Science:Math Exam Resources/Courses/MATH221/Syllabus

Official Course Syllabus here.

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

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

2.5 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

4.6 Discrete dynamical systems

5.1 Inner product, length, and orthogonality

5.2 Orthogonal sets

5.3 Orthogonal projections

5.5 Least-squares problem

5.6 Applications to linear models