EV5: prompt for understanding about solutions AND spanning/independence

[StevenClontz]

I'm grading https://library.tbil.org/2024/linear-algebra/exercises/#/bank/EV5/1/ and I wish we had this rigged to dig into students' understanding of not only "this equation has exactly one solution for every vector", but also explicitly connecting to their knowledge about spanning and independence.

I don't have any clever suggesitons for how to do so offhand, but noting this here for discussion.

[jkostiuk]

EV_5 (dragged).pdf

Here is what I've done for EV5 in the past. It was inspired because the sample solutions would address part (a) even though the checkit bank asked for part (b). Now I have them write the statement both ways.

Perhaps this is a starting point?