Kernel and Range of Linear Transformations | Linear Algebra

Опубликовано: 21 Август 2024
на канале: Wrath of Math

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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

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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

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