Standard Matrix of a Linear Transformation | Find and Apply to Vectors - Step-by-Step Guide

In this video, part of our Linear Algebra series, we'll dive into Section 1.9 on the Standard Matrix of a Linear Transformation. I'll walk you through the process of finding the standard matrix and explain its geometric interpretation. We'll work through three detailed examples, where we find the standard matrix of linear transformations and use it to determine vector transformations. By the end of the video, you'll have a clear understanding of how to work with standard matrices and apply them to transform vectors in R².

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
1:00 Geometric Understanding of the Standard Matrix
3:00 Example 1: Finding the Image of a Vector
6:30 Example 2: A More Complex Example
12:00 Example 3: Solving for Transformations

*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 #MathTutorial #UnderstandTheMath #MatrixTransformations #StandardMatrix #LinearTransformations #FreeMathNotes