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- Matrices
o Definition of Matrix
o Types of Matrices
o Order of Matrices
o Properties of Matrices
o Operation of Matrices
- Determinant of Matrices
o Determinant of (2×2)-Matrix
o Determinant of (3×3)-Matrix
- Expanding Minors and Cofactors Method
- Column Rotation Method
- Inverse Matrix
o Inverse Matrix (2×2)
- Using First Method
- Using Identity Matrix
o Inverse Matrix (3×3)
- Determinant, Cofactor and Adjoint Method
- Using Identity Matrix
o Unitary Matrix and Identity Matrix
o Singular and Non-Singular Matrix
- Solving Linear Equations Using Inverse Matrix
o by Using Inverse Matrix [ (2×2) and (3×3) Matrix ]
- Solving Linear Equations Using Cramer’s Rule
o by Using Cramer’s Rule [ (2×2) and (3×3) Matrix ]
- Solving Linear Equations Using Row Echelon Form (REF) and Reduced Row Echelon Form (RREF)
o Gaussian Elimination [ (2×2) and (3×3) Matrix ]
o Gauss-Jordan Elimination [ (2×2) and (3×3) Matrix ]
- Consistent Matrix
o Linear Dependent Matrix
- Inconsistent Matrix
o Linear Independent Matrix
o Coincident Dependent Matrix
- Area of Triangle and Collinearity
o Area of a Triangle Using Matrix
o Test for Collinear Points.
Sequences and Series
- Sequence and Series
o Definition of Sequence and Series
o Difference between Sequence and Series
o Difference between Sequence Notation and Function Notation
o General Term ( N-th Term )
o Recursively Defined Sequence
o Alternating Sequence
o n-Factorial
o Summation Notation ( Sigma Notation )
o Properties of Summation Notation
- Arithmetic Sequence and Series
o Common Difference
o N-th Term ( General Term ) of an Arithmetic Series
o N-th Partial Sum of an Arithmetic Series
- Geometric Sequence and Series
o Common Ratio
o N-th Term ( General Term ) of a Geometric Sequence
o N-th Partial Sum of a Geometric Series
o N-th Sum of an Infinite Geometric Series