KERNEL of a Linear Transformation | FREE Linear Algebra Course

In this video, we define the kernel of a linear transformation. We compute the kernel of a linear transformation. We prove that the kernel of a linear transformation is a subspace, and we show that a linear transformation is injective if and only if its kernel is trivial.

This video is part of a linear algebra course

Students often ask is linear algebra important and is linear algebra hard. They wonder can anyone learn linear algebra and why some can't understand linear algebra. It is important to show to the students how linear algebra is used in data science, machine learning, AI, computer science, image processing, computer graphics, and in real life in general. This is a free video course in linear algebra for everyone, even beginners. It covers linear algebra with applications.

CHAPTERS:
0:00 Intro and learning outcomes
0:29 Pre-image
1:45 What is the kernel of a linear transformation?
2:18 How to compute the kernel of a linear transformation
3:19 Kernel is a subspace
5:31 Kernel and pre-image
6:30 Kernel of an injective linear transformation is trivial
10:12 How to use kernel to show that a linear transformation is not injective
10:29 Now what?

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