Lesson 4.2 · 17 of 25 lessons
Area scale
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
Before the transform, basis vectors i and j form a unit square of area 1
- 02
Apply A to the basis and grid, sending the unit square to a parallelogram
- 03
The same measurement is now area 3
det(A)=3 means every area is scaled by 3
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 4/5
grid off
relative-grid on
basis on
coordinates off
2 1 #A
1 2
det(i, j) #area@
// Before the transform, basis vectors {{i}} and {{j}} form a unit square of area 1
checkpoint Area scale
// Apply {{A}} to the basis and grid, sending the unit square to a parallelogram
A
// The same measurement is now area 3\n`det({{A}})=3` means every area is scaled by **3**03 · 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.