Introduction to Matrix Algebra
- know vectors and their linear combinations and dot products
know why we need matrix algebra and differentiate between various special matrices
carry unary operations on matrices
- carry binary operations on matrices
- differentiate between inconsistent and consistent system of equations via finding rank of matrices
- differentiate between unique and infinite solution system of equations
- use Gaussian elimination methods to find solution to a system of equations
- use LU decomposition to find solution to system of equations and know when to choose the method over Gaussain elimination
- use Gauss-Seidel method to solve a system of equations iteratively
- find quantitatively how adequate your solution is through the concept of condition numbers
- find eigenvectors and eigenvalues of a square matrix
- College Algebra
Matrix algebra is used in a very diverse field of studies. Some of these fields include engineering, mathematics, and business. This course starts with the basics of matrix algebra with questions like: "What is a vector?" No precursory knowledge about matrix algebra is required on the part of the student, so not to worry if you are new to the subject! If you already have some knowledge of beginner concepts, just skip to the area of the course that's right for you! The video lectures are short; covering only one topic at a time, so it's easy to jump right to your level of knowledge.
The course has several important components that are all essential to the student's understanding of the material.
Textbook: Each section or chapter will start with the textbook chapter for that section.
Video Lectures: Next, there will be a series of video lectures; one micro lecture per topic. There are several types of video lectures, the two most common being theory or example (usually in that order). First, Dr. Kaw will talk about the theory or background behind a particular concept or topic. He will then proceed to work out an example using that concept.
Practice Problems: Each section will be concluded with a set of practice problems. These practice problems are meant to give the student a medium of testing their mastery of the concepts. Combined with these practice problems are the full solutions to each question. These solutions can be used to check your approach and final answer.
- Students who are in a STEM major in college. It is also suited for finance and economics majors. If your exposure to college algebra is limited, this course is not for you!