Matrices and systems of linear equations are important mathematical tools used in many fields
such as physics, engineering, computer science, and data analysis. This lecture introduces
matrices as a useful way to organize and solve linear systems.
We will start by learning basic matrix operations like addition, multiplication, and finding inverses.
Then, we will explore different methods for solving systems of linear equations, including Gaussian
elimination, Cramer’s rule, and matrix inversion. We will also focus on understanding when a
system has one solution, many solutions, or no solution by looking at the coefficient matrix.
By the end of this lecture, students will have a good understanding of how matrices work and how
they help solve real-world problems. These ideas will also be useful for more advanced topics in
mathematics and applied sciences.