Lesson 4.1 · 16 of 25 lessons
Determinants
Read a determinant as an area or volume scale and watch a dimension disappear when it is zero.
Open the interactive animation01 · Story
What to verify in this scene
Follow the explanations and operations, then identify the mathematical evidence that remains in the final scene.
- 01
The determinant is the signed area made by two vectors
- 02
det(a, b) = 3, so the parallelogram has area 3
- 03
Now compare two vectors pointing in the same direction
- 04
When det(p, q) = 0, the area disappears
The vectors are linearly dependent
02 · Notebook
The runnable notebook
This source creates the mathematical objects and controls the order of operations and animation. Read it here, then play the same scene yourself.
2d
zoom 1
coordinates on
2, 1 #a@
1, 2 #b@
// The **determinant** is the signed area made by two vectors
det(a, b) #area@
focus a b
checkpoint Determinants · 1
// `det({{a}}, {{b}}) = 3`, so the parallelogram has area **3**
checkpoint Determinants · 2
focus -
clear
// Now compare two vectors pointing in the same direction
1, 1 #p@
2, 2 #q@
det(p, q) #zero@
// When `det({{p}}, {{q}}) = 0`, the area disappears\nThe vectors are **linearly dependent**
focus p q03 · Unit 4
Lessons in this unit
Determinants — Read a determinant as an area or volume scale and watch a dimension disappear when it is zero.