What you'll learn
Vectors in the plane and in the space: dot product and cross product of vectors; lines and planes; distances between points, lines, and planes
Vector spaces and spanning subspaces; linearly independence; basis; dimension
Matrix theory: operations on matrices; transpose of a matrix; invertible matrices; elementary row operations; diagonalization;
Systems of linear equations: matrix form of a system; elementary operations on systems of linear equations; determinants and Cramer's rule
Requirements
No college algebra is required
Description
"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.
Who this course is for
Undergraduate students
Homepage

https://www.udemy.com/course/vectors-and-matrices/