Review of Concepts and Formulas for Linear Algebra

1.1 Systems of Linear Equations

1.2 Row Reduction and Echelon Forms

1.3 Vector Equations

1.4 The Matrix Equation Ax=b

1.5 Solution Sets of Linear Systems

1.7 Linear Independence

1.8 Introduction to Linear Transformations

1.9 The matrix of a linear transformation

2.1 Matrix Operations

2.2 The Inverse of a Matrix

2.3 Characterizations of Invertible Matrices

2.8 Subspaces of R^n

2.9 Dimension and Rank

3.1 Introduction to Determinants

3.2 Properties of Determinants

3.3 Cramer's Rule, Volume, and Linear Transformations

4.1 Vector Spaces and Subspaces

4.2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations

4.3 Linearly Independent Sets; Bases

4.5 The Dimension of a Vector Space

5.1 Eigenvectors and Eigenvalues

5.2 The Characteristic Equation

5.3 Diagonalization

5.4 Eigenvectors and Linear Transformations

5.5 Complex Eigenvalues

5.7 Applications to Differential Equations

6.1 Inner Product, Length, and Orthogonality

6.2 Orthogonal Sets

6.3 Orthogonal Projections

6.4 The Gram-Schmidt Process

6.5 Least-Squares Problems

6.7 Inner Product Spaces

7.1 Diagonalization of Symmetric Matrices

Midterm 1 Review

Midterm 2 Review