Lesson 1.2 · 2 of 25 lessons
Gaussian elimination
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
Subtract twice the first row of A from the second to create a zero below the first pivot
- 02
This row operation is the same as multiplying A on the left by elementary matrix E
- 03
U now has a zero below its first pivot, creating an upper-triangular structure for back substitution
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
1 1 #A
2 -1
1 0 #E
-2 1
// Subtract twice the first row of {{A}} from the second to create a zero below the first pivot
mark row(A, 2)
checkpoint Gaussian elimination
mark -
// This row operation is the same as multiplying {{A}} on the left by elementary matrix {{E}}
E * A #U@
// {{U}} now has a zero below its first pivot, creating an **upper-triangular structure** for back substitution
mark staircase(U)03 · Unit 1
Lessons in this unit
Matrices & Gaussian elimination — Connect row and column pictures of a system to elimination, LU, and inverse matrices.