Determinants (original) (raw)

A Determinant is a scalar value computed from a square matrix that tells us whether the matrix is invertible, how it scales space, and whether a system of equations has a unique solution. For a matrix A, the determinant is written as det(A) or |A|.

Find the Determinant of A = \begin{bmatrix}3 & 2\\2 & 3\end{bmatrix}.

Determinant of A = \begin{bmatrix}3 & 2\\2 & 3\end{bmatrix}_{2\times2} is calculated as,

| A | = \begin{vmatrix}3 & 2\\2 & 3\end{vmatrix}

| A | = 3 × 3 - 2 × 2
= 9 - 4
= 5

**Foundations

Start with the basics to understand what a determinant is, why it matters, and how it is used.

• Introduction to Determinants
• Formula
• Properties of Determinants
• Applications of Determinants

**Computing Determinants – By Matrix Size

Learn step-by-step methods to calculate determinants of different matrix sizes.

• Determinant of a 2×2 Matrix
• Determinant of a 3×3 Matrix
• Determinant of a 4×4 Matrix
• Determinant of a Square Matrix

**Minors, Cofactors and Adjoint

Understand these core concepts as they form the foundation for advanced calculations.

• Cofactor of a Matrix
• Adjoint of a Matrix
• Singular Matrix

Inverse of a Matrix using Determinants

Understand how determinants help in finding the inverse and solving equations.

• Inverse of a Matrix
• How to Solve a System of Equations using the Inverse of Matrices

**Applications of Determinants

Explore practical uses like area, collinearity, and solving linear equations.

• Area of a Triangle using Determinants
• Cramer's Rule

For Programmers

• Program to find Determinant of a Matrix
• Practice
• Determinant using NumPy