Lesson 1.5 · 5 of 25 lessons
Inverse matrices
Connect row and column pictures of a system to elimination, LU, and inverse matrices.
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
When A moves space, x moves from (1, 1) to (3, 2)
- 02
First apply A to see the forward transformation
- 03
Now apply inverse matrix B to undo A
- 04
x returned to (1, 1)
An inverse matrix cancels the original transformation
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 9/10
grid off
relative-grid on
coordinates on
2 1 #A
1 1
1 -1 #B
-1 2
1, 1 #x@
// When {{A}} moves space, {{x}} moves from `(1, 1)` to `(3, 2)`
checkpoint Inverse matrices · 1
// First apply {{A}} to see the forward transformation
A
checkpoint Inverse matrices · 2
// Now apply inverse matrix {{B}} to undo {{A}}
B
// {{x}} returned to `(1, 1)`\nAn inverse matrix **cancels the original transformation**
focus x03 · Unit 1
Lessons in this unit
Matrices & Gaussian elimination — Connect row and column pictures of a system to elimination, LU, and inverse matrices.