| 解一次不定方程的初等变换方法 |
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| 引用本文： | 王路群,刘英,李凤霞,刘冬丽.解一次不定方程的初等变换方法[J].高师理科学刊,2011,31(4):33-37. |
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| 作者姓名： | 王路群 刘英 李凤霞 刘冬丽 |
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| 作者单位： | 哈尔滨师范大学 恒星学院信息科学系,黑龙江哈尔滨,150025 |
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| 基金项目： | 黑龙江省高等学校教学改革工程项目(一般项目序号96) |
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| 摘 要： | 利用线性代数中的初等变换方法解一次不定方程,主要结论为:设A=(a1 …an -b In O)为n+1阶整数矩阵,若A的n列子块经若干列初等变换以及cn+1+aci(1≤i≤n)型初等变换化为矩阵 D=(d 0…0 0 C b1…bn)（d≠0,C=(cij)∈znxn）,则不定方程a1x1+…+anxn=b有解且...
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| 关 键 词： | 不定方程 整数矩阵 初等变换 最大公约数 |
Elementary transformation method of solving linear indeterminate equation of the first degree |
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| WANG Lu-qun,LIU Ying,LI Feng-xia,LIU Dong-li.Elementary transformation method of solving linear indeterminate equation of the first degree[J].Journal of Science of Teachers＇College and University,2011,31(4):33-37. |
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| Authors: | WANG Lu-qun LIU Ying LI Feng-xia LIU Dong-li |
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| Institution: | WANG Lu-qun,LIU Ying,LI Feng-xia,LIU Dong-li(Department of Information Science,Star College,Harbin Normal University,Harbin 150025,China) |
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| Abstract: | Discussed using elementary transformations of linear algebra to solve indeterminate equation,the mainly results as follows,let A=（a1…an-b In O） be an（n＋1）×（n-1） integral matrix.If A can be taken into the following matrix D=（d0…0 0 b1…b1 c）（d≠0,C=（cij）∈Zn×n） by applying several column elementary transformations and cn＋1＋a ci（1≤i≤n）forms elementary transformations to blocks of A,then indeterminate equation has solution and all solutions are xi=bi＋ci2t2＋…＋cintn（i=1,…,n,t2,…,tn∈Z）. |
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| Keywords: | indeterminate equation integer matrix elementary transformation greatest common divisor |
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