Kernel and Range of Linear Transformations | Linear Algebra

🛍 Check out the coolest math clothes in the world! https://mathshion.com/ Linear Algebra course:    • Linear Algebra   Linear Algebra exercises:    • Linear Algebra Exercises   📚 Get the textbook for this course! https://amzn.to/45KYgmA Business Inquiries: [email protected] We introduce the kernel and range of a linear transformation. The kernel is the extension of the null space to general linear transformations and the range is the extension of the column space to general linear transformations. We go over the definitions of these terms, see several examples, and then prove a theorem stating the kernel is a subspace of the domain and the range is a subspace of the codomain. #linearalgebra ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● TikTok:   / wrathofmathedu   ● X: https://x.com/wrathofmathedu 0:00 Intro 1:54 Definitions of Kernel and Range 4:06 Zero Transformation Kernel and Range 4:59 Kernel and Range of Projection onto xy Plane 6:51 Kernel and Range of Rotation 7:38 Subspace Theorem 8:14 Kernel is a Subspace 10:28 Range is a Subspace 13:20 Conclusion