IITJEE Advance • Mathematics New Syllabus
Module 02: Matrices & Determinants Hub
Master the mathematics of arrays and linear systems. Explore matrix algebra, properties of determinants, adjoints, inverses, and advanced applications in solving systems of linear equations.
Topic 1.1 • Matrix Fundamentals
Types of Matrices, Operations, Trace, Symmetric, and Skew-Symmetric Matrices
Topic 1.2 • Determinants
Evaluation of Determinants, Properties, and Operations on Rows and Columns
Topic 2.1 • Matrix Transformations
Adjoint of a Matrix, Inverse, and their Advanced Properties and Theorems
Topic 2.2 • Advanced Algebra
Characteristic Equations, Cayley-Hamilton Theorem, and Matrix Polynomials
Topic 3.1 • Linear Systems I
Solutions using Cramer’s Rule, Conditions for Consistency, and Homogeneous Systems
Topic 3.2 • Linear Systems II
Solving Linear Systems via Inverse Matrix Method and Consistency Analysis
Topic 4.1 • Complex Matrices
Hermitian, Skew-Hermitian, Unitary, Orthogonal, Nilpotent, and Involutory Matrices
Topic 4.2 • Geometry & Applications