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Brutus shows his nobility in Act 2.1 when he is deciding whether or not to join the conspiracy to assassinate Caesar:
It must be by this death. And for my part
I know no personal cause to spurn at him.
But for the general [good]. He would be crowned:
How that might change his nature, there's the question.
It is the bright day that brings forth the adder [snake],
And that craves wary walking. Crown him that,
And then I grant we put a sting in him
That at his will he may do danger with. (Act 2.1.10-18)
Brutus has no personal reason to want Caesar dead. If he joins the conspiracy, it will be for the general good. He worries that once Caesar is crowned, he may become a tyrant and do harm to Rome.
Brutus shows nobility by thinking of the common good of Rome. He may be correct or incorrect in his judgment of Caesar, but his motives are pure.