Matrix Representations and INVERTIBLE Linear Transformations | FREE Linear Algebra Course

In this video, we prove that a linear transformation is invertible if and only if its matrix representation is an invertible matrix. Moreover, the matrix representation of the inverse linear transformation is the matrix inverse of the matrix representation of the original linear transformation. We use matrix inverses to determine if a linear transformation is invertible and to find it inverse linear transformation.

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
0:40 Matrix representations of invertible linear transformations
7:11 How to compute inverse of a linear transformation using matrix inverse
10:41 Invertible matrices and invertible linear transformations
13:20 Non-singular matrix equivalences
13:41 Now what?

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