"Vectors and Matrices" is a one-term course for first-year undergraduate students containing the geometry of the plane and the space, and the most important part of linear algebra. It is taught through lectures and in-class exercises combined: in each class, I will first give a lecture, and then give one or two problems to be solved in class. No additional assignments are required. I taught this course in the Fall Semester of 2021, and all the students passed the course.

The course covers the following topics.

1. Vectors in the plane and the space: we will discuss dot product and cross product of vectors; equations of lines and planes; distances between points, lines, and planes.

2. Vector spaces: we will discuss subspaces and spanning subspaces; linear independence of vectors; the basis of a subspace; the dimension of a vector space.

3. Matrix theory: we will discuss operations on matrices (addition, subtraction, scalar multiplication, and multiplication of matrices); transpose of a matrix; invertible matrices; elementary row operations of matrices; eigenvalues and eigenvectors; diagonalization;

4. Systems of linear equations: we will discuss the matrix form of a system; elementary operations on systems of linear equations; determinants and Cramer's rule.

If you want to learn the most important part of linear algebra quickly, you are advised to take this course.

Coupon code: 14A8BFD67243B606B9E8 (CA$16.99)