Linear Algebra in 2D - Chapter 7: Determinants

Determinants are a wonderful tool to study linear maps and matrices. We motivate them from geometric considerations and derive their basic properties. At the end, we see how determinants can be applied to yield closed form solutions for systems of linear equations.

Sections
00:00:00 Greetings
00:00:36 Area and determinants
00:04:44 Area of a parallelogram
00:12:57 Sign as orientation
00:14:52 Definition of the determinant det(A)
00:17:00 Some examples
00:21:06 Properties of determinants
00:21:56 The transposed matrix
00:24:21 Determinant is alternating
00:25:53 Determinant is multilinear
00:39:52 det(AB) = det(A) det(B)
00:46:31 Determinants characterize invertibility
00:49:29 Invariance under change of basis
00:52:42 Determinants and linear equations
00:53:17 Closed formula for the inverse matrix
00:56:05 Closed formular for the solution of a linear system

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