Essence of linear algebra edits (#426)

* fix vector lesson images for firefox

* Fix images for firefox in span lesson

* Partial progress for linear transformations, testing visual diff when the file changes

* Add file change

* Fix images for firefox in linear transformations lesson

* Fix images for firefox in 3d-transformations lesson

* Fix images for firefox in nonsquare-matrices lesson

* Fix images for firefox in dot-products lesson

* Fix images for firefox in cross-products lesson

* Fix images for firefox in cross-products-extended lesson

* Add the rest of the links to figma pages for the visual

* Update notes.txt

* Fix color of vector

* Fix broken image

* Fix broken image

* Fix broken image

* Fix broken image

public/content/lessons/2016/3d-transformations/index.mdx

@@ -92,6 +92,7 @@ To see where your vector lands, you multiply those coordinates by the correspond
 
 <Figure
     image="./figures/three-dimensions/Question1Transformation3d.svg" 
+    video="./figures/three-dimensions/Question1AnswerTransformation3d.mp4" 
     width="720px"
 />
 
@@ -150,10 +151,6 @@ $$
 \end{aligned}
 $$
 
-<Figure
-    video="./figures/three-dimensions/Question1AnswerTransformation3d.mp4" 
-/>
-
 </Question>
 
 ## Examples

public/content/lessons/2016/3d-transformations/notes.txt

@@ -1,3 +1,4 @@
 Notes from Kurt:
 
+- Link to figma page: https://www.figma.com/design/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?node-id=32-2
 - Could add a visual & animation at the end of the combining transformations section. Something like, "We can double check our work visually to see that the basis vectors do indeed correspond to the columns of the resulting matrix."

public/content/lessons/2016/abstract-vector-spaces/notes.txt

@@ -1,4 +1,6 @@
+Notes from Kurt:
 
+- Link to figma page: https://www.figma.com/design/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?node-id=759-11
 
 - Removed the following section from the very end:
 

public/content/lessons/2016/change-of-basis/notes.txt

@@ -1,4 +1,5 @@
 Notes from Kurt:
 
+- Link to figma page: https://www.figma.com/design/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?node-id=759-8
 - Removed this text right after calculating the inverse: "One way to interpret this is that from Jennifer's perspective, our first basis vector $\hat{\imath}$ has the coordinates $\left[\begin{array}{c} 1/3 \\ -1/3 \end{array}\right]$, and our second basis vector $\hat{\jmath}$ has coordinates $\left[\begin{array}{c} 1/3 \\ 2/3 \end{array}\right]$."
 - See figma page for illustrations: https://www.figma.com/file/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?type=design&node-id=759-8&mode=design

public/content/lessons/2016/cross-products-extended/notes.txt

@@ -1,3 +1,6 @@
+Notes from Kurt:
+
+- Link to figma page: https://www.figma.com/design/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?node-id=45-2
 - The last line "Next up is a really important concept in linear algebra: Change of basis." contradicts that the next lesson is about Cramer's Rule.
 - Should lesson links try and avoid mentioning the chapter number and instead use the chapter title or something like it?
 - The typesetting of $\left[ \begin{array}{c} x \\ y \\ z \end{array} \right]$ disrupts the paragraph grouping, so I updated the text to use $\vec{\mathbf{u}}$ instead. I've also had it where teachers write vectors horizontally, but I think I prefer the variable approach instead?

public/content/lessons/2016/cross-products/index.mdx

@@ -124,7 +124,7 @@ This is because a matrix whose columns represent $\vec{\mathbf{v}}$ and $\vec{\m
 The determinant is all about measuring how areas change due to a transformation, and the prototypical area to look at is the unit square resting on $\hat{\imath}$ and $\hat{\jmath}$. After the transformation, that square turns into the parallelogram we care about. So the determinant, which generally measures the factor by which areas are changed, gives the area of this parallelogram, since it evolved from a square that started with area 1. 
 
 <Figure
-    image="./figures/compute-with-determinant/determinant-basis-vectors-transformed-orientation.png" 
+    image="./figures/compute-with-determinant/DeterminantBasisVectorsTransformedOrientation.svg"
 />
 
 What's more, if $\vec{\mathbf{w}}$ is a _clockwise_ rotation away from $\vec{\mathbf{v}}$, it means orientation is flipped during the transformation, which is what it means for a determinant to be negative.

public/content/lessons/2016/cross-products/notes.txt

@@ -1,6 +1,11 @@
+Notes from Kurt:
+
+- Link to figma page: https://www.figma.com/design/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?node-id=487-23664
 - In the video the example starts as [3 2] cross [2 -1], but then changes to [3 1] cross [1 -2] between sections. Note, both have the same cross product of -7.
 - TODO: change colors of "two dimensions" section to be yellow and purple
 - Possibly reword sentence containing the word "prototypical"
 - Should the parallelogram always be the same color as the first operand vector in the cross product?
 - Should there be some comprehension questions applying the notational trick formula? Or should the student be encouraged into the next more in-depth lesson?
-- TODO: replace `./figures/compute-with-determinant/determinant-basis-vectors-transformed-orientation.png` with image callback from chapter five
+- TODO: replace `./figures/compute-with-determinant/determinant-basis-vectors-transformed-orientation.png` with image callback from chapter five
+
+- TODO: have before-and-after for image following "This is because a matrix whose columns represent v and w corresponds with a linear transformation that moves the basis vector..."

public/content/lessons/2016/dot-products/notes.txt

@@ -1,3 +1,4 @@
+- Link to figma page: https://www.figma.com/design/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?node-id=282-245
 - From Kurt: I think the end of the "unit vector" section and the "duality" section are going to be the hardest for the student, I tried to create a good question, but maybe there are some other considerations here.
 - From Grant: The section on linear transformations and duality could also be broken out as a separate article. In that case, we'd simply end this one with the question, prompting one to read the next article if they want to see the connection.
     "There's also another big question other than the order: Why on earth does this numerical process of matching coordinates, multiplying pairs, and adding them together have anything to do with projection?"

public/content/lessons/2016/eigenvalues/notes.txt

@@ -1,5 +1,6 @@
 Notes from Kurt:
 
+- Link to figma page: https://www.figma.com/design/mrGqFEpSdqWmWCgv0Yer6I/Essence-of-Linear-Algebra?node-id=759-9
 - Left introduction in first person because it is an opinion.
 - Changed sneaky vector to [1 -1] from [-1 1] for formatting purposes.
 - Most transformations are illustrated using a before and after image. Some of these could be made more compact by comparing them left-to-right, but I left most of them as top-to-bottom comparisons because it was faster to illustrate.