Does Shakespeare want us to believe that the witches in Macbeth are real, supernatural or projections of Macbeth's imagination?

I think Shakespeare definitely wants his audience to believe that the Weird Sisters are real and have some supernatural ability for several reasons.  First of all, they speak and make decisions in the play even before Macbeth is aware of their existence.  Secondly, the Weird Sisters cannot simply be projections of Macbeth's imagination because Banquo sees and interacts with them as well.  Further, the Weird Sisters do meet with Hecate, goddess of witchcraft, an interaction...

I think Shakespeare definitely wants his audience to believe that the Weird Sisters are real and have some supernatural ability for several reasons.  First of all, they speak and make decisions in the play even before Macbeth is aware of their existence.  Secondly, the Weird Sisters cannot simply be projections of Macbeth's imagination because Banquo sees and interacts with them as well.  Further, the Weird Sisters do meet with Hecate, goddess of witchcraft, an interaction that could not occur if they were not truly otherworldly.

Also, and perhaps most telling, is the fact that the audience sees the Weird Sisters, too.  We can tell this even if we only read the text because they have stage direction.  When Macbeth is hallucinating, as he does at the end of Act 2, Scene 1, he must tell us exactly what he sees because we cannot see it.  He must describe the dagger that appears in front of him, as well as all the changes it undergoes, because it is not really there.  Because the Weird Sisters are not treated in the same way by the text, we can understand that they do exist outside of Macbeth's mind.