Kernel and Range of Linear Transformations in Linear Algebra

Explore the concepts of kernel and range in linear transformations through this 14-minute video. Learn how these concepts extend null space and column space to general linear transformations. Discover the definitions, examine various examples, and delve into a theorem proving that the kernel is a subspace of the domain and the range is a subspace of the codomain. Gain insights into zero transformation, projection onto the xy plane, and rotation as they relate to kernel and range. Follow along with the step-by-step explanations and proofs to enhance your understanding of these fundamental linear algebra concepts.

Intro
Definitions of Kernel and Range
Zero Transformation Kernel and Range
Kernel and Range of Projection onto xy Plane
Kernel and Range of Rotation
Subspace Theorem
Kernel is a Subspace
Range is a Subspace
Conclusion