# Linear Algebra

## Section 1

Introduction to VectorsSubspaces

Spanning Sets and Linear Independence

Dot Product and Length

Projections

Cross Products

## Section 2

Matrix Representations of SystemsReduced Row Echelon Form and Rank

## Section 3

Matrix OperationsMatrix Transposes

Matrix Multiplication

Matrix and Linear Mappings

Geometric Transformations

Identity and Inverse Matrices

## Section 4

Determinates in Terms of CofactorsElementary Row Operators and Determinates

Matrix Inverses and Cramer's Rule

Eigenvalues and Eigenvectors