Practical No3 MT112 Practical course on Matrix Algebra FYBSC KBCNMU chavanmathsindia

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#practicalcourseonmatrixalgebra • #matrixalgebra • CLASS: F.Y.B.Sc Sem.-I • Subject: MT-112 Practical course on Matrix Algebra • Prepared by:- Prof. Achyut A. chavan • University:-KBCNMU JALGAON • F. Y. B. Sc. (Mathematics) • As per NEP 2020 for Affiliated Colleges With effect from June 2024 • Practical No.-1: Adjoint of a matrix • Types of a matrices, elementary operations on matrices, Minors and Co-factors • of a matrix, Adjoint of a matrix. • Practical No.-2: Inverse of a matrix • Inverse of a matrix, Existence uniqueness theorem of inverse of a matrix, • Properties of inverse of a matrix • Practical No.-3: Elementary matrices and normal form of a matrix • Elementary transformations, Elementary matrices, Inverse of matrices using • elementary transformations, Reduction to normal form, Normal form (canonical • form) of a matrix. • Practical No.-4: Rank of a Matrix • Rank of matrix, Invariance of rank under elementary transformations, Rank of • product of two matrices. • Practical No.-5: Application of matrices to solve the system of linear equations • Homogeneous and non-homogeneous system of linear equations, Consistency • and non-consistency of system of linear equations, Solution the system of linear • equations using matrices. • Practical No.-6: Eigen values and Eigen vectors of matrices • Characteristic equation of a matrix, Cayley Hamilton theorem (statement only) • and its use to find the inverse of a matrix, Eigen values and Eigen vectors of • matrices. • Practical No.-7: Orthogonal Matrices • Orthogonal Matrices, Properties of Orthogonal Matrices. • Practical No.-8: Quadratic Forms • Quadratic forms: matrix representations, Elementary congruent • transformations, Diagonal form of a quadratic form, Canonical forms.

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