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### Title – Algebra (Code-09010101)

 S.N Unit Content of the topics Learning objects Teaching Guidelines Methodology Time (Hrs) 1 one ·   Symmetric, Skew- Symmetric matrices ·   Hermitian, Skew- Hermitian matrices ·   ,Elementary operations on matrices ·   Rank of matrices ,inverse of matrices ·   L.D and L.I. of rows and columns ·   Eigen values, eigenvectors and Char. Equation of a matrix ·   Minimal polynomial of a matrix ·   Cayley Hamilton Theorem and find inverse of a matrix. Students will be able to   1. Understand matrix operations and rank of matrices. 2. Eigen values and eigen vectors. 3. Caley Hamilton theorem and its application. Lecture should be effective so that student can grasp the topics easily. 1. Lecture. 2.  Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5.  Discussion on Assignment. 6. Evaluation of Assignment. 15 2 Two ·   Homogeneous and non Homogeneous ·   Application of matrices to a system of linear equations, ·   Theorems on consistency of a system of linear equation ·   Unitary and orthogonal matrices, ·    Bilinear and Quadratic forms of matrices. Students will be able to 1.   Understand matrix operations and rank of matrices. 2.   Eigen values and eigen vectors. 3.   Caley Hamilton theorem and its application. Lecture should be effective so that student can grasp the topics easily. 1.    Lecture. 2.     Seminar. 3.    Discussion. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15 3 Three ·   Relation between the roots and coefficients of general polynomial equation in one variable, ·   Solutions of polynomial equation having conditions on roots, ·   Common roots and multiple roots, ·   Transformation of equation. To make students familiar with Relation between the roots and coefficients of general polynomial equation in one variable, and its application in various field. Lecture should be effective sothat student can grasp the topics easily. 1.    Lecture. 2.    Seminar. 3.    Discussion. 4.    Assignment. 5.    Discussion on Assignment. 6.    Evaluation of Assignment 15