View this video (10 min): The determinant explained by 3Blue1Brown: https://youtu.be/Ip3X9LOh2dk

Read: 

  • Schaum subchapters 8.1-8.3 (introduction; determinants of order 1, 2 and 3)

View this video (31 min): Properties of determinants: https://youtu.be/19qaYFGZ-cA

Read:

  • Schaum subchapters 8.6-8.8 (properties of determinants; minors and cofactors; evaluation of determinants)
  • Schaum subchapter 8.10 (applications to linear equations, Cramer law)
  • Schaum subchapter 8.12 (block matrices and determinants; determinants and volume; determinants of a linear operator)

Relevant exercises: 8.1-8.4, 8.9-8.13, 8.38-8.43, 8.52-8.54, 8.60-8.65, 8.67; Important (theorems): 8.26-8.33, 8.35-8.36, 8.69

Note: section (iii) in theorem 8.2 (pg. 269) is a very important property of the determinant:
if A is a triangular matrix then the determinant equals the product of the diagonal elements.
Formally, if A is triangular then det(A)=|A|=a11*a22*...*ann
This follows directly from the Laplace expansion (see theorem 8.8 in subsection 8.7: Properties of determinants). 

For the algebraic definition of the determinant and proofs of its properties - you may view the links in the corresponding resource. This is very helpful, but not required in this course.

Last modified: Wednesday, 16 August 2023, 10:40