I'm just starting 1.4. I agree with you about the informality (and also general terseness) but it's something I assume I'm going to acclimate myself to.

Trying to catch up; just starting the exercises to 1.4.

Keep going and I'll catch up someday!

I'm going to be offline for a few days this week, and might not be able to work on exercises. Will post when back. Keep going you guys!

I'm back and will get back into the exercises and post as soon as I can. What's others' status?

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.)

The answer to my question is that the proof derives an identity, so you need to reverse the steps to get back from there.