bad reformatting and confusing statements I am very new to the course

Answer 1

I think that since you’re just beginning, it would be best to include the dead state in your graphical description of the automaton. (Indeed, some instructors will require you to do so.) You need to include it in the full symbolic description anyway, and the automaton is so simple that including it in the graph doesn’t really add any clutter: even with the dead state it has only three states altogether.

To answer the question in your title, the dead state has transitions only to itself, but it may have transitions from many states, some of them final (acceptor) states and some not.