Feedback on systems-of-eqns

[danmargalit]

In reference to version 79e5138

In my slides (and I think in yours as well) we show that students that row replacement pivots one plane around the solution set. Is it worth putting this in the book? It could be a remark.

(Does this really explain the term "pivot"? It at least relates the word pivot to the geometric picture.)

[QBobWatson]

Actually I don't do that in my slides. I've honestly never thought about the geometry of row operations before. I could imagine doing this with a nice animated demo, but I'm not sure it's worth the effort. Do you want to try to write something?

I would've said a row replacement is more of a shear than a pivot.

[danmargalit]

Happy to write something one we have my laptop working. What I do in class is to show the system x+y=2 and x-y=0. Then I draw the two lines with the point of intersection (1,1). Then I do the row operation where I add the two rows, so it's x+y=2 and 2x=2. Then I draw the new line 2x=2 and an arrow from the line x-y=0 to the line 2x=2. I agree it's a shear, but it looks like you are pivoting the first line to the second around the solution. I think this is a good picture to keep in mind when doing row operations: the planes that you are intersecting are varying all over the place, but they stay "stuck" on the solution set and pivot around it.

[QBobWatson]

Sounds good; I'm happy if you write something. Let me know if you want me to make a figure.

[danmargalit]

Yes, please make the figure. There is a red line and a blue line. See the text.