Reflections as Matrix Transformations | Linear Algebra

We study the reflection operators in R^2 and R^3 as matrix transformations, which are also linear transformations. We will use our intuitive knowledge of reflections geometrically to understand what these matrix transformations should do geometrically, and then use the transformations of the standard basis vectors to find the standard matrix for each rotation operator. We will also do some examples of reflecting a vector across an axis or plane using matrix multiplication by the standard matrix for the reflection. #linearalgebra

This is What Matrix Transformations Are: (coming soon)

Linear Algebra course:    • Linear Algebra  
Linear Algebra exercises:    • Linear Algebra Exercises  

Join Wrath of Math to get exclusive videos, music, and more:
   / @wrathofmath  

0:00 Intro
0:45 Reflections in R^2
3:54 Use Standard Matrix for Reflection in R^2
5:36 Reflections in R^3
7:13 Use Standard Matrix for Reflection in R^3
8:49 Conclusion

◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Abstract Algebra: https://amzn.to/3IjoZaO
Linear Algebra: https://amzn.to/43xAWEz
Calculus: https://amzn.to/3PieD1M
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd

★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons  
◆ Donate on PayPal: https://www.paypal.me/wrathofmath

Thanks to Loke Tan, Raül Beienheimer, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon!

Outro music is mine. You cannot find it anywhere, for now.

Follow Wrath of Math on...
● Instagram:   / wrathofmathedu  
● Facebook:   / wrathofmath  
● Twitter:   / wrathofmathedu  

My Math Rap channel:    / @mathbars2020