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Suci Rahmawati
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Religion Agriculture, Biological Sciences & Forestry Arts Humanities Civil Engineering, Building, Construction & Architecture Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Environmental Science Health Professions Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Library & Information Science Materials Science & Nanotechnology Mathematics Medicine & Pharmacology Nursing Public Health Social Sciences Veterinary Other

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Journal : contemporary mathematics and applications conmatha

 1 
Existence and Uniqueness of Homogeneous Linear Equation Solutions in Supertropical Algebra Yuliati, Dian; Suci Rahmawati
Contemporary Mathematics and Applications (ConMathA) Vol. 6 No. 2 (2024)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v6i2.63757

Abstract

This research investigates the existence and uniqueness of solutions to homogeneous linear equations in supertropical algebra. We analyze the structure of supertropical matrices to identify the conditions in which nontrivial solutions exist for the system of equations A⊗? ⊨ ?, where A is a matrix over a supertropical semiring and x is a vector. By applying determinant-based criteria, we demonstrate how tropical and supertropical values influence the solution space. The research applies theorems that determine the presence of trivial and nontrivial solutions and uses examples to illustrate practical methods for solving homogeneous matrix systems. This highlights the distinct characteristics of supertropical algebra compared to classical linear algebra. Our findings provide a deeper insight into solution behaviors in supertropical systems, paving the way for further research in tropical mathematics.
Co-Authors Abraham Pranata Sitinjak ABS, M Khoirul Adam Agung Darmawan Ahmad Yani Alfian Anhar Angella Putri Ramadhani Anisa Rahma Annisa Fitriani Ayuni Harianti Az-zhara Diah Putri Nugroho Azizah Azis Azmia Siti Munasifah Chika Muthi’atul Fadhilah Didin Nurwahidin Difana Meilani Dimas Ganjar Pinasti Dwi Ishartani Dwi Kurnia Edhi Nurhartadi Elisabeth Brielin Sinu Falha Himatul Aliyah Farly Oktriany Haning Fauzan Adhipratama Arasyid Firdaus Annas Firmansyah Firmansyah Gun Faisal Hasim . Hermandra ' I Made Alit Widnyana Ilone Virginia Oktavian Ina Nazirotun Mubarokah Insan Saputra Joni Ahmad Mughni Kamelia Agnesta Kurnia Dewiani Lina Marlina Liss Dyah Dewi Arini Liza Efriyanti, liza Lusi Susanti Lutfiyah Hakim M. Agus Salim Mangatur Sinaga MARIA LOBO Mohonia Sabarito Sitohang Muhamad Nauval Ardani Muhammad Farhan Zein Muhammad Yusuf Nasution Muhyi, Asep Abdul Mulis . Nazar Faddilah Nazla Maharani Umaya Neng Nazma Aulia Nisa Afrawasih Novianti Novianti Novrita, Sri Zulfia Nurul Hafiza Ainanur Nurur Ramadan Palahudin Palahudin Pedia Aldy Pipit Prima Fithri Puji Hujria Suci Puspaneli Puspaneli Raihani Fauziah Ratu Ilma Indra Putri Regina Bhayangkara Rina Erlita Rizky Arta Harianto Rossana Sapta Kusumah Sabrina Salsabila Salsanabilah Rahmawati Septi Permatasari Sherly Afiyani Nurhidayati siti bariroh Siti Hindun Siti Khulasoh Siti Nadya Safira Supriadi Try Susanti Tsazkiya Aqiila Salsabila Tuti Anggriani Utama Ulfa Nadiatur Rahmi Vania Nabila Arisanti Wafa Jannatul Ma’wa Wafa Syakila Wan Muhammad Fariq Widiarti Permana Sari Wildan Ahmad Wulan Indriani Yetti Purnama Yuliati, Dian Yusanti, Linda Yusuf Andika Rachmat