Changing bases in linear algebra can feel abstract — but it’s really just like converting between different units in the real world. In this video, we’ll use a simple food example to show how changing from one “unit system” to another works the same way as changing bases with matrices. You’ll see how context can help you build the change-of-basis matrix, and how to set up and solve problems even without a real-world story. By the end, you’ll finally understand how change of basis works and why it’s just a matter of the right multiplication. Change of Basis Part 1: Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?” Donate: Instagram: Twitter/X: Facebook: Email: MathTheWorld@ Created by Doug Corey Script: Doug Corey and Jennifer Canizales Audio: Doug Corey Animation: Jennifer Canizales Music: Coma Media © 2025 BYU