| Conditional square matrices of order 2 with give determinant |
| کد مقاله : 1106-SLAA10 |
| نویسندگان |
|
مهدی حسنی * گروه ریاضی، دانشکده علوم، دانشگاه زنجان، زنجان، ایران |
| چکیده مقاله |
| In search of a method to generate matrices o order 2 with large positive integer elements and having small determinant, we prove that for given positive integers $d$, $M$ and $a_{ij}$ with $1\leqslant i,j\leqslant 2$ there exists many infinitely matrices $A=[a_{ij}]_{1\leqslant i,j\leqslant 2}$ with integer elements satisfying $a_{ij}\geqslant M$ and $\det A=d$. Our proof, which is based on the theory of linear diophantine equations with two variables, has capacity to be followed numerically. Hence, we present several practical examples of these conditional square matrices running over a Maple code. |
| کلیدواژه ها |
| Determinants, Linear Diophantine equation |
| وضعیت: پذیرفته شده مشروط برای ارائه شفاهی |