Lesson 1.1 · 1 of 25 lessons

Two views of a system

Connect row and column pictures of a system to elimination, LU, and inverse matrices.

Open the interactive animation

01 · Story

What to verify in this scene

Follow the explanations and operations, then identify the mathematical evidence that remains in the final scene.

01
The column view mixes columns c1 and c2 of A to make target b
02
Match the solution (2, 1) by changing the coefficient of c1 to 2
03
The sum out reached target b
The column-view solution gives how many of each column to use
04
The row view treats the same problem as the shared conditions of lines R1 and R2
05
Their intersection sol is also (2, 1)
Both views describe the same solution

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
coordinates on

1 1  #A
2 -1

col(A, 1)  #c1@
col(A, 2)  #c2@
point(3, 3)  #b@
// The column view mixes columns {{c1}} and {{c2}} of {{A}} to make target {{b}}
focus c1 c2
checkpoint Two views of a system · 1

focus -
sum(c1, c2)  #out@
// Match the solution `(2, 1)` by changing the coefficient of {{c1}} to 2
c1 * 2
// The sum {{out}} reached target {{b}}\nThe column-view solution gives **how many of each column** to use
focus out b
checkpoint Two views of a system · 2

focus -
clear
A +
x + y = 3  #R1
2x - y = 3  #R2
// The row view treats the same problem as the shared conditions of lines {{R1}} and {{R2}}
checkpoint Two views of a system · 3

solution(R1, R2)  #sol@
// Their intersection {{sol}} is also `(2, 1)`\nBoth views describe the **same solution**
focus sol

Open the interactive animation

03 · Unit 1

Lessons in this unit

Matrices & Gaussian elimination — Connect row and column pictures of a system to elimination, LU, and inverse matrices.