Week 1: Introduction to Systems of Linear Equations and Matrices
i) Recognize a linear equation in n variables.
ii) Find a parametric representation of a solution set of a system of linear equations.
iii) Write a system of linear equations in matrix form.
iv) Solve a system of linear equations by Gaussian elimination, Gauss-Jordan elimination and Cramer’s Rule.
v) Matrices and Matrix Operations, Algebraic Properties of Matrices, Types of matrices.
Chapter 1 (Linear Algebra and its Applications by Howard Anton and Chris Rorres)
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Course Material
- Week 1: Introduction to Systems of Linear Equations and Matrices
- Week 2: LU-Factorization, Inversion method in matrices, Elementary matrices and a method for finding A^-1
- Week 3: Determinants by Cofactor Expansion, Evaluating Determinants by Row Reduction, Properties of Determinants
- Week 4: Vectors in 2-Space, 3-Space, and n-Space, Norm and Distance, Orthogonality, Dot Product, Cross Product
- Week 5: Vector Spaces and Subspaces
- Week 6: Linear combination, Linearly dependent and Linearly Independent
- Week 7: Coordinates and Basis, Dimension
- Week 8: Eigenvalues and Eigenvectors, Diagonalization.
- Week 09: Mid Term Exam
- Week 10: Complex vectors and matrices; complex numbers, Hermitian and Unitary matrices
- Week 11: Row Space, Column Space, and Null Space
- Week 12: Rank, Nullity, and the Fundamental Matrix Spaces
- Week 13: Linear algebra for functions
- Week 14: Symmetric matrices, Positive Definite matrices, Singular Value Decomposition
- Week 15: Inner product space
- Week 16: Orthogonal bases and Gramm-Schmidt process
- Week 17: Applications; Markov matrices, matrices in engineering, graph and networks.
- Week 18: Final Term Exam
- Chapters 18
- Department CS & IT
- Teacher
Iqrar Ansari
