ANALISIS KESALAHAN MENYELESAIKAN SOAL MATEMATIKA DALAM MATERI MATRIKS PADA SISWA KELAS XI IPS SMA NEGERI 1 ENDE

This study aims to determine: (1) mistakes have been made by the XI IPS grade students of SMA Negeri 1 Ende in solving matrix questions. (2) the factors that cause the XI IPS grade students of SMA Negeri 1 Ende in solving the matrix problem. (3) the efforts to solve students' errors in solving matrix questions in class XI IPS SMA Negeri 1 Ende. This study used a qualitative research approach using triangulation of sources and triangulation of techniques. The research subjects were 15 students of class XI IPS 3. The consideration of subject taking is based on the results of the error analysis according to the Newmann procedure. Methods of data collection using diagnostic tests, interviews, and documentation. The results of the research are: (1) the types of student errors are errors in understanding the concept of matrix count operations, process errors in solving matrix problems, and errors in concluding. 2) the factors that cause student errors are, students, choose the wrong formula, are not careful in solving matrix calculation operation problems, students are afraid to ask the teacher, and students' assumptions that mathematics is complicated, causing errors in determining the final answer. 3) while the efforts made were learning using rainbow matrix media which proved to be effective in learning matrix count operations.

Analisis kesalahan siswa kelas X agribisnis tanaman perkebunan SMK Negeri 1 Batang Gansal dalam menyelesaikan soal matriks

SMK N 1 Batang Gansal’s students have difficulty learning the matrix material. This can be seen from the result of students who get test scores below score 60. Especially in class x agribusiness plantations 1 with the percentage of daily test scores below score 60, which is 82.6%. Therefore, an analysis is needed to determine the types of errors that students tend to make in solving matrix problems. In this study, data collection was carried out using test and questionnaire methods, with data analysis using descriptive statistics. Based on the data analysis, it was concluded that the mistakes made by students in solving matrix problems were concept errors, principal errors and operational errors, with a tendency for errors in conceptual errors. The causes of errors are not understanding the concepts of matrix material, not listening when the teacher explains the material, not having complete notes or a summary of the matrix material, and not studying the matrix material at home, and not practicing working on various matrix questions so that they are unable to use formulas. matrix well.

A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator

Infinite-dimensional Newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations (PDEs). In computer-assisted proofs of PDEs, the original problem is transformed into the infinite-dimensional Newton-type fixed point equation $$w = - {\mathcal {L}}^{-1} {\mathcal {F}}(\hat{u}) + {\mathcal {L}}^{-1} {\mathcal {G}}(w)$$ w = - L - 1 F ( u ^ ) + L - 1 G ( w ) , where $${\mathcal {L}}$$ L is a linearized operator, $${\mathcal {F}}(\hat{u})$$ F ( u ^ ) is a residual, and $${\mathcal {G}}(w)$$ G ( w ) is a nonlinear term. Therefore, the estimations of $$\Vert {\mathcal {L}}^{-1} {\mathcal {F}}(\hat{u}) \Vert $$ ‖ L - 1 F ( u ^ ) ‖ and $$\Vert {\mathcal {L}}^{-1}{\mathcal {G}}(w) \Vert $$ ‖ L - 1 G ( w ) ‖ play major roles in the verification procedures . In this paper, using a similar concept to block Gaussian elimination and its corresponding ‘Schur complement’ for matrix problems, we represent the inverse operator $${\mathcal {L}}^{-1}$$ L - 1 as an infinite-dimensional operator matrix that can be decomposed into two parts: finite-dimensional and infinite-dimensional. This operator matrix yields a new effective realization of the infinite-dimensional Newton method, which enables a more efficient verification procedure compared with existing Nakao’s methods for the solution of elliptic PDEs. We present some numerical examples that confirm the usefulness of the proposed method. Related results obtained from the representation of the operator matrix as $${\mathcal {L}}^{-1}$$ L - 1 are presented in the “Appendix”.

ANALISIS KESULITAN MAHASISWA DALAM MENYELESAIKAN SOAL MATRIKS

This study aims to describe the type and location of student difficulties in solving matrix problems. This research is a survey research with quantitative and qualitative approaches. The sample in this study were 13 students from the Civil Engineering Study Program at Mataram UNMAS Denpasar Campus. Retrieval of data using test instruments and analyzed using quantitative-qualitative analysis. The results of this study indicate that the type of student difficulties related to facts is 13.64%, the difficulty in the concept is 31.31%, the difficulty in principle is 28.79% and the difficulty in the skill is 26.36%. While the location of students' difficulties on points is known to be 12.52%, points were asked at 12.52%, formula points were 4.46%, systemic completion points were 15.78%, inter-concept links were 11.15%, relationship points facts - concepts 12.35%, mathematical basic operating points 12.41% and final answer points 16.81%. The type and location of the most dominant difficulties students have in solving matrix problems lies in understanding the concepts and final answers of students.

Streamlined solutions to multilevel sparse matrix problems

We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints for the challenging, albeit rarer in applications, higher-level versions of the problem. While our linear system solutions are a concise recasting of existing results, our matrix inverse sub-block results are novel and facilitate streamlined computation of standard errors in frequentist inference as well as allowing streamlined mean field variational Bayesian inference for models containing higher-level random effects. doi: 10.1017/S1446181120000061

A better heuristic approach for n-job m-machine flow shop scheduling problem

Scheduling problem has its origin in manufacturing industry.In this paper we describe a simple approach for solving the flow shop scheduling problem. The result we obtained has been compared with Palmers Heuristic and CDS algorithms along with NEH. It was found that our method will reach near optimum solution within few steps compared to CDS and NEHalgorithm and yield better result compared to Palmers Heuristic with objective of minimizing the Makespan for the horizontal rectangular matrix problems.