浅析行列式的计算技巧 毕业论文 13页

本科学年论文设计题目浅析行列式的计算技巧学院统计与数理学院专业数学与应用数学班级2007级1班学号姓名指导教师教务处制二一年六月摘要本文通过引用例题来对一些特殊行列式的求解技巧进行归纳分析，主要演示了化三角形法，降阶法，递推法，数学归纳法，辅助行列式法，拉普拉斯定理的应用，范德蒙得行列式的应用以及方阵特征值和行列式的关系的应用等方法。引言在平常的学习及其考试中经常能遇见有关特殊行列式计算的题目，如果不能掌握正确的方法和思维方式，此类型的题将会是考生的一个障碍，本人希望通过对若干经典考题的解析，使得学生对行列式求解类型的题目有章可循。A1A0A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A19A20A18A21A22A23A2A24A3A25A26A15A22A23A19A28A27A15A29A30A31A32A19A34A0A33A21A22A23A35A3A36A31A37A19A39A3A8A9A10A15A6A38A40A8A41A42A15A43A44A46A45A47A48A49A50A51A52A47A51A52A53A54A55A56A57A58A59A60A61A62A63A53A64A65A66A67A68A54A55A56A61A62A63A69A70A55A56A61A62A63A71A72A73A74A75A76A57A77A78A58A71A72A61A62A63A73A79A80A76A57A81A82A76A57A83A74A77A84A64A85A86A61A62A63A73A87A88A89A90A91A92A65A66A67A68A54A55A56A61A62A63A69A70A55A56A61A62A63A73A93A94A59A61A62A63A53A64A54A55A56A61A62A63A71A72A77A95A96A97A98A99A100A101A102A103A104A105A106A107A101A102A103A108A109A110A111A112A113A114A115A101A102A103A116A117A118A119A120A121A122A108A101A102A103A98A123A124A125A126A127A128A98A129A130A131A131A132A133A116A134A135A98A123A136A137A126A127A128A98A138A139A140A106A107A101A102A103A108A109A110A141A142A143A112A144A145A146A147A148A115A98A149A141A142A111A112A113A114A115A101A102A103A116A150A151A151A152A152A152A129A130A128A102A101A102A103A108A147A15312312341345121221NNNNDNNNLLLMMMMMLA154A155A156A155A156A157A158A159A160A161A162A163A164A165A166A167A168A169A170A171A172A173A174A175A171A176A177A178A179A180A181A182A183A184A168A169A170A185A186A187A188A189A190A191A192A193A194A195A196A197A198A199A200A195A201A202A200A195A203A204A205A206A194A207A208A209A210A194A211A212A213A214A215A195A216A211A217A218A212A219A192A193A205A206A194A195A196A197A220A221A222A194A223A191A193A205A195A212A193A205A206A224A195A220A221A222A194A223A191A193A205A206A194A195A212A200A225A191A193A200A195A220A221A222A194A223A191A193A224A195A226A227A228A229A193A194A215A220A221A222A194A223A191A230A215A231A212A232A233A234A235A236A237A238A239A215A195A216A212A240A241A242A243A244A245A246A226A247A248112,2,1111111111121111100031111200011111000100000010000020011120002000000100112IINNINRRINRRNNNDNNNNNNNNNNNNNNNNNNNNNNNNLLLLLLLLMMMMMMMMMMLLLLLLLLMMMMMMMMLLLL12121121112NNNNNNNA249A250A251A252A253A254A255A194A203A212A1A227A209A194A37A224A212A75A212A205A206A194A37A205A76A205A207A208A49A0A2A212A80A3A4A5A209A84A6A37A84A7A37A75A37A84A8A9A10A37A84A8A9A7A76A205A207A11A12A13A211A208A49A0A2A212A215A195A216A14A15A3A240A241A16A91A229A76A61A215A195A216A17A236A94A0A2A215A195A216A95A226A18A10A19A192A35A20A21A191A200A22A212A100A23A195A215A195A216A1020121101223411230,0,1,1NNNNIAAAAAAAADACINAAAAAAAALLMMMMLLLA24A25A1030121101223411230NNNAAAAAAAAAAAAAAAAALLMMMMLLA104A26A27A28A29A30A105A31A47A106A32A33A34A108A109A105A36A110A38A111A29A112A39A4010111102121231111201011201121230111011,NNNNNNNNNNNNNNNNNNNAAUAUUAAUAUAUUUUAAUAUUAAUAUAAUAUAUAUAUAUAUAUAUALLQMMLLLLML这里用到等）120111221112011111NNNNNNNNNUAAUAUUUUAUUFUFUAAUAUUULMLLM其中2122COSSIN1,101,NKNKKWNNWWKNWWWPIPIL设I为N次本原单位根有于是互异且为单位根2011101101011001111,0,1,1,JJJNNJIJJNNNNNWWJNWWWWWWAWFWWAWAWAWAWFWWFWWFWWFWWWWFWLLMLLLO记方阵则由上述知故）12210111111111,11NNNNNNWWWWWWWWWWL显然A31A41A42A43A44A45A46110A11NNNWWWFFWFWAWADFFWFWLL从而有A116A48A50A51A52A78A53A54A55A56A57A58A59A60A62A55A56A63A64A65A66A67A48A50A57011120102NNNNAAAAAADAAALLMMMLA64A120A681221NNNNDD而与只相差（）个符号121201,121121,1,2,1,123112NNNNNKNNNDFFWFWAAANUWFUUUNUFNLLLLL即得1从而当（时对单位根总有2111NFUUFUUUUNNNFUUL12111111,111111NNKNKNKKXXWXXXXXWNLL而又令则有121212122111211121121111121111121112112NNNNNNNNNNNNKKNNNNNNDFFWFWNNNWWWNNNWNNNNNLL从而有11A69A70A71A72A73A70A73A70A124NIJDAA74NA125A77A79A81A52A82A83A77A79A81A54A85A77A86A79A87A127A88A89A90A9211221,2,NIIIIININDAAAAAAINLLA13011221,2,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