Linear Algebra 6.5 – Applications of Linear Transformations

In this lesson, we explore some of the most important geometric transformations in linear algebra and how they act on the coordinate plane. Using clear visuals and intuitive examples, we walk through reflections, expansions and contractions, shears, and rotations—building a strong foundation for understanding how matrices transform vectors.

You’ll see how each transformation changes the shape, orientation, or position of objects, and how these ideas connect directly to matrix multiplication.

Video Chapters:
0:00 Intro
0:17 Reflections over the x-axis
1:42 Reflections over the y-axis
2:47 Reflection across the line y = x
4:03 Horizontal expansions and contractions
6:25 Vertical expansions and contractions
7:51 Horizontal shear transformations
9:57 Vertical shear transformations
11:18 Rotations around the z-axis
12:41 Up Next

Textbook: Elementary Linear Algebra 8e, Ron Larson

Slide Decks: https://bellevueuniversity-my.sharepoint.com/:f:/g/personal/kbrehm_bellevue_edu/IgDVnTt2BohsRLsMfseN5FijAXYDd49YlIkHeq5cfmCxG2g?e=ZwTt3c

Playlist: https://youtube.com/playlist?list=PLl-gb0E4MII1RjTV2GegmXFTJwTrek8OI&si=g3Xc3yHB5GkmxMF4