I have found 1.5 harder to follow, but pretty interesting once you figure it out. The heart of it is the proof (if you can call it that!) of A = LU on pp. 34-35

I have found 1.5 harder to follow, but pretty interesting once you figure it out. The heart of it is the proof (if you can call it that!) of A = LU on pp. 34-35. It is quite beautiful - just one simple idea. But I have a question. From p. 35: Both sides of (7) end up equal to the same matrix U, and the steps to get there are all reversible. What is the importance of "and the steps to get there are all reversible"? I don't see how the argument uses this fact. (On a practical note, I suppose a new thread is in order as we can no longer post top-level comments on this one. If no one else creates one, I'll do so after I've worked through the exercises in 1.5.)