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• Week 01:Representation of Linear equations in Matrix form, Operations on Matrices
• Week:02 Echelon and Reduced Echelon form, Solution of linear system, Gauss-Jordan method, Gaussian elimination
• Week 03: Inverse of a matrix (by elementary row operations), Determinants and their Computations
• Week 04:. Definition of higher order determinants. Properties of Determinants, Expansion of determinants
• Week 05: Introduction to Vector Spaces,examples and preliminary results
• Week 06: Subspace : Definition ,Examples and related results
• Week 07: Linear combination of a set of vectors,Linearly independent set of vectors: Definition ,examples and results
• Week 08: Basis of a Vector space:Definition ,examples and related results
• Week 09: Mid Term Exam
• Week 10 : Dimension of a vector space :Definition ,examples and related results
• Week 11: Change of Basis,Linear transformation ;Definition,Examples ,results
• Week 12: Null Space ,Basis for Solution space of Homogeneous System rank of Matrix
• Week 13: Kernel and Image of a linear transformation ,Rank and Nullity of Linear Transformation
• week 14 : Linear Transformations ,reflection ,projections homotheties, matrix of linear transforamtion
• Week 15: . Eigen-values and eigenvectors. Theorem of Hamilton-Cayley.
• Week 16 : Diagonalization ,Inner Product spaces with properties
• Week 17 ;Inner product Spaces:Projection,Cauchy inequality,Orthogonal and orthonormal basis. Gram Schmidt Process.
• Week 18 : Final Term Exam