A Brief Introduction to the Linear Algebra Systems of Linear Equations and a Collection of Tasks in MATLAB (original) (raw)
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A Brief Introduction to the Linear Algebra Systems of Linear Equations
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The publication is intended for the Bachelor of Technical and Natural Sciences students. It aims to provide the necessary theoretical knowledge and the different methods on how to solve the systems of linear equations. Examples of solutions for practicing theoretical knowledge are included in this version. Additionally, the publication contains a chapter dealing with the resolution of the examples using the MATLAB and SageMath Systems. The database with the main terms of the subject is provided in the Register of this publication. * Keywords: the system of linear equations, determinant, regular matrix, inverse matrix, Gauss-Jordan elimination, the rank of a matrix, the linear combination of vectors, the linear dependence of vectors, infinitely many solutions, no solution, linear transformations, Computer Algebra, Matlab, SageMath, Bottleneck Algebra. ** Publication type: Textbook, University publication, e-book (online) version. *** Subject area: Mathematics - Linear Algebra - elementary level. Solved tasks of the publication: https://www.mathworks.com/matlabcentral/fileexchange/74889-linear-algebra-a-collection-of-tasks-in-matlab
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Solving linear systems is a fundamental task in several areas of mathematics and engineering, playing a crucial role in solving real-world problems. MATLAB, a powerful numerical computing platform, offers a wide range of tools and resources to efficiently address this type of problem. For the purposes of this article, we will explore how MATLAB can be used to solve linear systems. Additionally, MATLAB offers the ability to work with matrices, making it particularly suitable for dealing with systems of linear equations represented in this form. Through practical examples, we will illustrate how to use MATLAB functionalities to solve linear systems of different sizes and complexities. Finally, we will highlight the advantages of using MATLAB to solve linear systems, including its computational efficiency, ability to deal with large and complex systems, and the ease of visualizing results, making it a great tool to help students in their studies and research.
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Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the most fundamental topics.
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Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the most fundamental topics. r Hundreds of examples and exercises, including solutions, give students plenty of hands-on practice r End-of-chapter sections summarise material to help students consolidate their learning r Ideal as a course text and for self-study r Instructors can use the many examples and exercises to supplement their own assignments r Both authors have extensive experience of undergraduate teaching and of preparation of distance learning materials.
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Mat 320-Linear Algebra I Summary of Lectures
2012
Linear equations, translations to matrices, pages 4-6 in [1], [2] p'2. 1.2 January 11 Elementary row operations on matrices, Row Echelon Form (REF) of a matrix, solutions of system of linear equations using REF.Equivalent systems of equations. Lead and free variables. Pages 7-12 in [1], [2] pages 3-9, without matrix notation. 1.3 January 13 Reduced row echelon form of a matrix. How to find solutions of systems of equations using reduced row echelon form. Pages 13-14 in [1], Pages 46-49 [2]. Discussed system of homogeneous equations. Showed that for m homogeneous equations in n unknowns, with m < n one has always a nontrivial solutio