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Suci Rahmawati
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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 Annisa Fitriani Ayuni Harianti Az-zhara Diah Putri Nugroho Azizah Azis Azmia Siti Munasifah Azya Maharani Oktaputri Chika Muthi’atul Fadhilah Didin Nurwahidin Difana Meilani Dio aguswantoro Dwi Ishartani Dwi Kurnia Edhi Nurhartadi Elisabeth Brielin Sinu Falha Himatul Aliyah Farly Oktriany Haning Firmansyah Firmansyah Gun Faisal Hasim . Hermandra ' I Made Alit Widnyana Ilone Virginia Oktavian Insan Saputra Joni Ahmad Mughni Kamelia Agnesta Kurnia Dewiani Lina Marlina Liss Dyah Dewi Arini 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 Neng Nazma Aulia Nisa Afrawasih Novianti Novianti Novrita, Sri Zulfia Nurul Hafiza Ainanur 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 Salsanabilah Rahmawati Septi Permatasari Sherly Afiyani Nurhidayati siti bariroh Siti Hindun Siti Khulasoh Siti Nadya Safira Sularno Supriadi 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