Algebra Commons^™

Linear Algebra, Daniel Scully

Math Faculty Publications

Table of Contents:

1. Systems of Linear Equations and Matrices

• Systems of Linear Equations
• Elementary Row Operations
• Row Reduction and Reduced Row-Echelon Form
• Solutions of Systems of Linear Equations
• Matrix Operations
• Matrix Inverses

2. Euclidean 2-Space and 3-Space

• Vectors in the Plane and in Space
• The Dot Product
• Cross Product
• Lines in Space
• Planes in Space

3. Determinants

• The Definition of Determinant
• Elementary Row Operations and the Determinant
• Elementary Matrices and the Determinant
• Applications of the Determinant

4. Vector Spaces and Subspaces

• Vector Spaces
• Subspaces
• Linear Dependence and Independence
• Basis and Dimension

5. Linear Transformations

• Definition of Linear Transformation
• The …