Matrices and Determinants

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

This topic covers concepts, such as, Types of Matrices, Row 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, Existence of Multiplicative Inverse in Matrices, Algebraic Properties of Matrix Addition, Existence of Non-zero Divisors & Complex Conjugate of a Matrix etc.

This topic covers concepts, such as, Transpose of a Matrix, Order of Transpose of a Matrix & Properties of Transpose of a Matrix 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, Periodic Matrix, Nilpotent Matrix, Involuntary Matrix, Orthogonal Matrix & Unitary Matrix 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, Inverse of a Matrix, 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 Method to Solve System of Linear Equations & Rank of a Matrix etc.

This topic covers concepts, such as, Consistent and Inconsistent System of Linear Equations, Cramer's Rule: Consistency of a System of Linear Equations & 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.