Master Solutions Sets of Linear Systems | Examples and Geometric Interpretations

In this video, we explore Section 1.5 of our Linear Algebra series, diving into how to find solution sets of linear systems. We'll break down both homogeneous and non-homogeneous systems, explain how to write solutions in parametric vector form, and demonstrate their geometric interpretations. Whether you're new to linear algebra or brushing up, this video will guide you step by step.

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.

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*Timestamps*
00:00 Introduction
01:00 Homogeneous Linear Systems
05:00 Solving a Homogeneous Linear System
07:30 Non-Homogeneous Linear Systems
10:30 Parametric Vector Form & Geometry
15:30 Simultaneous Systems & Augmented Matrices

*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.

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