Matrices and Determinants

This topic covers concepts such as Matrices, Definition of a Matrix, Rows and Columns of a Matrix, and Order of a Matrix.

This topic covers concepts such as Row Matrix, Column Matrix, Zero Matrix (Null Matrix), Square Matrix, Diagonals of a Square Matrix, Diagonal Matrix, Scalar Matrix, Unit Matrix (Identity Matrix), Upper Triangular Matrix, and Lower Triangular Matrix.

This topic covers concepts such as Equality of Matrices, Addition of Matrices, Algebraic Properties of Matrix Addition, Condition for Addition of Two Matrices, Commutative Property of Matrix Addition, Associative Property of Matrix Addition, etc.

This topic covers concepts such as Transpose of a Matrix, Order of Transpose of a Matrix, and Properties of Transpose of a Matrix.

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

This topic covers concepts such as Determinant and Determinant of a Square Matrix.

This topic covers concepts such as Minors and Cofactors and Value (Cofactor Expansion) of a Determinant.

This topic covers concepts such as Properties of Determinants, Properties of Determinants under Elementary Transformations, Value of a Determinant Having Identical Rows/Columns, Value of a Determinant Having an entire Row/Column of Zeros, etc.

This topic covers concepts such as Cramer's Rule (Determinants Method) to Solve System of Linear Equations and Application of Determinants in Finding Area of Triangle.

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

This topic covers concepts such as Inverse of a Matrix, Invertible Matrices, Properties of Inverse of Matrices, Singular and Non-singular Matrices, Inverse of a Matrix Using Adjoint, Inverse of a Matrix by Elementary Transformations, etc.

This topic covers concepts such as Idempotent Matrix and Orthogonal Matrix.

This topic covers concepts such as Elementary Operation (Transformation) of a Matrix, Interchange of Rows/Columns of a Matrix, Multiplication of Rows/Columns of a Matrix by Non-zero Number, Addition of a Row/Column to Another Row/Column, 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, etc.