Matrices and Determinants

This topic covers concepts, such as, Matrices, Definition of a Matrix, Upper Triangular Matrix & Lower Triangular Matrix etc.

This topic covers concepts, such as, Elementary Operation (Transformation) of a Matrix, Interchange of Rows/Columns of a Matrix, Matrix Polynomial & Matrix Polynomial Equation etc.

This topic covers concepts, such as, Symmetric and Skew-symmetric Matrices, Symmetric Matrix, 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, Hermitian and Skew-hermitian Matrices & Properties of Hermitian and Skew-hermitian Matrices etc.

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

This topic covers concepts, such as, Application of Determinants in Finding Area of Triangle, Application of Determinants in Finding Line through Two Points, Circulant Determinant & Application of Determinants in Geometry etc.

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

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

This topic covers concepts, such as, System of Linear Equations, Solutions of System of Linear Equations, Rank of a Matrix & Rank Method: Consistency of a System of Linear Equations etc.

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