Feedback on vectors

[danmargalit]

In reference to version 30f811f

I feel like we should add to the end of this section a sample question of the form: is this vector a linear combination of these other ones? Or maybe move that chunk from the next section to this one.

Or what about saying at the end: A basic kind of problem we will want to understand is whether a given vector is a linear combination of some other vectors. As we will see, this question is closely related to the problem of solving linear systems!

[danmargalit]

Wait, I think we should do this at the end of 3.1. It motivates the whole idea of a vector equation at the start of 3.2. That way they will have actually seen one instead of just being told they should care about vector equations.

[QBobWatson]

Actually, I think our motivation for vector equations is backwards. We care that we can translate a linear system into a vector equation, not the other way around. So perhaps add a paragraph at the end of 3.1 to show this, and have essentially the same paragraph at the beginning of 3.2? Then that motivates why we care about linear combinations.