add GT5 checkit

[StevenClontz]

Closes #770

[github-actions]

🚀 Preview available 🚀

https://64b0b6e3.tbil.pages.dev

• GT5 checkit: https://64b0b6e3.tbil.pages.dev/preview/linear-algebra/instructor/exercises/GT5/
• MX3 checkit: https://64b0b6e3.tbil.pages.dev/preview/linear-algebra/instructor/exercises/MX3/

[StevenClontz]

I wonder if GT5 should be folded into MX3. The quizzes are very similar at the end of the day, and MX3 is pretty short as-is. Thoughts @jkostiuk ?

[siwelwerd]

The GT5 one seems to be missing some margin or padding.

[StevenClontz]

The GT5 one seems to be missing some margin or padding.

This is just how CheckIt renders this content. (Consider it wontfix, sorry.)

[StevenClontz]

😢 drew stop peer pressuring me into making things better on the internet

[jkostiuk]

hmmm, while the quizzes might be similar, I think the ideas in GT5 and MX3, at least as written, aren't quite connected enough for that be a cohesive lesson.

However, your comment sparked the following reorganization brainstorm, so how do you and drew like the sound of this:

1. merge MX3 into MX2. Given the way we defined the inverse and inverse matrix, I think it follows naturally in that lesson that we can use the inverse matrix to solve a system of equations. then, in the MX2 checkit, we can have task 1 be "explain why this matrix isn't invertible" task 2 can be your reworked "find the inverse" and then we can add a short task 3 that's "use your inverse to solve the system". While this makes MX2 a little longer, the ideas are well-connected: we defined the inverse matrix/trafo to be "the unique solution to this equation" so it would make thematic sense for the lesson to end with "now we can easily compute this unique solution".
2. Then, GT5 becomes a new MX3.
3. If we do this, then I think we can add 2-3 activities to GT4 to do some version of diagonalization (i.e., after computing a basis of eigenvectors, use that to diagonalize a matrix).

What do you think?

[siwelwerd]

I'd suggest opening an issue to discuss anything of that scope. Others that aren't reading PRs they aren't working on might have insights.