Intro to Systems of Linear Equations (Linear Algebra)

0:00 What is a System of Linear Equations? 0:59 Use of Variables in Linear Algebra 1:37 Solution Sets, Consistent & Inconsistent 3:15 Matrix Representation & Size 4:20 Coefficient & Augmented Matrices 5:18 Common Solution Methods in Beginning Algebra This video is an introduction to linear algebra, in particular systems of linear equations. We cover what a linear equation is and how we typically see these written in linear algebra versus beginning algebra. Different types of solution sets are discussed: no solution, one unique solution, and infinitely many solutions. An introduction to matrix representation for linear systems of equations is contained, which also shows how to determine the size of a matrix (its number of rows and number of columns). We compare side-by-side a system of linear equations, its coefficient matrix, and its augmented matrix. We go through a brief review and reminder of the three beginner methods of solving basic systems of equations from algebra: graphing, substitution, and elimination, remarking that a new kind of elimination will be the most common solution method for systems of linear equations in linear agebra.