MathIsimple
Part V

Determinants

The determinant measures how a matrix scales volume. It determines invertibility and appears throughout linear algebra.

5
Courses
11-16
Hours
Core
Level

Courses

LA-5.1
Determinant Definition
Available
Axiomatic and permutation-based definitions
3-4 hours
Axioms
Permutation Formula
Existence & Uniqueness
LA-5.2
Determinant Properties
Available
Multiplicativity, transpose, and special matrices
2-3 hours
det(AB) = det(A)det(B)
det(Aᵀ)
Triangular Matrices
LA-5.3
Computation Methods
Available
Row reduction and cofactor expansion
2-3 hours
Row Reduction
Cofactors
2×2 and 3×3 Formulas
LA-5.4
Laplace Expansion
Available
Expansion along any row or column
2-3 hours
Cofactor Expansion
Minor
Recursive Computation
LA-5.5
Adjugate Matrix
Available
Adjugate, Cramer's rule, and inverse formula
2-3 hours
Adjugate Definition
A⁻¹ = adj(A)/det(A)
Cramer's Rule