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At the end of his speech, the Architect explicitly states that Trinity is going to die and there is nothing Neo can do to prevent this.

The door to your right leads to the Source, and the salvation
of Zion. The door to the left leads back to the Matrix, to her, and to the end of your species. As you adequately put, the problem
is choice. But we already know what you're going to do, don't we? Already I can see the chain reaction, the chemical precursors
that signal the onset of emotion, designed specifically to overwhelm logic, and reason. An emotion that is already blinding you
from the simple, and obvious truth: she is going to die, and there is nothing that you can do to stop it.

Even though Neo saves Trinity at that instant, she dies only the next day, and Neo returns to the Source and to the salvation of Zion. The only difference is that Neo rejected choosing 16 females and 7 males to construct a new Zion.

The Architect has full knowledge of everything that is going to happen within the Matrix. His knowledge includes emotions as well, in spite of his inability to understand them. Thus, there is no way he cannot know Neo is going to save Trinity, yet he still states she is going to die.

One assumption might be him bluffing to goad Neo to go to the Source, however, he also states he is incapable of lies and deceptions as well.

I have your word?

What do you think I am? Human?

So, my question is, how did the Architect know that Trinity will die outside the Matrix?

First, we need to establish a preliminary fact: the Architect knew -- or at least had very good reason to believe -- that Trinity would be killed by the Agents chasing her unless Neo somehow miraculously saved her. You can see in the background that the TVs in the Architect's room show that Trinity was being chased by multiple (upgraded) Agents in the Matrix, and it doesn't take an Oracle to surmise that Trinity probably would not survive that encounter. If you look closely at the scene, though, (e.g. in this clip) you can actually see Trinity when she is shot while falling out of the skyscraper before it has actually happened. We don't know exactly how the Architect's TV can show an event before it has happened,¹ but the point is that the Architect knows Trinity will be shot while falling out of a skyscraper -- therefore, it would take some sort of miraculous intervention by Neo to save Trinity from the Agents.

Having established that only Neo can hope to save Trinity from the Agents, we can consider what the Architect believes would happen depending on which door Neo chose (to go to the Source or return to the Matrix):

1. 
   If Neo goes to the Source he is effectively abandoning Trinity to her death in the Matrix at the hands of the Agents. Normally Neo would be able to choose Trinity as one of the initial 16 females of Zion, but she would already have been killed by the Agents.


2. If Neo returns to the Matrix he can try to save Trinity, though he'd probably still fail. Nonetheless, even if Neo managed to save Trinity from the Agents he's only delayed the inevitable: by failing to go to the Source the Matrix will collapse and, combined with the destruction of Zion, mankind will become extinct. Trinity will die by the time mankind becomes extinct.

So, the Architect believes Trinity will die either way.

One assumption might be him bluffing to goad Neo to go to the Source, however, he also states he is incapable of lies and deceptions as well.

This isn't actually true. The machines have no qualms about deceptions and lies -- the Matrix and the system of the One are both huge deceptions by the machines. The Architect actually states that he (i.e. the machines) will keep his word. The machines will lie and deceive, but they won't break their promises. Neo made a deal with the machines to destroy Smith if the machines would allow humans to leave the Matrix, and since Neo upheld his end of the deal the machines will honor theirs.

¹The Oracle predicted Trinity's fall because Neo dreamed about it, so I suspect that's how the Architect's TV was able to show Trinity falling and being shot before it actually happened. Furthermore, while Neo originally had the dream of Trinity falling in the real world, the machines may have been able to produce the exact image by recording Neo's brain waves when he was recalling his dream while talking to the Oracle in the Matrix.

The Architect did not predict Trinity's death in the real world that was simply coincidence. Neo did not stop Trinity's death in matrix he reversed it so The Architect was telling the truth.

On a more meta note Trinity would have died someday, of old age if nothing else and there was nothing Neo could do to stop it. The Architect is probably not above telling the truth in a manipulative matter if it gets him what he desires.