Matrices and Determinants

This topic covers concepts such as Matrices and Determinants, Matrices, Definition of a Matrix, Rows and Columns of a Matrix, Order of a Matrix, Submatrix of a Matrix, Number of Submatrices of a Matrix, Types of Matrices, Horizontal Matrix, etc.

This topic covers concepts such as Comparable Matrices, Equality of Matrices, Operations on Matrices, Addition of Matrices, Algebraic Properties of Matrix Addition, Condition for Addition of Two Matrices, Closure Property of Matrix Addition, etc.

This topic covers concepts such as Symmetric and Skew-symmetric Matrices, Symmetric Matrix, Properties of Symmetric Matrices, Properties of Skew-Symmetric Matrices, Square Matrix as a Sum of Symmetric and Skew-Symmetric Matrices, etc.

This topic covers concepts such as Special Types of Matrices, Idempotent Matrix, Periodic Matrix, Nilpotent Matrix, Involuntary Matrix, Orthogonal Matrix, Hermitian and Skew-hermitian Matrices, Hermitian Matrix, Skew-hermitian Matrix, etc.

This topic covers concepts such as Determinant, Determinant of a Square Matrix, Minors and Cofactors, Product of a Row/Column with Cofactors of Another Row/Column, Value (Cofactor Expansion) of a Determinant, and Transpose of a Determinant.

This topic covers concepts such as Properties of Determinants, Equality of Determinant and Its Transpose, Properties of Determinants under Elementary Transformations, Value of a Determinant Having Identical Rows/Columns, Circulant Determinant, etc.

This topic covers concepts such as Adjoint of a Matrix, Cofactor Matrix, and Properties of Adjoint of Matrices.

This topic covers concepts such as Existence of Multiplicative Inverse in Matrices, Cancellation Law in Matrix Multiplication, Inverse of a Matrix, Invertible Matrices, Properties of Inverse of Matrices, Methods to Find Inverse of a Matrix, etc.

This topic covers concepts such as System of Linear Equations, Non-homogeneous System of Linear Equations, Homogeneous System of Linear Equations, Solutions of System of Linear Equations, Consistent and Inconsistent System of Linear Equations, etc.

This topic covers concepts such as Inverse of a Matrix Using Given Polynomial Equation, Characteristic Equation (Polynomial) of a Matrix, and Eigenvalue of Characteristic Equation of a Matrix.