Lesson 1.3 · 3 of 25 lessons
Matrix columns
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
Columns c1 and c2 of A are the destinations of basis vectors i and j
- 02
Hide the column arrows, then apply A to send the basis and grid to those destinations
- 03
i reached the first column and j reached the second
A matrix lists the new destinations of the basis
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 on
relative-grid off
basis off
coordinates on
1 1 #A
0 1
col(A, 1) #c1@
col(A, 2) #c2@
// Columns {{c1}} and {{c2}} of {{A}} are the destinations of basis vectors {{i}} and {{j}}
focus c1 c2
checkpoint Matrix columns
clear
basis on
relative-grid on
// Hide the column arrows, then apply {{A}} to send the basis and grid to those destinations
A
// {{i}} reached the first column and {{j}} reached the second\nA matrix **lists the new destinations of the basis**03 · Unit 1
Lessons in this unit
Matrices & Gaussian elimination — Connect row and column pictures of a system to elimination, LU, and inverse matrices.