Topic: Fundamental Subspaces and Rank

Full Rank for Rectangular Matrices

Four Fundamental Subspaces of a Matrix

Finding Column-Space and Row-Space Bases

Dimensions of the Four Fundamental Subspaces

Diagnostic Problems on Fundamental Subspaces

Constructing a Rank Factorization

Consistency Through the Column Space

Computing a Basis for the Left Null Space

Common Misreadings of Pivot, Rank, and Nullity

Column Space and Reachable Right-Hand Sides