Week 8: Linear Combination, Linearly Dependent and Independent vectors. Basis and dimensions of a vector space.
Linear Combination, Linearly Dependent and Independent vectors. Basis and dimensions of a vector space.
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Course Material
- Week 1: Introduction to Matrices. Vectors and system of linear equations.
- Week 2: Solving system of linear equations using Gaussian Elimination Method, Gauss Jordan Method.
- Week3: Inversion method in matrices, methods to calculate inverse of the given matrix.
- Week 4: Introduction to Determinents. Determinents by Cofactor Expansions Evaluation Determinents by row reduction.
- Week 5: Properties and Applications of Determinents. Area and Volume of triangle and parallelogram.
- Week 6: Introduction to Vector Space and Subspace. Norm, distance, Dot product, Cross product.
- Week 7: Vector in 2-dimensional, 3-dimensional and n-dimensional space. Row space, Column space and Null space.
- Week 8: Linear Combination, Linearly Dependent and Independent vectors. Basis and dimensions of a vector space.
- Week 9: Mid Term Exam
- Week 10: Eigen values and Eigen vectors, Diagonalization.
- Week 11: Rank, nullity and the fundamental matrix spaces.
- Week 12: Orthogonal Bases and Gram Schmidt Ortho normalization Process.
- Week 13: Complex vectors and matrices, Complex numbers. Unitary and Hermitian matrices.
- Week 14: Markov Matrices, Linear Algebra for functions.
- Week 15: Symmetric Matrices, Positive Definite Matrices, Singular Value Decomposition.
- Week 16: Inner product spaces.
- Week 17: Applications of Matrices in Engineering, Graphs, Networks.
- Week 18: Final Term Exam.
- Chapters 18
- Department CS & IT
- Teacher
Bisma Kazmi
