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Linear Algebra: BSSE Course Outline

Linear Algebra is a branch of Mathematics which includes lines, planes and subspaces but it deals with properties of all common vector spaces

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Reference Books

Course Outline

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

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