This course is all about matrices, and concisely covers the linear algebra that an engineer should know. We define matrices and how to add and multiply them, and introduce some special types of matrices. We describe the Gaussian elimination algorithm used to solve systems of linear equations and the corresponding LU decomposition of a matrix. We explain the concept of vector spaces and define the main vocabulary of linear algebra. We develop the theory of determinants and use it to solve the eigenvalue problem. After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed and drop out. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in the lecture notes for the course. The mathematics in this matrix algebra course is presented at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but student's are expected to have a certain level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join. Lecture notes may be downloaded at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Watch the course overview video at https://youtu.be/IZcyZHomFQc