Chapter 2

Vectors

Span, Independence, and the Language of Linear Algebra

Master the language of vectors: how to add, scale, combine, and span with them — and discover the deep notions of linear independence, subspace, and basis.

17 sections~149 minutes

Sections

2.1

Vectors as Data Packages

8 min · 2 quiz questions

2.2

Visualizing Vectors in Space

8 min · 1 quiz question · Interactive diagram

2.3

Vector Addition

7 min · 1 quiz question

2.4

Scalar Multiplication

7 min · 1 quiz question

2.5

Algebraic Properties of Vectors

8 min · 1 quiz question

2.6

Applications: Physics, Graphics, Audio, Images

8 min · 1 quiz question

2.7

Linear Combinations

10 min · 1 quiz question

2.8

Span: The Reach of a Set of Vectors

10 min · 1 quiz question · Interactive diagram

2.9

Linear Dependence

12 min · 2 quiz questions · Interactive diagram

2.10

Logic and Proof Techniques

8 min · 1 quiz question

2.11

The Hammer Lemma and Span Structure

10 min · 1 quiz question

2.12

Subspaces

10 min · 1 quiz question

2.13

Basis: Minimal Spanning Sets

11 min · 1 quiz question

2.14

Dimension

9 min · 1 quiz question

2.15

The Basis Theorem

9 min · 1 quiz question

2.16

Affine Sets Revisited

8 min · 1 quiz question

2.17

Chapter Summary

6 min · 1 quiz question

Start Chapter 2