From 01f08ebdcf3bd3333790a74874d98a62e5966b9d Mon Sep 17 00:00:00 2001
From: Kurt Bruns <12160501+kurtbruns@users.noreply.github.com>
Date: Thu, 23 May 2024 10:28:11 -0700
Subject: [PATCH] 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
---
.../ComposingTransformations.svg | 98 +--
.../MatrixMultiplication.svg | 135 ++-
.../figures/three-dimensions/BasisVectors.svg | 104 ++-
.../three-dimensions/FollowBasisVectors.svg | 242 ++---
.../Question1Transformation3d.svg | 179 +++-
.../Rotate90DegreesAroundYAxis.svg | 230 +++++
.../three-dimensions/Transform3dVector.svg | 291 ++++---
.../three-dimensions/TransformGrid.svg | 44 +-
.../three-dimensions/TransformManyVectors.svg | 824 +++++++++---------
.../three-dimensions/TransformMatrix.svg | 394 ++++-----
.../TransformationFunction.svg | 96 +-
.../three-dimensions/TransformationMatrix.svg | 183 +++-
.../VectorAsTransformationAfter.svg | 152 ++--
.../VectorAsTransformationBefore.svg | 112 +--
.../lessons/2016/3d-transformations/index.mdx | 5 +-
.../lessons/2016/3d-transformations/notes.txt | 1 +
.../2016/abstract-vector-spaces/notes.txt | 2 +
.../lessons/2016/change-of-basis/notes.txt | 1 +
.../conclusion/CrossProductFormula.svg | 118 ++-
.../the-idea/CrossProductGeometryVolume.svg | 163 +++-
.../2016/cross-products-extended/notes.txt | 3 +
.../compute-with-determinant/ChangeOfArea.svg | 137 ++-
.../ComputeCrossProduct.svg | 130 ++-
...nantBasisVectorsTransformedOrientation.svg | 153 ++++
.../DeterminantNegative.svg | 145 ++-
.../DeterminantPositive.svg | 144 ++-
.../DeterminantExample.svg | 64 +-
.../DeterminantExampleQuestion1.svg | 90 +-
...DeterminantExampleQuestion1Calculation.svg | 149 +++-
...terminantExampleQuestion1Parallelogram.svg | 157 +++-
.../DeterminantTransformation.svg | 173 +++-
.../standard-view/RightHandRuleExample1.svg | 121 ++-
.../standard-view/RightHandRuleExample2.svg | 121 ++-
.../RightHandRuleExample2Parallelogram.svg | 111 ++-
.../two-dimensions/AreaOfParallelogram.svg | 91 +-
.../AreaOfParallelogramCalculation.svg | 109 ++-
.../AreaOfParallelogramFormula.svg | 122 ++-
.../AreaOfParallelogramNegative.svg | 127 ++-
.../AreaOfParallelogramPositive.svg | 126 ++-
.../AreaOfParallelogramQuestion1.svg | 91 +-
.../AreaOfParallelogramQuestion1Answer.svg | 108 ++-
.../AreaOfParallelogramQuestion2.svg | 91 +-
.../AreaOfParallelogramQuestion2Answer.svg | 104 ++-
.../two-dimensions/BasisVectorsSign.svg | 16 +-
.../lessons/2016/cross-products/index.mdx | 2 +-
.../lessons/2016/cross-products/notes.txt | 7 +-
.../PositiveAndNegativeOutputQuestion.svg | 124 ++-
.../NumberLineFormedByUnitVector.svg | 193 +++-
.../NumberLineFormedByUnitVectorIHatJHat.svg | 173 +++-
...umberLineFormedByUnitVectorManyVectors.svg | 211 ++++-
...FormedByUnitVectorManyVectorsProjected.svg | 220 ++++-
...NumberLineFormedByUnitVectorVisualTest.svg | 225 ++++-
.../UnitVectorProjectArbitraryVector.svg | 188 +++-
.../UnitVectorScaleScaleByThree.svg | 170 +++-
.../lessons/2016/dot-products/notes.txt | 1 +
.../lessons/2016/eigenvalues/notes.txt | 1 +
.../examples/LinearlyDependentColumns.svg | 185 +++-
.../figures/examples/Rotation.svg | 169 +++-
.../figures/examples/RotationMatrix.svg | 66 +-
.../figures/examples/RotationMatrixTex.svg | 98 ++-
.../figures/examples/RotationQuestion1.svg | 287 +++---
.../figures/examples/Shear.svg | 134 ++-
.../figures/examples/ShearMatrix.svg | 45 +-
.../figures/examples/ShearMatrixTex.svg | 94 +-
.../examples/TransformationFromMatrixAlt.svg | 562 ++++++------
.../formal-properties/AlgebraicProperties.svg | 103 ++-
.../ApplyingTheTransformation.svg | 82 +-
.../LinearCombinationOfBasisVectors.svg | 145 +++
.../LinearCombinationOfBasisVectorsAfter.svg | 158 +++-
.../MatrixFromTwoVectors.svg | 230 ++++-
.../matrices/HowToDescribeTransformation.svg | 77 +-
.../LinearTransformationCombination.svg | 180 +++-
.../matrices/LinearTransformationFormula.svg | 197 ++++-
.../LinearTransformationManyVectors.svg | 381 ++++++++
.../matrices/LinearTransformationSetup.svg | 74 +-
.../LinearTransformationTechnique.svg | 169 ++--
.../matrices/MatrixIntuitionVisual.svg | 369 +++++++-
.../MatrixIntuitionVisualQuestion1.svg | 637 +++++++-------
.../matrices/MatrixIntutionTexQuestion.svg | 100 ++-
.../figures/matrices/MatrixNotation2x2.svg | 85 +-
.../matrices/MatrixNotation2x2InputOutput.svg | 192 ++--
.../MatrixNotation2x2InputOutputGeneral.svg | 198 ++---
.../matrices/MatrixNotationIntuition.svg | 97 ++-
.../figures/matrices/Question1Answer.svg | 100 ++-
.../Question1LinearTransformation.svg | 246 ++++++
.../matrices/RecordWhereBasisVectorsLand.svg | 258 +++---
.../InputOutput.svg | 91 +-
.../TransformGrid.svg | 262 ++++++
.../VectorTransformation.svg | 85 +-
.../2016/linear-transformations/index.mdx | 8 +-
.../2016/linear-transformations/notes.txt | 1 +
.../2d-to-1d/TransformationFunction2dTo1d.svg | 66 +-
.../figures/2d-to-3d/Input3dOutput2d.svg | 2 +-
.../2d-to-3d/InputSpaceOutputSpace.svg | 26 +-
.../InputSpaceOutputSpaceBasisVectors.svg | 12 +-
.../figures/2d-to-3d/MatrixNotation2x3.svg | 48 +-
.../figures/2d-to-3d/MatrixNotation3x2.svg | 103 ++-
.../2d-to-3d/MatrixNotation3x2RowsColumns.svg | 90 +-
.../2d-to-3d/TransformationFunction2dTo3d.svg | 80 +-
.../lessons/2016/nonsquare-matrices/notes.txt | 1 +
.../DifferentBasisSpanExample1.svg | 99 ++-
.../DifferentBasisSpanExample2.svg | 94 +-
.../DifferentBasisSpanExample3.svg | 94 +-
.../DifferentBasisVectors.svg | 99 ++-
.../figures/introduction/BasisVectors.svg | 1 -
.../CoordinatesAsScalarsOfBasisVectors.svg | 119 ++-
.../span/figures/introduction/UnitVectors.svg | 96 +-
.../VectorCoordinatesAsScalars.svg | 106 ++-
...ectorCoordinatesAsScalarsOfUnitVectors.svg | 121 ++-
.../span/figures/introduction/VectorRecap.svg | 101 ++-
.../LinearCombinationLinearlyDependent.svg | 107 ++-
.../LinearCombinationScalarsRangeFree.svg | 100 ++-
.../LinearCombinationVectorsAndLines.svg | 111 ++-
.../LinearCombinationWithDescription.svg | 167 +++-
.../span/figures/questions/AnyOldBasis.svg | 127 ++-
.../questions/IndependentOrDependent.svg | 87 +-
.../questions/IndepentOrDependent3d.svg | 177 ++++
.../questions/LinearCombinationQuestion.svg | 89 +-
.../figures/questions/OrthogonalBasis.svg | 91 +-
.../questions/OrthogonalBasisAnswer.svg | 1 -
.../span-in-3d/IndepentOrDependent.svg | 1 -
.../span-in-3d/LinearCombination3d.svg | 136 ++-
.../LinearCombinationOfThreeVectors.svg | 156 ++++
...nearCombinationOfThreeVectorsWithLines.svg | 160 +++-
.../figures/span-in-3d/LinearlyDependent.svg | 105 ++-
.../span-in-3d/LinearlyDependent3d.svg | 188 +++-
.../span-in-3d/LinearlyIndependent3d.svg | 184 +++-
.../figures/span-in-3d/SpanOfThreeVectors.svg | 199 +++++
.../span-in-3d/SpanOfTwoVectorsIn3d.svg | 137 ++-
.../SpanOfTwoVectorsIn3dNoPlane.svg | 127 ++-
.../span-in-3d/ThirdVectorIsInSpan.mp4 | 3 +
.../span-in-3d/ThirdVectorIsInSpan.svg | 129 ++-
.../span-in-3d/ThirdVectorIsNotInSpan.svg | 210 ++++-
.../2016/span/figures/span/Question1.svg | 107 ++-
public/content/lessons/2016/span/index.mdx | 5 +-
public/content/lessons/2016/span/notes.txt | 7 +-
.../CoordinateSystemGrid.svg | 76 +-
.../CoordinateSystemTickMarks.svg | 54 +-
.../coordinate-systems/VectorAsArrow.svg | 78 +-
.../coordinate-systems/VectorCoordinates.svg | 106 ++-
.../VectorCoordinates3d.svg | 147 +++-
.../figures/introduction/VectorExample.svg | 208 ++++-
.../figures/introduction/perspectives.svg | 476 ++--------
.../figures/vector-operations/NumberLine.svg | 168 +++-
.../vector-operations/VectorAddition.svg | 119 ++-
.../vector-operations/VectorAdditionPrep.svg | 96 +-
.../vector-operations/VectorScaling.svg | 5 +
.../vector-operations/VectorScalingBy2.svg | 1 -
.../VectorScalingByNegativeOnePointFive.svg | 97 ++-
.../VectorScalingByOneOverThree.svg | 101 ++-
.../vector-operations/VectorScalingByTwo.svg | 98 +++
public/content/lessons/2016/vectors/index.mdx | 7 +-
public/content/lessons/2016/vectors/notes.txt | 6 +-
.../lessons/2019/cramers-rule/notes.txt | 1 +
.../lessons/2021/quick-eigen/notes.txt | 4 +
155 files changed, 16931 insertions(+), 2923 deletions(-)
create mode 100644 public/content/lessons/2016/3d-transformations/figures/three-dimensions/Rotate90DegreesAroundYAxis.svg
create mode 100644 public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantBasisVectorsTransformedOrientation.svg
create mode 100644 public/content/lessons/2016/linear-transformations/figures/formal-properties/LinearCombinationOfBasisVectors.svg
create mode 100644 public/content/lessons/2016/linear-transformations/figures/matrices/LinearTransformationManyVectors.svg
create mode 100644 public/content/lessons/2016/linear-transformations/figures/matrices/Question1LinearTransformation.svg
create mode 100644 public/content/lessons/2016/linear-transformations/figures/transformations-are-functions/TransformGrid.svg
delete mode 100644 public/content/lessons/2016/span/figures/introduction/BasisVectors.svg
create mode 100644 public/content/lessons/2016/span/figures/questions/IndepentOrDependent3d.svg
delete mode 100644 public/content/lessons/2016/span/figures/questions/OrthogonalBasisAnswer.svg
delete mode 100644 public/content/lessons/2016/span/figures/span-in-3d/IndepentOrDependent.svg
create mode 100644 public/content/lessons/2016/span/figures/span-in-3d/LinearCombinationOfThreeVectors.svg
create mode 100644 public/content/lessons/2016/span/figures/span-in-3d/SpanOfThreeVectors.svg
create mode 100644 public/content/lessons/2016/span/figures/span-in-3d/ThirdVectorIsInSpan.mp4
create mode 100644 public/content/lessons/2016/vectors/figures/vector-operations/VectorScaling.svg
delete mode 100644 public/content/lessons/2016/vectors/figures/vector-operations/VectorScalingBy2.svg
create mode 100644 public/content/lessons/2016/vectors/figures/vector-operations/VectorScalingByTwo.svg
diff --git a/public/content/lessons/2016/3d-transformations/figures/combining-transformations/ComposingTransformations.svg b/public/content/lessons/2016/3d-transformations/figures/combining-transformations/ComposingTransformations.svg
index f377eb88..47a5b01f 100644
--- a/public/content/lessons/2016/3d-transformations/figures/combining-transformations/ComposingTransformations.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/combining-transformations/ComposingTransformations.svg
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diff --git a/public/content/lessons/2016/3d-transformations/figures/combining-transformations/MatrixMultiplication.svg b/public/content/lessons/2016/3d-transformations/figures/combining-transformations/MatrixMultiplication.svg
index dc3ac461..0d8abc10 100644
--- a/public/content/lessons/2016/3d-transformations/figures/combining-transformations/MatrixMultiplication.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/combining-transformations/MatrixMultiplication.svg
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\ No newline at end of file
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diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/BasisVectors.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/BasisVectors.svg
index 2d27f5c5..9e7cbe2f 100644
--- a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/BasisVectors.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/BasisVectors.svg
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diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/FollowBasisVectors.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/FollowBasisVectors.svg
index 6a597dd8..d1589d25 100644
--- a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/FollowBasisVectors.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/FollowBasisVectors.svg
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diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Question1Transformation3d.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Question1Transformation3d.svg
index 33eca147..286f752d 100644
--- a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Question1Transformation3d.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Question1Transformation3d.svg
@@ -1,11 +1,168 @@
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\ No newline at end of file
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diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Rotate90DegreesAroundYAxis.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Rotate90DegreesAroundYAxis.svg
new file mode 100644
index 00000000..4e32b745
--- /dev/null
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Rotate90DegreesAroundYAxis.svg
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diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Transform3dVector.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Transform3dVector.svg
index 16b7e6ee..462aa255 100644
--- a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Transform3dVector.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/Transform3dVector.svg
@@ -1,169 +1,174 @@
diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformGrid.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformGrid.svg
index facb1d6c..c63d4af6 100644
--- a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformGrid.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformGrid.svg
@@ -56,15 +56,15 @@
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diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformManyVectors.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformManyVectors.svg
index c149060c..1c188a90 100644
--- a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformManyVectors.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/TransformManyVectors.svg
@@ -1,23 +1,23 @@
diff --git a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/VectorAsTransformationBefore.svg b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/VectorAsTransformationBefore.svg
index 7c58fddf..b3b1ed53 100644
--- a/public/content/lessons/2016/3d-transformations/figures/three-dimensions/VectorAsTransformationBefore.svg
+++ b/public/content/lessons/2016/3d-transformations/figures/three-dimensions/VectorAsTransformationBefore.svg
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diff --git a/public/content/lessons/2016/3d-transformations/index.mdx b/public/content/lessons/2016/3d-transformations/index.mdx
index 8c3d29c5..340f43ab 100644
--- a/public/content/lessons/2016/3d-transformations/index.mdx
+++ b/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
@@ -150,10 +151,6 @@ $$
\end{aligned}
$$
-
-
## Examples
diff --git a/public/content/lessons/2016/3d-transformations/notes.txt b/public/content/lessons/2016/3d-transformations/notes.txt
index a8579031..5a64ce88 100644
--- a/public/content/lessons/2016/3d-transformations/notes.txt
+++ b/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."
diff --git a/public/content/lessons/2016/abstract-vector-spaces/notes.txt b/public/content/lessons/2016/abstract-vector-spaces/notes.txt
index caad8e9e..40ff7684 100644
--- a/public/content/lessons/2016/abstract-vector-spaces/notes.txt
+++ b/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:
diff --git a/public/content/lessons/2016/change-of-basis/notes.txt b/public/content/lessons/2016/change-of-basis/notes.txt
index d41e9c61..d414cc5e 100644
--- a/public/content/lessons/2016/change-of-basis/notes.txt
+++ b/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
diff --git a/public/content/lessons/2016/cross-products-extended/figures/conclusion/CrossProductFormula.svg b/public/content/lessons/2016/cross-products-extended/figures/conclusion/CrossProductFormula.svg
index 15051e9f..a47d99c1 100644
--- a/public/content/lessons/2016/cross-products-extended/figures/conclusion/CrossProductFormula.svg
+++ b/public/content/lessons/2016/cross-products-extended/figures/conclusion/CrossProductFormula.svg
@@ -1 +1,117 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products-extended/figures/the-idea/CrossProductGeometryVolume.svg b/public/content/lessons/2016/cross-products-extended/figures/the-idea/CrossProductGeometryVolume.svg
index 1318def9..31cb4e5e 100644
--- a/public/content/lessons/2016/cross-products-extended/figures/the-idea/CrossProductGeometryVolume.svg
+++ b/public/content/lessons/2016/cross-products-extended/figures/the-idea/CrossProductGeometryVolume.svg
@@ -1 +1,162 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products-extended/notes.txt b/public/content/lessons/2016/cross-products-extended/notes.txt
index 19f4ba99..8981d0f3 100644
--- a/public/content/lessons/2016/cross-products-extended/notes.txt
+++ b/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?
diff --git a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ChangeOfArea.svg b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ChangeOfArea.svg
index 0d627feb..07346f57 100644
--- a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ChangeOfArea.svg
+++ b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ChangeOfArea.svg
@@ -1 +1,136 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ComputeCrossProduct.svg b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ComputeCrossProduct.svg
index 1066da39..c1660e8d 100644
--- a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ComputeCrossProduct.svg
+++ b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/ComputeCrossProduct.svg
@@ -1,3 +1,127 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantBasisVectorsTransformedOrientation.svg b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantBasisVectorsTransformedOrientation.svg
new file mode 100644
index 00000000..146f8fe6
--- /dev/null
+++ b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantBasisVectorsTransformedOrientation.svg
@@ -0,0 +1,153 @@
+
diff --git a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantNegative.svg b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantNegative.svg
index 581fa0d5..7b546d47 100644
--- a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantNegative.svg
+++ b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantNegative.svg
@@ -1 +1,144 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantPositive.svg b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantPositive.svg
index 0f805f78..3357ef9b 100644
--- a/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantPositive.svg
+++ b/public/content/lessons/2016/cross-products/figures/compute-with-determinant/DeterminantPositive.svg
@@ -1 +1,143 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExample.svg b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExample.svg
index 70d9d9f6..8dc1c7d9 100644
--- a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExample.svg
+++ b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExample.svg
@@ -1 +1,63 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1.svg b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1.svg
index 700d651c..701c586f 100644
--- a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1.svg
+++ b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1.svg
@@ -1 +1,89 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Calculation.svg b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Calculation.svg
index ab9553e0..7b5d5070 100644
--- a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Calculation.svg
+++ b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Calculation.svg
@@ -1 +1,148 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Parallelogram.svg b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Parallelogram.svg
index 7fad2633..ec1a5d26 100644
--- a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Parallelogram.svg
+++ b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantExampleQuestion1Parallelogram.svg
@@ -1 +1,156 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantTransformation.svg b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantTransformation.svg
index 7483da4a..cd3ae9cd 100644
--- a/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantTransformation.svg
+++ b/public/content/lessons/2016/cross-products/figures/determinant-example/DeterminantTransformation.svg
@@ -1 +1,172 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample1.svg b/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample1.svg
index c5a6b00f..cf2e0a91 100644
--- a/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample1.svg
+++ b/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample1.svg
@@ -1 +1,120 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2.svg b/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2.svg
index c5538b50..23646cee 100644
--- a/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2.svg
+++ b/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2.svg
@@ -1 +1,120 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2Parallelogram.svg b/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2Parallelogram.svg
index 7eb7aa89..afb15e09 100644
--- a/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2Parallelogram.svg
+++ b/public/content/lessons/2016/cross-products/figures/standard-view/RightHandRuleExample2Parallelogram.svg
@@ -1 +1,110 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogram.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogram.svg
index b098a986..5580ef7a 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogram.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogram.svg
@@ -1 +1,90 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramCalculation.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramCalculation.svg
index c36aeadf..94484525 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramCalculation.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramCalculation.svg
@@ -1,3 +1,106 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramFormula.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramFormula.svg
index 9b5d3d66..41cac4c9 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramFormula.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramFormula.svg
@@ -1 +1,121 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramNegative.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramNegative.svg
index 239eb6ee..91cab6a0 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramNegative.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramNegative.svg
@@ -1,3 +1,124 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramPositive.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramPositive.svg
index 47860715..09611010 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramPositive.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramPositive.svg
@@ -1,3 +1,123 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1.svg
index 02c917eb..4ddc3f48 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1.svg
@@ -1 +1,90 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1Answer.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1Answer.svg
index 2358b270..68f7bf26 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1Answer.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion1Answer.svg
@@ -1,3 +1,105 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2.svg
index 228f1258..10f30ad4 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2.svg
@@ -1 +1,90 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2Answer.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2Answer.svg
index 7d8834e7..9212f100 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2Answer.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/AreaOfParallelogramQuestion2Answer.svg
@@ -1,3 +1,101 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/cross-products/figures/two-dimensions/BasisVectorsSign.svg b/public/content/lessons/2016/cross-products/figures/two-dimensions/BasisVectorsSign.svg
index e7cf7da2..42171ab5 100644
--- a/public/content/lessons/2016/cross-products/figures/two-dimensions/BasisVectorsSign.svg
+++ b/public/content/lessons/2016/cross-products/figures/two-dimensions/BasisVectorsSign.svg
@@ -42,12 +42,12 @@
-
-
-
+
+
+
-
-
+
+
@@ -92,12 +92,12 @@
-
+
-
+
-
+
diff --git a/public/content/lessons/2016/cross-products/index.mdx b/public/content/lessons/2016/cross-products/index.mdx
index c0c26c0b..1b1b06a7 100644
--- a/public/content/lessons/2016/cross-products/index.mdx
+++ b/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.
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.
diff --git a/public/content/lessons/2016/cross-products/notes.txt b/public/content/lessons/2016/cross-products/notes.txt
index 6cda1ae6..b2027941 100644
--- a/public/content/lessons/2016/cross-products/notes.txt
+++ b/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
\ No newline at end of file
+- 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..."
\ No newline at end of file
diff --git a/public/content/lessons/2016/dot-products/figures/geometric-interpretation/PositiveAndNegativeOutputQuestion.svg b/public/content/lessons/2016/dot-products/figures/geometric-interpretation/PositiveAndNegativeOutputQuestion.svg
index 76372967..03dabeca 100644
--- a/public/content/lessons/2016/dot-products/figures/geometric-interpretation/PositiveAndNegativeOutputQuestion.svg
+++ b/public/content/lessons/2016/dot-products/figures/geometric-interpretation/PositiveAndNegativeOutputQuestion.svg
@@ -1 +1,123 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVector.svg b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVector.svg
index f2b95731..2caf3f75 100644
--- a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVector.svg
+++ b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVector.svg
@@ -1 +1,192 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorIHatJHat.svg b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorIHatJHat.svg
index e68cbed3..c6d02d9b 100644
--- a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorIHatJHat.svg
+++ b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorIHatJHat.svg
@@ -1 +1,172 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectors.svg b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectors.svg
index 2444fc37..96eee83f 100644
--- a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectors.svg
+++ b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectors.svg
@@ -1 +1,210 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectorsProjected.svg b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectorsProjected.svg
index 34d801c5..e3cd5482 100644
--- a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectorsProjected.svg
+++ b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorManyVectorsProjected.svg
@@ -1 +1,219 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorVisualTest.svg b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorVisualTest.svg
index bad78c03..4a99523a 100644
--- a/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorVisualTest.svg
+++ b/public/content/lessons/2016/dot-products/figures/unit-vector/NumberLineFormedByUnitVectorVisualTest.svg
@@ -1 +1,224 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorProjectArbitraryVector.svg b/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorProjectArbitraryVector.svg
index ff66cb13..7c10b594 100644
--- a/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorProjectArbitraryVector.svg
+++ b/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorProjectArbitraryVector.svg
@@ -1 +1,187 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorScaleScaleByThree.svg b/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorScaleScaleByThree.svg
index 4acd8075..d7506f67 100644
--- a/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorScaleScaleByThree.svg
+++ b/public/content/lessons/2016/dot-products/figures/unit-vector/UnitVectorScaleScaleByThree.svg
@@ -1 +1,169 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/dot-products/notes.txt b/public/content/lessons/2016/dot-products/notes.txt
index 95169ece..4224c04b 100644
--- a/public/content/lessons/2016/dot-products/notes.txt
+++ b/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?"
diff --git a/public/content/lessons/2016/eigenvalues/notes.txt b/public/content/lessons/2016/eigenvalues/notes.txt
index e9addd16..c7632337 100644
--- a/public/content/lessons/2016/eigenvalues/notes.txt
+++ b/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.
diff --git a/public/content/lessons/2016/linear-transformations/figures/examples/LinearlyDependentColumns.svg b/public/content/lessons/2016/linear-transformations/figures/examples/LinearlyDependentColumns.svg
index e0a1b894..903dfb0f 100644
--- a/public/content/lessons/2016/linear-transformations/figures/examples/LinearlyDependentColumns.svg
+++ b/public/content/lessons/2016/linear-transformations/figures/examples/LinearlyDependentColumns.svg
@@ -1 +1,184 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/linear-transformations/figures/examples/Rotation.svg b/public/content/lessons/2016/linear-transformations/figures/examples/Rotation.svg
index 1bbb60e5..2ccb78de 100644
--- a/public/content/lessons/2016/linear-transformations/figures/examples/Rotation.svg
+++ b/public/content/lessons/2016/linear-transformations/figures/examples/Rotation.svg
@@ -1,5 +1,164 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrix.svg b/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrix.svg
index b5b3b74c..16687c8f 100644
--- a/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrix.svg
+++ b/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrix.svg
@@ -1,6 +1,60 @@
-
\ No newline at end of file
+
diff --git a/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrixTex.svg b/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrixTex.svg
index a9fef409..a20efc07 100644
--- a/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrixTex.svg
+++ b/public/content/lessons/2016/linear-transformations/figures/examples/RotationMatrixTex.svg
@@ -1,14 +1,84 @@
-
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+
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