MTH 141: Study Session 6 (Linear Transformations)

This linear algebra video contains discussions and practice problem solutions relating to Linear Transformations. Notably: 5.1-5.4 from the Kuttler textbook titled: "A First Course in Linear Algebra".

Timestamps:
0:00:00 Overview of Linear Transformations + Kuttler: 5.1: Linear Transformations
0:08:17 Example: Showing a Transformation is Linear
0:28:00 Kuttler: 5.2: The Matrix Representation of a Linear Transformation I
0:29:31 Example: Finding the Matrix Representation by Applying the Transformation to the Basis Vectors
0:43:35 How to Find the Matrix Representation by using BA^(-1)
0:50:35 Example: Finding the Matrix Representation by using BA^(-1)
1:04:18 Nicholson: 7.1.4 b) ([T] using BA^(-1))
1:21:18 Alternative way to Find the Matrix Representation by Looking at T(x)
1:44:44 Kuttler: 5.3: Properties of Linear Transformations
1:44:45 Example: Finding T(v) using Linear Combinations
1:54:53 Discussion on Span (continuation of previous question)
2:00:12 Composite Linear Transformations
2:05:37 Example: Finding the Matrix Representation of a Composite Linear Transformation
2:13:45 Inverse Transformation
2:16:00 Example: Finding the Inverse of a Transformation
2:18:00 Kuttler: 5.4: Special Linear Transformations in R^(2) (R_(theta) and Q_(m))
2:18:01 Examples: Rotation by Theta (R_(theta))
2:24:20 Rotations in R^(3) Around an Axis by Theta
2:28:20 Reflection over the line y = mx (Q_(m))
2:31:35 Example: Matrix Representation of a Rotation Composed with a Reflection
2:43:51 Nicholson: 2.6.8 d) (Determining the Transformation from the Matrix Representation)
2:51:50 Nicholson: 2.6.8 b) (Determining the Transformation from the Matrix Representation)

Previously titled: (12/13/2020) MTH 141 Test 3 Session 1