Lesson 2.1 · 6 of 25 lessons

Vectors & scalars

Grow from linear combinations to independence, bases, the fundamental subspaces, and transformations.

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
A vector is an arrow with both magnitude and direction
02
Now multiply v by 2 to double its length
03
The direction stays fixed while only the length doubles
04
Now multiply the current v by -1/2
05
A negative scalar changes the size and reverses the direction

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 1
coordinates on

// A **vector** is an arrow with both magnitude and direction
2, 1  #v@
focus v
checkpoint Vectors & scalars · 1

focus -
// Now multiply {{v}} by 2 to double its length
v * 2
// The direction stays fixed while **only the length doubles**
checkpoint Vectors & scalars · 2

// Now multiply the current {{v}} by `-1/2`
v * -1/2
// A negative scalar changes the size and **reverses the direction**
focus v

Open the interactive animation

03 · Unit 2

Lessons in this unit

Vector spaces & transformations — Grow from linear combinations to independence, bases, the fundamental subspaces, and transformations.