Lesson 1.4 · 4 of 25 lessons
LU factorization
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
L remembers elimination multipliers while U is the upper-triangular result
- 02
Multiply L and U to check that they reconstruct the original A
- 03
LU equals A
A = LU stores elimination in two matrices
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.
field board
2 1 #A
4 3
1 0 #L
2 1
2 1 #U
0 1
// {{L}} remembers elimination multipliers while {{U}} is the upper-triangular result
checkpoint LU factorization
// Multiply {{L}} and {{U}} to check that they reconstruct the original {{A}}
L * U #LU@
// {{LU}} equals {{A}}\n`A = LU` **stores elimination in two matrices**03 · Unit 1
Lessons in this unit
Matrices & Gaussian elimination — Connect row and column pictures of a system to elimination, LU, and inverse matrices.