scholarly journals Necessary and Sufficient Conditions for The Solutions of Linear Equation System

2020 ◽  
Vol 17 (1) ◽  
pp. 82-88
Author(s):  
Gregoria Ariyanti
Keyword(s):  
Linear Equation ◽  
Commutative Semigroup ◽  
Algebraic Structure ◽  
Identity Element ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Equation System ◽  
Distributive Property ◽  
Linear Equation System ◽  
Necessary And Sufficient

A Semiring is an algebraic structure (S,+,x) such that (S,+) is a commutative Semigroup with identity element 0, (S,x) is a Semigroup with identity element 1, distributive property of multiplication over addition, and multiplication by 0 as an absorbent element in S. A linear equations system over a Semiring S is a pair (A,b)  where A is a matrix with entries in S  and b is a vector over S. This paper will be described as necessary or sufficient conditions of the solution of linear equations system over Semiring S viewed by matrix X  that satisfies AXA=A, with A in S.  For a matrix X that satisfies AXA=A, a linear equations system Ax=b has solution x=Xb+(I-XA)h with arbitrary h in S if and only if AXb=b.

scholarly journals Profil Berpikir Siswa dalam Menyelesaikan Soal Sistem Persamaan Linear

2019 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
K. Ayu Dwi Indrawati ◽  
Ahmad Muzaki ◽  
Baiq Rika Ayu Febrilia
Keyword(s):  
Qualitative Research ◽  
Linear Equation ◽  
Linear Equations ◽  
Equation System ◽  
Mathematical Ability ◽  
System Of Linear Equations ◽  
Mathematics Ability ◽  
Linear Equation System ◽  
Thinking Process ◽  
Descriptive Qualitative

This research aimed to describe the thinking process of students in solving the system of linear equations based on Polya stages. This study was a descriptive qualitative research involving six Year 10 students who are selected based on the teacher's advice and the initial mathematical ability categories, namely: (1) Students with low initial mathematics ability, (2) Students with moderate initial mathematics ability, and ( 3) students with high initial mathematics ability categories. The results indicated that students with low initial mathematical ability category were only able to solve the two-variable linear equation system problems. Students in the medium category of initial mathematics ability and students in the category of high initial mathematics ability were able to solve the problem in the form of a system of linear equations of two variables and a system of three-variable linear equations. However, students found it challenging to solve problems with complicated or unusual words or languages.

scholarly journals On the solvability of systems of linear equations on commutative semigroup

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Nguyen Thi Thu Huyen ◽  
Nguyen Minh Tuan
Keyword(s):  
Linear Operator ◽  
Linear Space ◽  
Commutative Semigroup ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Operator Equations ◽  
Systems Of Linear Equations ◽  
Necessary And Sufficient ◽  
Linear Operator Equations

AbstractThis paper deals with the solvability of systems of linear operator equations in a linear space. Namely, the paper provides necessary and sufficient conditions for the operators under which certain kinds of systems of operator equations are solvable.

scholarly journals IMPULSIVE AND REFLECTIVE STUDENTS’ UNDERSTANDING TO LINEAR EQUATIONS SYSTEM: AN ANALYSIS THROUGH APOS THEORY

MATHEdunesa ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 128-135
Author(s):  
Dinda Ayu Rachmawati ◽  
Tatag Yuli Eko Siswono
Keyword(s):  
Linear Equation ◽  
Cognitive Style ◽  
Junior High School ◽  
Linear Equations ◽  
Equation System ◽  
Mathematical Concept ◽  
Apos Theory ◽  
Process Stage ◽  
Linear Equation System ◽  
Action Process

Understanding is constructed or reconstructed by students actively. APOS theory (action, process, object, schema) is a theory that states that individuals construct or reconstruct a concept through four stages, namely: action, process, object, and scheme. APOS theory can be used to analyze understanding of a mathematical concept. This research is a qualitative research which aims to describe impulsive and reflective students’ understanding to linear equations system based on APOS theory. Data collection techniques were carried out by giving Matching Familiar Figure Test (MFFT) and concept understanding tests to 32 students of 8th grade in junior high school, then selected one subject with impulsive cognitive style and one subject with reflective cognitive style that can determine solutions set and solve story questions of linear equation system of two variables correctly, then the subjects were interviewed. The results show that there were differences between impulsive and reflective subjects at the stage of action in explaining the definition and giving non-examples of linear equation system of two variables, show the differences in initial scheme of two subjects. At the process stage, impulsive and reflective subjects determine solutions set of linear equation system of two variables. At the object stage, impulsive and reflective subjects determine characteristics of linear equation system of two variables. At the schema stage, impulsive and reflective subjects solve story questions of of linear equation system of two variables, show the final schematic similarity of two subjects.Keywords: understanding, APOS theory, linear equations system of two variables, impulsive cognitive style, reflective cognitive style.

scholarly journals How to Teach Mathematical Concept Easily? (Learning Trajectory of Two-Variable Linear Equation System Topic in Junior High School)

2020 ◽  
pp. 5-13 ◽  
Author(s):  
H. Retnawati ◽  
E. Sulistyaningsih ◽  
R. Rasmuin
Keyword(s):  
High School ◽  
High School Students ◽  
Linear Equation ◽  
Junior High School ◽  
Design Research ◽  
Junior High ◽  
Linear Equations ◽  
Equation System ◽  
Learning Trajectory ◽  
Linear Equation System

The intention of this study was to find the learning trajectory of two-variable linear equations system in Junior High School. This study was design research using validation study. The participants of this study were Junior High School students in grade IX SMPIT Luqman al-Hakim Yogyakarta Indonesia. Data were collected through observation and interview. Data were analysed using Milles & Huberman model. Result revealed that the learning trajectory of the two-variables linear equation system were to deepen the mastery of algebra and one-variable linear equation system, model the two-variable linear equation system, solve the experiments, complete the two-variable linear equation using graphs, complete two-variable linear equations by substitution, simple elimination, complex elimination, and mixed method, and solve two-variable linear equation system problems. Keywords: learning trajectory, two-variable linear equation system, design research.

scholarly journals Analysis of Student Errors in Solving Mathematics Problems Based on Watson's Criteria on the Subject of Two Variable Linear Equation System (SPLDV)

2021 ◽  
Vol 1 (2) ◽  
pp. 125-131
Author(s):  
Hastuty Musa ◽  
R. Rusli ◽  
Ilhamsyah ◽  
A. Yuliana
Keyword(s):  
Linear Equation ◽  
Linear Equations ◽  
Equation System ◽  
Hierarchy Problem ◽  
Response Level ◽  
Descriptive Research ◽  
Mathematics Problems ◽  
Linear Equation System ◽  
Class Viii ◽  
Student Errors

The purpose of the study was to describe the types of student errors and the factors that caused students to make mistakes in solving a two-variable system of linear equations based on Watson's criteria for class VIII MTs Pattuku. This type of research is descriptive research using a qualitative approach. The subjects in this study were students of class VIII MTs Pattuku then chose 3 subjects to be interviewed who had the most types of errors based on Watson's criteria. The research instrument used was a diagnostic test consisting of 3 questions about a two-variable linear equation system and interview guidelines. From the results of this study, it shows that there are no students who make mistakes in missing data (committed data) and indirect manipulation (undirected manipulation). 16% made incorrect data errors (innapropriate data), 40% made incorrect procedural errors (innapropriate procedure), 68% made an omitted conclusion error, 24% made a response level conflict error, 36% made mistakes in the skill hierarchy problem, and 48% made mistakes other than the 7 categories above (above other).

scholarly journals Development E-Module Three Variables Linear Equations System Based On Mathematic Communication

2021 ◽  
Vol 5 (2) ◽  
pp. 377
Author(s):  
Latifah Rani ◽  
Samsul Maarif
Keyword(s):  
Linear Equation ◽  
Electronic Device ◽  
Technological Development ◽  
Human Life ◽  
Linear Equations ◽  
Equation System ◽  
New Paradigm ◽  
Laptop Computer ◽  
Mathematical Communication ◽  
Linear Equation System

This rapid technological development has a very significant impact on various aspects of human life, one of which is in the aspect of education. The existence of technological developments in the aspect of education gave rise to a new paradigm in which participants acted as constructors in managing the information gained knowledge and educators as facilitators who guide students in learning activities with the aid of an electronic device. However, the use of electronic devices in the form of laptops/computers has not been well implemented to make students passive, and mathematical communication skills are not optimal. Students still consider the material of the Three Variable Linear Equation System to be quite difficult. So, we need innovative learning media in the form of e-modules. The purpose of this study was to develop the contents and find out the quality of e-modules in the material of the Mathematical Communication Based Three Variable Linear Equation System. This research is development research that adapts the ADDIE development model. The results of this study are in the form of an e-module on the material of the Three Variable Linear Equation System based on mathematical communication that can be operated on a laptop/computer offline. The product has been validated by media experts and material experts and gets results in the Good category. The product was also tested on 46 respondents and obtained results in the Good category. Thus, the e-module of the Three Variable Linear Equation System based on mathematical communication is appropriate for use in learning. Keywords: e-module, Linear Equation System of three variables, mathematical communication.

scholarly journals PENERAPAN MEDIA SIMULASI MATLAB BERBASIS INTERACTIVE CONCEPTUAL UNTUK MENINGKATAN PEMAHAMAN KONSEP MAHASISWA

2017 ◽  
Vol 6 (2) ◽  
pp. 189
Author(s):  
Davi Apriandi ◽  
Reza Kusuma Setyansah
Keyword(s):  
Linear Equation ◽  
Linear Equations ◽  
Equation System ◽  
Student Understanding ◽  
Student Response ◽  
Matlab Simulation ◽  
Research Subjects ◽  
Linear Equation System ◽  
Comprehension Tests ◽  
Academic Year

This study aims to know the extent to which the use of Matlab simulation media based conceptual Interactive can overcome the difficulties of students in understanding the Linear Equation System in the course of Numerical Analysis and improve student understanding. This study is a classroom action research, which is carried out in two cycles. Research subjects as many as 25 students grade 7C Prodi Mathematics Education University PGRI Madiun academic year 2016/2017. Research instruments are researchers, learning observation sheets, concept comprehension tests, student response questionnaires and interview guides. Based on the result of the research, it can be concluded that the application of Matlab simulation media based on conceptual interactive in learning can increase the students understanding on Linear Equation System. This is shown by the improvement of students' ability in understanding the system of linear equations in each cycle. The data is also supported by a positive response given by students in learning.

Teaching Materials of Problem-Based Linear Equation System with Two-Variables for Eighth-Grade Students in Junior High School

2021 ◽  
Vol 1 (1) ◽  
pp. 119-123
Author(s):  
Nurhayati Abbas ◽  
Nancy Katili ◽  
Dwi Hardianty Djoyosuroto
Keyword(s):  
High School ◽  
Linear Equation ◽  
Junior High School ◽  
Junior High ◽  
Equation System ◽  
Eighth Grade ◽  
Teaching Material ◽  
Teaching Materials ◽  
Linear Equation System ◽  
Eighth Grade Students

This research is motivated by the lack of mathematics teaching materials that can make students learn on their own. The teaching material can be created by teachers as they are the ones who possess the knowledge about their students’ characteristics. Further, learning materials are a set of materials (information, tools, or texts) that can aid teachers and students to carry out the learning process. The two-variable linear equation system (SPLDV) is one of the mathematics materials taught to eighth-grade students of junior high school; it contains problems related to daily life. However, it is found that this material is still difficult to master by most students. Therefore, it is necessary to develop the SPLDV teaching materials that can help students learn and solve problems as well as be used as examples by teachers in developing other materials. This research aimed to make problem-based SPLDV teaching materials. The research method refers to the Four-D Model by Thiagarajan, Semmel, and Semmel (1974). It consisted of defining, designing, developing, and disseminating. The results showed that problem-based SPLDV teaching materials could be used in learning activities as the students and the teachers had shown their positive responses after going through expert assessments. This study also suggested that the teachers use this teaching material and adopt teaching materials for other similar materials.

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