Syllabus

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 equations
1.6 Applications of linear systems (skip balancing chemical equations)
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 (skip elementary matrices)
2.3 Characterizations of invertible matrices
2.5 Subspaces of Rn
2.6 Dimension and rank
3.1 Introduction to determinants
3.2 Properties of determinants
4.1 Eigenvalues and eigenvectors
4.2 The characteristic equation
4.3 Diagonalization
4.4 Eigenvectors and linear transformations (skip pages 168, 169, 170, 171 upper half)
4.6 Discrete dynamical systems (skip pages 187, 188, 189)
5.1 Inner product, length, and orthogonality
5.2 Orthogonal sets
5.3 Orthogonal projections
5.5 Least-square problems