Skip to content

ThemeSystemLightDark

Text sizeSmallNormalLarge

WidthNormalWideFull

[ and ] go to the previous and next page.

1Vector spaces
2Linear maps and matrices
3Linear systems and row reduction
4Dimension
5Determinants
6Inner product spaces
7Eigenvalues and diagonalization
8The spectral theorems
9The singular value decomposition
10Generalized eigenspaces and Jordan form
11Markov chains and positive matrices
12Bilinear and quadratic forms
13Duality and multilinear algebra*
14Linear algebra and abstract algebra*
15Infinite-dimensional vector spaces*
16Applications to data and machine learning*
ASets, functions, and proofs
BComplex numbers
1. Overview
2. B.1Complex numbers
CThe Fundamental Theorem of Algebra*
1. Overview
2. C.1Proofs of the Fundamental Theorem of Algebra

Index of techniques
Practice
PDF

Chapter 3

3Linear systems and row reduction

Gauss–Jordan elimination as the engine of the theory, rank, and the Fundamental Theorems completed.

In this chapter

3.1Linear systems
3.2Elementary matrices
3.3Gauss–Jordan elimination
3.4Solving linear systems
3.5Rank and the Fundamental Theorems
3.6Proof patterns

PreviousProblems for Chapter 2 Next3.1Linear systems