# Linear Algebra

Prerequisites: Qualifying math score and successful completion of AP Calculus BC or equivalent; completion of Multivariable Calculus preferred

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: One full year of high school credit equal to or greater than an AP class or one semester of college credit

Course Code: LIN

## Course Description

Description

Linear Algebra is an online and individually-paced course equivalent to a first-year college linear algebra course. This course covers the entire syllabus from the Johns Hopkins semester-based, in-person Linear Algebra course, plus several additional topics. Computer based interactives, homework and quizzes help to reinforce concepts taught in the class. Projects covering advanced applications will introduce students to mathematical typesetting with LaTeX. Online course materials supplement the required textbook.

Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructor via email with any questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include quizzes, homework, midterm exams, and a cumulative final. Instructors use virtual classroom software allowing video, voice, text, screen sharing and whiteboard interaction.

### Topics include:

• Linear Equations
• Matrix Algebra
• Determinants
• Vector Spaces
• Eigenvalues
• Orthogonality
• Least Squares
• Symmetric Matrices

For a detailed list of topics, click the "List of Topics" tab.

## Materials Needed

A textbook purchase is required for this course:

Linear Algebra and its Applications, 5th edition, by David C. Lay, Steven R. Lay, and Judi J. McDonald

## List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

### Linear Equations in Linear Algebra

• Systems of Linear Equations
• Row Reduction and Echelon Form
• Vector Equations
• The Matrix Equation Ax->=b->
• Solution Sets of Linear Systems
• Applications of Linear Systems
• Linear Independence
• Introduction to Linear Transformations
• The Matrix of a Linear Transformation

### Matrix Algebra

• Matrix Operations
• The Inverse of a Matrix
• Characterizations of Invertible Matrices
• Subspaces of Rn
• Dimension and Rank

### Determinants

• Introduction to Determinants
• Properties of Determinants
• Cramer's Rule, Volume, and Linear Transformations

### Eigenvalues and Eigenvectors

• Eigenvalues and Eigenvectors
• The Characteristic Equation
• Diagonalization
• Eigenvalues and Linear Transformations
• Complex Eigenvalues
• Discrete Dynamical Systems

### Vector Spaces

• Vector Spaces and Subspaces
• Null Spaces, Column Spaces, and Linear Transformations
• Linearly Independent Sets; Bases
• Coordinate Systems
• The Dimension of a Vector Space
• Rank
• Change of Basis
• Applications to Difference Equations
• Applications to Markov Chains

### Orthogonality and Least Squares

• Inner Products Length, and Orthogonality
• Orthogonal Sets
• Orthogonal Projections
• The Gram-Schmidt Process
• Least-Squares Problem
• Inner Product Spaces

### Symmetric Matrices and Quadratic Forms

• Diagonalization of Symmetric Matrices
• The Singular Value Decomposition

Sample Video

## Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.