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All Journal Jurnal Penelitian Pendidikan IPA (JPPIPA) Jurnal Perspektif
Hamidah Nasution
State University of Medan
Agriculture, Biological Sciences & Forestry Arts Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Economics, Econometrics & Finance Education Engineering Materials Science & Nanotechnology Physics Other

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Cofactor Expansion Approaches for Generalized Determinants of Non-Square Matrices Mulyono Mulyono; Hamidah Nasution; Rizki Habibi; Silvya Ajeng Saraski
Jurnal Penelitian Pendidikan IPA Vol 11 No 11 (2025): November
Publisher : Postgraduate, University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jppipa.v11i11.12335

Abstract

Determinants are conventionally defined only for square matrices, which leaves the theoretical discussion of rectangular matrices relatively undeveloped. This study aims to extend determinant theory by introducing a generalized form of the cofactor expansion applicable to non-square matrices. The method employed in this research is a theoretical–analytical approach that begins with identifying fundamental determinant axioms and proceeds with the construction of a recursive cofactor expansion for   matrices with . Worked examples are used to demonstrate the linearity, antisymmetry under row interchange, and reduction consistency of the proposed formulation when applied to square matrices. The findings indicate that the generalized expansion preserves essential algebraic properties and shows compatibility with established rectangular determinant definitions, including the Radić determinant. Overall, this study provides a coherent theoretical foundation for the generalized determinant of rectangular matrices and contributes to broader applications of determinant-based analysis in linear algebra
Development of Mathematics Learning Devices Based on Problem Based Learning Integrated with STEM to Improve Critical Thinking Abilities and Mathematical Communication Abilities Rizkiyan Hadi; Hamidah Nasution; Asmin Asmin
Jurnal Perspektif Vol 9 No 1 (2025): Jurnal Perspektif
Publisher : UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/jp.v9i1.340

Abstract

Penelitian ini bertujuan untuk:  Mendeskripsikan kevalidan, kepraktisan, keefektifan perangkat pembelajaran matematika berbasis problem based learning terpadu STEM untuk meningkatkan kemampuan berpikir kritis dan kemampuan komunikasi matematis siswa; Mendeskripsikan peningkatan kemampuan berpikir kritis dan kemampuan komunikasi matematis siswa setelah belajar dengan perangkat pembelajaran matematika berbasis problem based learning terpadu STEM. Metode penelitian merupakan penelitian pengembangan dengan menggunakan model ADDIE.  Penelitian ini dilaksanakan di kelas VII  semester I T.A 2024/2025. Hasil penelitian ini diperoleh bahwa:LKPD model problem based learning berbasis STEM yang dikembangkan dinyatakan sudah valid,praktis dan efektif; Peningkatan kemampuan berpikir kritis dan kemampuan komunikasi matematis siswa kelas VII MTs Riyadhussholihin melalui LKPD  berbasis PBL yang dikembangkan dinyatakan meningkat dari uji coba I ke uji coba II  dilihat dari N-Gain. Pada uji coba I, Pada uji coba II, peningkatan kemampuan berpikir kritis dan kemampuan komunikasi matematis siswa matematis sebesar 0,46 dan peningkatan kemandirian belajar siswa sebesar 0,42. Pada uji coba II peningkatan kemampuan berpikir kritis dan kemampuan komunikasi matematis siswa matematis memiliki N-gain yaitu sebesar 0,59 sedang.
Co-Authors Asmin Asmin mulyono mulyono Rizki Habibi Rizkiyan Hadi Silvya Ajeng Saraski