This is the first course of a two semester sequence in linear algebra. This course gives a working knowledge of: systems of linear equations, matrix algebra, determinants, eigenvectors and eigenvalues, finite-dimensional vector spaces, matrix representations of linear transformations, matrix diagonalization, changes of basis, Separable and first-order linear equations with applications, 2nd order linear equations with constant coefficients, method of undetermined coefficients, Systems of linear ODE's with constant coefficients, Solution by eigenvalue/eigenvectors, Non homogeneous linear systems.
Class Schedule: M, W 17:00-18:15 (Acad Block A13)
Office Hours: M, W 11:00-13:00. (SSE- MATH 9B30)
TAs Office Hours: Check LMS (https://lms.lums.edu.pk/)
Resources:
For resources click here.
Weekly Breakdown:
[Week 1] Linear systems, Matrices, and their properties, Solution of a linear system.
[Week 2] Geometry of solutions of a linear system, Echelon and Reduced Echelon Forms, Gauss and Gauss Jordan Elimination methods.
[Week 3] Matrix operations, Transpose and Trace of a matrix, Inverse of a matrix, Computing inverse of a 2x2 system.
[Week 4] Cramer's rule, Inverse of an nxn matrix.
[Week 5] Determinants, Properties of determinants, Singular matrices.
[Week 6] Homogenous and Non-homogenous systems.
[Week 7] Vector in Rn, Vector operations, vector (inner) products in n-space, Norms.
[Week 8] Real vector space, Subspaces, Dimension and Bases.
Midterm (24-03-23)
[Week 9] Linear Transformations, Matrix of a linear Transformation, Composition of Transformations.
[Week 10] Invertible Linear Transformations, Kernel and Range, Row-space, Column space.
[Week 11] Rank and nullity theorem, Eigenvalues, Eigenvectors, Defective matrices and Diagonalization, Similar matrices.
[Week 12] Introduction to Differential equations, Basic notions, First order ODE.
[Week 13] Separable, Linear, Bernoulli, Homogenous, substitution method and exact ODE.
[Week 14] System of first order Differential equations and their solutions using eigenvalues and eigenvectors.
Ex-Lec P1 (Zoom Recording)
Ex-Lec P2 (Zoom Recording)