Matrices
- Introduction to Matrices
- Algebra of Matrices
- Elementary row operations
- Inverse of a matrix by using elementary row operations
- Applications of matrices
Determinants
- Introduction to Determinants
- Properties of determinants of order n
- Application of determinants
Linear Systems of Equations:
- Introduction to Linear systems
- Homogeneous and non-homogeneous linear equations
- Echelon and reduce Echelon form
- Gaussian Elimination and Gauss-Jordan Methods
- Consistency criterion for solution of homogeneous and non-homogeneous systems of linear equations
- Applications of systems of linear equations
Vector Spaces and Subspaces
- Vector spaces and subspaces
- Linear combination
- Linear independence and linear dependence
- Linear Transformations
- Applications of Transformations
Eigen Values and Eigen Vectors
- Introduction to Eigen values and Eigen vectors
- Diagonalization
- Applications of Eigen values and Eigen vectors
Inner Product Spaces
- Inner Products
- Gram Schmidt Orthonormalization Process
- Applications of Inner Products
