Applications of Linear Systems | Traffic Flow and Balancing Chemical Equations

Welcome back to our Linear Algebra series! 🎉 In this exciting episode, we dive into Section 1.6, where we explore two fascinating applications of linear systems: **Network Flow** and **Balancing Chemical Equations**. Whether you’re a student looking to grasp these concepts or a curious learner wanting to see the practical applications of linear algebra, this video has something for everyone!

**🔍 What You’ll Learn:**

In this video, we’ll guide you through the essential steps to set up and solve traffic flow problems using linear systems, as well as demonstrate how to balance chemical equations using matrix methods. We’ll break down complex topics into manageable sections, ensuring you can follow along with ease.

**Key Points Covered:**

1. **Introduction to Network Flow:**
- Understand the concept of network flow and its real-world applications.
- Learn how to model traffic flow problems using systems of linear equations.
- **Example:** We’ll work through a sample problem involving multiple routes and intersections, demonstrating how to set up and solve the system.

2. **Balancing Chemical Equations:**
- Discover the importance of balancing chemical equations in chemistry and how linear algebra can simplify the process.
- Use matrices to represent chemical reactions and apply row operations to achieve balance.
- **Example:** We will balance a chemical reaction step-by-step, showcasing the matrix method in action.

**🌟 Benefits of Watching:**

- **Enhance Your Understanding:** This video not only teaches you how to solve specific problems but also deepens your understanding of linear systems and their applications in everyday life.
- **Visual Learning:** With clear explanations and visual aids, you’ll find it easier to grasp complex concepts.

Be sure to download the free guided notes (link below) to follow along and practice on your own. These notes include space to highlight key concepts and solve the example problems as we work through them.

*Link to Guided Notes*
Free downloadable pdf of guided notes that will help you follow along with the video and use later to review what you learned.

*Subscribe to My YouTube Channel*

*Visit the Understand The Math Website*
Find free guided notes, filled in guided notes for purchase, course outlines/playlists, and math merchandise.

*Connect on Social Media*

*Timestamps*
00:00 Introduction
00:27 Network Flow: Traffic Flow Example
06:28 Solving the Linear System for Traffic Flow
10:22 Balancing Chemical Equations
15:42 Solving the System for Balancing Equations
20:03 Final Balanced Equation

*More About Understand The Math*
Understand The Math provides students and lifelong learners with access to free, straightforward, and engaging mathematics instruction. I’m Cheryl Hile, the founder of Understand The Math, and I’m passionate about ensuring that accurate and engaging mathematics instruction is available to everyone! I have a Ph.D. in Engineering Science and Applied Mathematics and have over 25 years of teaching experience at the university level. This channel provides videos that contain clear explanations, step-by-step problem solving strategies, and carefully worked out example problems. In the video descriptions, you'll find a link to free guided notes. Students can use these notes to highlight concepts and fill in answers to example problems while watching the videos, and later, they can review what they've learned.

#LinearAlgebra #TrafficFlow #BalancingEquations #UnderstandTheMath #MathTutorial #MatrixMethods #NetworkFlow #Math