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, Operations on Matrices, Addition of Matrices, Comparable Matrices & Properties of Trace of a Square 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, Transpose of a Matrix, Order of Transpose of a Matrix, Properties of Transpose of a Matrix & Orthogonal 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, Existence of Multiplicative Inverse in Matrices, Multiplication of Matrices, Nilpotent Matrix & Involuntary Matrix etc.

This topic covers concepts, such as, Adjoint of a Matrix, Cofactor Matrix, Inverse of a Matrix by Elementary Transformations & Methods to Find Inverse of a Matrix etc.

This topic covers concepts, such as, System of Linear Equations, Solutions of System of Linear Equations, Cramer's Rule (Determinants Method) to Solve System of Linear Equations & Cramer's Rule: Consistency of a System of Linear Equations etc.

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