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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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