How has Macbeth and Banquo's relationship changed between Act 1, Scene 3 and Act 3, Scene 1?
In Act I, Scene 3, Macbeth and Banquo are clearly good friends. This is the scene where the two men encounter the witches, who prophesy that Macbeth will become Thane of Cawdor and King, and that Banquo's sons will become kings. Referring to Macbeth as "trusted home," a term of endearment, Banquo urges Macbeth not to place too much stock in the prophecies:
But ’tis strange;
And oftentimes, to win us to our harm,
The instruments of darkness tell us truths,
Win us with honest trifles, to betray's
In deepest consequence...
Macbeth clearly values his counsel, because he asks that they might speak again about what they have witnessed after they have both had time to think about it.
By Act III, Scene 1, the murder of Duncan and Macbeth's accession to the throne have soured his relationship with Banquo. The scene begins with a soliloquy in which Banquo shows his fears that Macbeth is responsible for the murder of Duncan:
Thou hast it now: King, Cawdor, Glamis, all,
As the weird women promised, and I fear
Thou play'dst most foully for't...
Banquo is somewhat encouraged, however, by the fact that Macbeth's prophecy has come true, since the witches also predicted that his sons would be kings. Banquo tells Macbeth that he is going riding with Fleance, and Macbeth asks a number of questions that could cause the audience to (correctly) predict that Macbeth plans further foul play on Banquo's riding excursion. Banquo has become an obstacle to Macbeth's ambition, and must be eliminated.