Chapter 5
Transpose and Row Rank
Rows, Columns, and a Surprising Equality
Discover the transpose operation and explore the deep symmetry between row space and column space through the Row Rank Theorem — one of the most elegant results in linear algebra.
7 sections~66 minutes
Sections
1
5.1
The Transpose
10 min · 3 quiz questions · Interactive diagram
2
5.2
Properties of the Transpose
8 min · 2 quiz questions
3
5.3
Row Rank
10 min · 2 quiz questions · Interactive diagram
4
5.4
The Row Rank Theorem: Proof via Factoring
12 min · 2 quiz questions
5
5.5
Triple Products and the Row Perspective
8 min · 2 quiz questions
6
5.6
Linear Systems Revisited via Row Rank
10 min · 2 quiz questions
7
5.7
Hyperplane Intersections
8 min · 2 quiz questions