BSc Computer Engineering Technology

Sir Syed University of Engineering
and Technology

Linear Algebra

Course Code
Credit Hours:
3+0 (3+0)

System of Linear Equations and Applications: Overview of linear system of equations, Cases of unique solution, No solution and infinite solutions, Echelon form, Gauss elimination method, Inversion of matrix in the context of solution of a system of equations, LU factorization, Row space and column space, Relevant engineering case studies such as Network analysis, Traffic Flows, Balancing chemical reaction, Leontief Input-output model, Finding max stress in compound cylinder, Applications of linear systems in force balancing of structures, Markov process. Vector Spaces and Transformations Vector Spaces: Real vector spaces, Subspaces, Basis and dimension, Rank, Nullity, Gram-Schmidt process for finding orthonormal basis, Linear Transformation, Kernel of Transformation, Range of Transformation, Matrix of Transformation, Applications: Cryptography, Coding and decoding, Breaking of codes, Robotic Applications of linear transformations. Eigenvalues and Eigen Vectors: Eigenvalues, Eigenvectors, Similar matrices, Diagonalization, Quadratic forms, Positive definite Matrices, Singular Value Decomposition, Inner product Spaces, Applications of linear Algebra: Constructing curves and surfaces, Computer graphics, Genetics, Linear Programming: Solution Introduction to linear programming, Optimization, Graphical method,, Simplex method, Optimization problems in engineering and economics, Dual simplex methods, Duality theory, Primal and dual problems, transportation models, north-west corner, least-cost and Vogel’s approximations methods, Assignment model, the transshipment model and other relevant engineering case studies. Application of Linear Algebra in Dynamical Systems: Numerical System of linear ODEs, Eigenvalue problems, Homogeneous and nonhomogeneous system of ODE. Dynamical systems, Population dynamics, Prey-Predator models, Stability analysis

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