Linear Algebra Tutorial: Determinants

Learn everything you need to know to solve problems involving determinants
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  • Lectures 36
  • Length 2 hours
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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    Available on iOS and Android
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About This Course

Published 4/2016 English

Course Description

In this course you learn everything you need to know to solve problems involving determinants. The course consists of theoretic as well as practice lectures. In the theoretic lectures I explain the statements of important theorems and give easy to understand examples. In practice lectures I go over solutions to exercises.

No preliminary knowledge beyond precalculus is assumed. Anyone who is interested in linear algebra are welcome to take the course.

However, the course is designed primarily for college students. It is great for those who'd like to get prepared ahead of live lectures, and those who need help with homework. You may also use this short course as a review before a college exam.

Like any other tutorial, this course is not a substitute to regular lectures. The goal of this tutorial is to help you learn how to solve problems in linear algebra rather than explain the proofs of theorems.

What are the requirements?

  • precalculus

What am I going to get from this course?

  • Theoretic as well as practice lectures
  • Learn properties of determinants
  • Get my help (post your question on the discussion board)

What is the target audience?

  • college students who would like an efficient tutorial
  • college students who need help with homework
  • college students who need a short review before an exam
  • anyone interested in College Linear Algebra

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Section 1: Introduction
Introduction
Preview
02:03
Matrices review
02:32
Section 2: Definition of determinants
Determinants of higher order: definition
Preview
03:28
Determinants of higher order: practice (easy)
Preview
03:56
Determinants of higher order: practice (intermediate)
02:26
Section 3: Cofactor expansion
Cofactor expansion: theorem
05:09
Cofactor expansion: practice (easy)
03:22
Cofactor expansion: practice (easy)
02:56
Section 4: Properties of determinants
Properties of determinants: theory
03:30
Properties of determinants: theory
03:10
Properties of determinants: theory
03:55
Properties of determinants: theory (review)
01:48
Properties of determinants: practice (intermediate)
02:13
Properties of determinants: practice (intermediate)
02:49
Properties of determinants: practice (difficult)
01:24
Properties of determinants: practice (difficult)
01:47
Properties of determinants: practice (difficult)
Preview
04:59
Section 5: Product of matrices
Products of matrices: review
03:14
Determinants of products of matrices: theory
02:09
Invertibility of matrices: theory
03:25
Invertibility of matrices: practice (intermediate)
01:43
Determinants of products of matrices practice difficult
01:47
Section 6: Systems of linear equations
Systems of linear equations review
02:33
Cramer’s rule theory
04:55
Cramer’s rule practice intermediate
06:13
Section 7: Additional lectures: Determinants of order 2
Determinants of order 2
03:14
Linearity: motivation
03:43
Linearity with respect to the first argument: theorem
06:59
Linearity with respect to the first argument: examples
03:16
Antisymmetry: theorem
03:33
Linearity with respect to the second argument: theorem
05:03
Summary of properties of determinants of order 2
05:38
Determinants of order 2: theorem
05:00
Signed area
06:56
The product of determinants: theorem
03:24
Invertibility of 2*2 matrices: theorem
04:54

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Instructor Biography

I am a professional mathematician. As a mathematician I worked in US, Mexico, Japan, Canada and Germany. I am an author of 16 research papers published in internationally renowned journals.

I taught courses ranging from middle school to PhD level, including such high level courses as Topological Quantum Field Theory, Moduli spaces of Riemann curves, and Topological Surgery Theory.

What you may expect from me is a well structured course with clearly explained notions and theory.


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