Mth501 Short Lecture 4 Row Reduction Echelon And Reduced Echelon Form Concept Building

Course Contents

Systems of Linear Equations, Row Reduction and Echelon Forms, Vector Equations, The Matrix Equation, Solution Sets of Linear Systems, Linear Independence, Linear Transformations, The Matrix of a Linear Transformation, Matrix Algebra, Iterative Solutions of Linear Systems, Determinants, Cramer’s Rule and Linear Transformations, Vector Spaces and Subspaces, Null Spaces, Column Spaces, and Linear Transformations, Linearly Independent Sets, Bases, Coordinate System, Dimension of a Vector Space, Rank, Change of Basis, Applications to Difference Equations,Eigenvalues and Eigenvectors, The Characteristic Equation,Diagonalization, Eigenvectors and Linear Transformations, Complex Eigenvalues, Discrete Dynamical Systems, Applications to Differential Equations, Iterative Estimates for Eigenvalues, Inner Product, Orthogonal and Orthonormal set, Orthogonal Decomposition, Orthogonal basis, Gram-Schmidt Process, Orthonormal basis, Least Square Solution, Inner Product Space, Application of inner product spaces.
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Course Synopsis
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. The goals of this subject are, how we can use Linear Algebra and its numerical applications in different fields.

Course Learning Outcomes
Upon completing this course students should be able :

To master the techniques for solving systems of linear equations.
To introduce matrix algebra as a generalization of single-variable algebra of high school.
To build on the background in Euclidean space and formalize it with vector space theory.
To relate linear methods to other areas of mathematics such as calculus and differential equations.
To develop an appreciation for how linear methods are used in a variety of applications.
Mth501 Short Lectures Mth501 Short Lecture 1 Mth501 Short Lecture 4 in Urdu Concept Building

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