Linear Systems
Geometry, Structure, and Solution Methods
Discover how systems of equations encode geometry, develop powerful elimination algorithms, and reveal the deep structure of solution sets.
Sections
Linear Equations in Two Variables
8 min · 2 quiz questions
Solutions as Geometric Objects
10 min · 2 quiz questions · Interactive diagram
Scalar Multiples and Equation Equivalence
7 min · 2 quiz questions
Exceptional Behavior: When Coefficients Vanish
8 min · 2 quiz questions
Linear Systems and Line Intersections
12 min · 2 quiz questions · Interactive diagram
Geometry of Intersecting Lines
10 min · 1 quiz question
Three Types of Exceptional Cases
8 min · 1 quiz question
Solution Space Shape, Affine Sets, and Dimension
12 min · 2 quiz questions
Three Variables and Plane Geometry
12 min · 1 quiz question · Interactive diagram
Normals and Geometric Insight in 3D
10 min · 2 quiz questions
Applications: Measurement, Laws, and Models
10 min · 1 quiz question
Echelon Form and Basic/Free Variables
14 min · 2 quiz questions · Interactive diagram
Gaussian Elimination
16 min · 2 quiz questions · Interactive diagram
Matrix Formulation and Forward Look
10 min · 2 quiz questions