Definition and Examples of DETERMINANT | FREE Linear Algebra Course

In this video, we define the determinant of a square matrix recursively. We establish cofactor expansion formulas for the determinant of a matrix using any row or column. We also prove that the transpose preserves the determinant. We show how to compute determinants of 3x3 and 4x4 matrices.

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
0:26 Motivation
0:51 Submatrices
2:04 Definition of the determinant
3:23 Formula for 2x2 determinants
4:19 Example: computing 3x3 determinant
6:46 Determinant expansion along rows
7:45 Determinant of transpose
10:33 Determinant expansion along columns
11:48 Example: computing 4x4 determinant
12:47 Now what?

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