SEAMIC_Algebra: Systems of Linear Equations

In this video the concept of systems of linear equations is introduced, including examples and definitions. A solution to a system of linear equations is defined as a set of n real numbers that satisfies all the equations in the system. The general solution of a system is the set of all solutions, while a particular solution is one specific solution obtained by giving a parameter a specific value. The video also covers the classification of systems based on their solutions: compatible and determined (one unique solution), incompatible (no solution), and compatible and indeterminate (infinite solutions). Additionally, the concept of equivalent systems is introduced, which are systems that have the same solutions, and can be transformed into each other using equivalent transformations. The video concludes by mentioning that these transformations will be used to solve systems of linear equations, specifically through methods such as Gaussian Elimination.