### The essential Topics

What else we cover from the book will be in part
determined by student interests.

- § 1.1 Solving Linear Systems.
- § 1.2 Row Echelon Form.
- § 1.3 Matrix Algebra.
- § 1.4 Elementary Matrices.
- § 1.5 Partitioned Matrices.
- § 2.1, § 2.2 Determinants.
- § 2.3 Determinants and some of Cramer's rule.
- § 3.1 Euclidean Space, Vector Space, Function Spaces.
- § 3.2 Subspaces.
- § 3.3 Linear Independence.
- § 3.4 Basis and Dimension.
- § 3.5 Change of Basis.
- § 3.6 Row space, Column space.
- § 4.1 Linear Transformations.
- § 4.2 Matrix Representation of linear transformations.
- § 4.3 Similarity.
- § 5.1 Scalar product.
- § 5.2 Orthogonality.
- § 5.3 Least Squares.
- § 5.5 Orthonormal sets.
- § 6.1 Eigenvalues and Eigenvectors.
- § 6.2 Systems of Linear Differential Equations.
- § 6.3 Diagonalization.