Abstract
We started this work with a theorem that shows in which case the abbreviation rule for neutrosophic real numbers is true. We then detail in which cases the division of two neutrosophic real numbers yields a new neutrosophic number. Then, the solution cases of a neutrosophic linear equation with one unknown were examined. After calculating the determinant of a square matrix and giving the necessary and sufficient conditions for a square matrix to be invertible, the solution conditions of the systems of equations with the number of unknowns equal to the number of equations were examined.
Keywords
neutrosophic matrices neutrosophic systems of linear equations determinant of a neutrosophic square matrix inverse of neutrosophic square matrix
References
- F. Smarandache, Neutrosophy: Neutrosophic Probability, Set and Logic, Rehoboth: USA, American Research Press, 72 pages, 1998.
- M. Abobala, “Partial foundation of neutrosophic number theory”, Neutrosophic Sets and Systems, 39, 120-132, 2021.
- Y. Çeven, Ş. S. Tekin, “Some properties of neutrosophic ıntegers”, Kırklareli University Journal of Engineering and Science, 6(1), 50-59, 2020.
- M. Abobala, “On some neutrosophic algebraic equations”, Journal of New Theory, 33, 26-32,2020.
- S. A. Edalatpanah, “Systems of neutrosophic linear equations”, Neutrosophic Sets and Systems, 33, 92-104, 2020.
- H. Sankari, M. Abobala, “Neutrosophic linear diophantine equations with two variables”, Neutrosophic Sets and Systems, 38, 399-408, 2020.
- A. N. Yurttakal, Y. Çeven, “Some elementary properties of neutrosophic ıntegers”, Neutrosophic Sets and Systems, 41, 106-112, 2021.
- M. Abobala, A. Hatip, N. Olgun, S. Broumi, A. A. Salama, H. E. Khaled, “The algebraic creativity in the neutrosophic square matrices”, Neutrosophic Sets and Systems, 40, 1-11,2021.
- Y. A. Alhasan, “Types of system of the neutrosophic linear equations and Cramer’s rule”, Neutrosophic Sets and Systems, 45, 402-413, 2021.
- M. Abobala, M. Bal, A. Hatip, “A review on recent advantages in algebraic theory of neutrosophic matrices”, International Journal of Neutrosophic Science, 17(1), 68-86, 2021.
Abstract
References
- F. Smarandache, Neutrosophy: Neutrosophic Probability, Set and Logic, Rehoboth: USA, American Research Press, 72 pages, 1998.
- M. Abobala, “Partial foundation of neutrosophic number theory”, Neutrosophic Sets and Systems, 39, 120-132, 2021.
- Y. Çeven, Ş. S. Tekin, “Some properties of neutrosophic ıntegers”, Kırklareli University Journal of Engineering and Science, 6(1), 50-59, 2020.
- M. Abobala, “On some neutrosophic algebraic equations”, Journal of New Theory, 33, 26-32,2020.
- S. A. Edalatpanah, “Systems of neutrosophic linear equations”, Neutrosophic Sets and Systems, 33, 92-104, 2020.
- H. Sankari, M. Abobala, “Neutrosophic linear diophantine equations with two variables”, Neutrosophic Sets and Systems, 38, 399-408, 2020.
- A. N. Yurttakal, Y. Çeven, “Some elementary properties of neutrosophic ıntegers”, Neutrosophic Sets and Systems, 41, 106-112, 2021.
- M. Abobala, A. Hatip, N. Olgun, S. Broumi, A. A. Salama, H. E. Khaled, “The algebraic creativity in the neutrosophic square matrices”, Neutrosophic Sets and Systems, 40, 1-11,2021.
- Y. A. Alhasan, “Types of system of the neutrosophic linear equations and Cramer’s rule”, Neutrosophic Sets and Systems, 45, 402-413, 2021.
- M. Abobala, M. Bal, A. Hatip, “A review on recent advantages in algebraic theory of neutrosophic matrices”, International Journal of Neutrosophic Science, 17(1), 68-86, 2021.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | November 23, 2023 |
| Published in Issue | Year 2023 |