Determinants

Board: CBSE Class: 12

Chapter Overview

Determinant of order 2: |A| = ad - bc. For order 3, use expansion by minors. Properties include: determinant of triangular matrix = product of diagonal, det(AB) = det(A)det(B), det(AT) = det(A). Minors, cofactors, adjoint (adj A), and inverse A^-1 = adj A / |A| for non-singular matrices. Cramers rule solves linear equations.

Topics Covered

Order 2 and 3 Determinants
Properties of Determinants
Minors and Cofactors
Adjoint and Inverse
Cramers Rule
System of Equations

Key Formulas

det(AB) = det(A)det(B)

A^-1 = adj(A)/|A|

|adj(A)| = |A|^(n-1)

Cramers: x_i = D_i/D

Real-World Applications

Applications: Solving linear systems, computer graphics, differential equations, eigenvalue problems.

Study Tips

Tip: Learn determinant properties well - they simplify computation

Tip: Master cofactor expansion

Tip: Practice Cramers rule