# 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

## 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