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 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: 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, 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

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

Numerical System of linear ODEs, Eigenvalue problems, Homogeneous and nonhomogeneous system of ODE.

Dynamical systems, Population dynamics, Prey-Predator models, Stability analysis