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Learn everything you need to know to solve problems involving determinants

## (1) Introduction

- Introduction
- Matrices review
- Determinants of higher order: definition
- Determinants of higher order: practice (easy)
- Determinants of higher order: practice (intermediate)
- Cofactor expansion: theorem
- Cofactor expansion: practice (easy)
- Cofactor expansion: practice (easy)
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory (review)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Products of matrices: review
- Determinants of products of matrices: theory
- Invertibility of matrices: theory
- Invertibility of matrices: practice (intermediate)
- Determinants of products of matrices practice difficult
- Systems of linear equations review
- Cramer’s rule theory
- Cramer’s rule practice intermediate
- Determinants of order 2
- Linearity: motivation
- Linearity with respect to the first argument: theorem
- Linearity with respect to the first argument: examples
- Antisymmetry: theorem
- Linearity with respect to the second argument: theorem
- Summary of properties of determinants of order 2
- Determinants of order 2: theorem
- Signed area
- The product of determinants: theorem
- Invertibility of 2*2 matrices: theorem

## (2) Definition of determinants

- Introduction
- Matrices review
- Determinants of higher order: definition
- Determinants of higher order: practice (easy)
- Determinants of higher order: practice (intermediate)
- Cofactor expansion: theorem
- Cofactor expansion: practice (easy)
- Cofactor expansion: practice (easy)
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory (review)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Products of matrices: review
- Determinants of products of matrices: theory
- Invertibility of matrices: theory
- Invertibility of matrices: practice (intermediate)
- Determinants of products of matrices practice difficult
- Systems of linear equations review
- Cramer’s rule theory
- Cramer’s rule practice intermediate
- Determinants of order 2
- Linearity: motivation
- Linearity with respect to the first argument: theorem
- Linearity with respect to the first argument: examples
- Antisymmetry: theorem
- Linearity with respect to the second argument: theorem
- Summary of properties of determinants of order 2
- Determinants of order 2: theorem
- Signed area
- The product of determinants: theorem
- Invertibility of 2*2 matrices: theorem

## (3) Cofactor expansion

- Introduction
- Matrices review
- Determinants of higher order: definition
- Determinants of higher order: practice (easy)
- Determinants of higher order: practice (intermediate)
- Cofactor expansion: theorem
- Cofactor expansion: practice (easy)
- Cofactor expansion: practice (easy)
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory (review)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Products of matrices: review
- Determinants of products of matrices: theory
- Invertibility of matrices: theory
- Invertibility of matrices: practice (intermediate)
- Determinants of products of matrices practice difficult
- Systems of linear equations review
- Cramer’s rule theory
- Cramer’s rule practice intermediate
- Determinants of order 2
- Linearity: motivation
- Linearity with respect to the first argument: theorem
- Linearity with respect to the first argument: examples
- Antisymmetry: theorem
- Linearity with respect to the second argument: theorem
- Summary of properties of determinants of order 2
- Determinants of order 2: theorem
- Signed area
- The product of determinants: theorem
- Invertibility of 2*2 matrices: theorem

## (4) Properties of determinants

- Introduction
- Matrices review
- Determinants of higher order: definition
- Determinants of higher order: practice (easy)
- Determinants of higher order: practice (intermediate)
- Cofactor expansion: theorem
- Cofactor expansion: practice (easy)
- Cofactor expansion: practice (easy)
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory (review)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Products of matrices: review
- Determinants of products of matrices: theory
- Invertibility of matrices: theory
- Invertibility of matrices: practice (intermediate)
- Determinants of products of matrices practice difficult
- Systems of linear equations review
- Cramer’s rule theory
- Cramer’s rule practice intermediate
- Determinants of order 2
- Linearity: motivation
- Linearity with respect to the first argument: theorem
- Linearity with respect to the first argument: examples
- Antisymmetry: theorem
- Linearity with respect to the second argument: theorem
- Summary of properties of determinants of order 2
- Determinants of order 2: theorem
- Signed area
- The product of determinants: theorem
- Invertibility of 2*2 matrices: theorem

## (5) Product of matrices

- Introduction
- Matrices review
- Determinants of higher order: definition
- Determinants of higher order: practice (easy)
- Determinants of higher order: practice (intermediate)
- Cofactor expansion: theorem
- Cofactor expansion: practice (easy)
- Cofactor expansion: practice (easy)
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory (review)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Products of matrices: review
- Determinants of products of matrices: theory
- Invertibility of matrices: theory
- Invertibility of matrices: practice (intermediate)
- Determinants of products of matrices practice difficult
- Systems of linear equations review
- Cramer’s rule theory
- Cramer’s rule practice intermediate
- Determinants of order 2
- Linearity: motivation
- Linearity with respect to the first argument: theorem
- Linearity with respect to the first argument: examples
- Antisymmetry: theorem
- Linearity with respect to the second argument: theorem
- Summary of properties of determinants of order 2
- Determinants of order 2: theorem
- Signed area
- The product of determinants: theorem
- Invertibility of 2*2 matrices: theorem

## (6) Systems of linear equations

- Introduction
- Matrices review
- Determinants of higher order: definition
- Determinants of higher order: practice (easy)
- Determinants of higher order: practice (intermediate)
- Cofactor expansion: theorem
- Cofactor expansion: practice (easy)
- Cofactor expansion: practice (easy)
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory (review)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Products of matrices: review
- Determinants of products of matrices: theory
- Invertibility of matrices: theory
- Invertibility of matrices: practice (intermediate)
- Determinants of products of matrices practice difficult
- Systems of linear equations review
- Cramer’s rule theory
- Cramer’s rule practice intermediate
- Determinants of order 2
- Linearity: motivation
- Linearity with respect to the first argument: theorem
- Linearity with respect to the first argument: examples
- Antisymmetry: theorem
- Linearity with respect to the second argument: theorem
- Summary of properties of determinants of order 2
- Determinants of order 2: theorem
- Signed area
- The product of determinants: theorem
- Invertibility of 2*2 matrices: theorem

## (7) Additional lectures: Determinants of order 2

- Introduction
- Matrices review
- Determinants of higher order: definition
- Determinants of higher order: practice (easy)
- Determinants of higher order: practice (intermediate)
- Cofactor expansion: theorem
- Cofactor expansion: practice (easy)
- Cofactor expansion: practice (easy)
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory
- Properties of determinants: theory (review)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (intermediate)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Properties of determinants: practice (difficult)
- Products of matrices: review
- Determinants of products of matrices: theory
- Invertibility of matrices: theory
- Invertibility of matrices: practice (intermediate)
- Determinants of products of matrices practice difficult
- Systems of linear equations review
- Cramer’s rule theory
- Cramer’s rule practice intermediate
- Determinants of order 2
- Linearity: motivation
- Linearity with respect to the first argument: theorem
- Linearity with respect to the first argument: examples
- Antisymmetry: theorem
- Linearity with respect to the second argument: theorem
- Summary of properties of determinants of order 2
- Determinants of order 2: theorem
- Signed area
- The product of determinants: theorem
- Invertibility of 2*2 matrices: theorem

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