Traditionally, the tragic hero is a good and noble person who fails because of some fault in his character. Determine whether or not Macbeth is a tragic hero, supporting your position with quotations.
Most (if not all) scholars will concede that Macbeth is a tragic hero. The definition is based upon Aristotle's definition: the man must be great (noble, highly regarded, etc.); he must die; and, his death must be caused by a tragic flaw in his character.
In Shakespeare's Macbeth, Macbeth begins the play as a man well-respected. He is one of Duncan greatest soldiers: he has just helped Scotland defeat Norway in battle, facing the traitor Macdonwald (referred to here as "slave"):
For brave Macbeth—well he deserves that name
Disdaining fortune, with his brandish'd steel...
carved out his passage
Till he faced the slave... (I.ii.18-19, 21-22)
The King praises Macbeth not just because he fought valiantly, but also because he killed a Scotsman (Macdonwald) that joined the enemy to fight against his countrymen. Treason was an intolerable act, and Macdonwald's death comes as good news to Duncan. When the King hears this good news, along with the defeat of Norway, he rewards Macbeth with a new title, and all that comes with it.
Ironically, the man who kills Macdonwald, the traitor, becomes a traitor himself by killing Duncan—who is his King, as well as his friend, his cousin, and his house-guest. Macbeth blames this weakness of character on what we see as Macbeth's tragic flaw (which will cause his death): vaulting ambition—an unquenchable desire to have and be more. Macbeth admits:
I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself,
And falls on th'other… (I.vii.25-28)
Finally, to be a tragic hero, this man—at one time greatly admired—must die because of his flaw. Macbeth's ambition is so great that he forgets to think clearly—his judgment is clouded. Shakespeare's Elizabethan audience (that would have been watching with foreboding) believed completely in the supernatural: witches, ghosts, fairies, etc. With every fiber of their being, they would have recognized the "weird sisters" as evil personified, and would have known that in listening to their advice, Macbeth's fate was sealed. For the Elizabethans believed that witches served the devil, and a witch's sole purpose was to trick a person into losing his/her immortal soul.
Macbeth believes the witches' double-speak, realizing too late that they have betrayed him. He refuses to surrender, and bravely commits himself to fight Macduff to the death. Macduff is victorious. He announces to Malcolm:
Hail, King! for so thou art. Behold where stands
The usurper's cursed head. (V.viii.63-64)
At first, Macbeth is a great man, but he dies because of his tragic flaw—a clear example of a tragic hero.
"Stay you Imperfect Speakers"
"By Sinal's death I know that I am thane of Glamis, but how of Cawdor"
"Is this a dagger I see before me, the handle toward my hand? Art thou fatal brain?"
"I will not succumb to one od women born, I live a charmed life"
"We will talk of this no longer, he hath honored me of late"