Basic Variables & Free Variables (Linear Algebra)

0:00 Leading Entries & Pivots (Reminder) 0:53 Reading Solution Sets From Matrices 2:17 Inconsistent Systems 2:57 Consistent Systems 3:20 Free Variables 4:40 Basic Variables 5:25 Example 1 7:05 Example 2 9:37 Example 3 11:51 Solution to Example From Previous Video This linear algebra video talks about how to use pivot entries and reduced echelon form to write solutions for systems. We cover the cases where the system is inconsistent (has no solution) and when the system is consistent (has at least one solution). We use several examples to show how to identify free variables and basic variables, and we practice using the reduced echelon form to write the solutions for systems with at least one free variable.