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  • 2022-06-16
     用正交变换 法将下列二次型化为标准形，并写出所作的正交变换的矩阵：[tex=12.929x1.357]CKlOGn/4oc+CIjd/NrEXYLzReNaNBndVcM3x5k1BscqqBTNxm1O35m/m+o6M8ADkIFbIKHTGp+1f1trx2pVTi6GTbBb4dXJ6vkppKLfTt1Q=[/tex]
    • [b]解  [/b]二次型 [tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex]的矩阵[tex=11.143x4.786]+HNIZcMaSzNwCe0LO7bsUtE7T/ezT3heRoWANqpeD09eLZlwyEoJwbKWaMHfngHBLush4fFULq846HhHX4nA17t9cPTFg/CR4hmdv7q7cTtJBttccKG7/VuHehSXQBkYz4xdGVCB6ypRDvwQIqdnrXE/exo8k1yxGGc0zEEfsOw=[/tex]矩阵 [tex=0.929x1.0]JkZEjSnuwtkZlFnZMXvQ5Q==[/tex]的特征多项式[tex=19.929x5.214]Ld41YouFXqd2n+lAjQyRIdTTvT/pyghQ23x/Y1VIONO9uIEhF3HmDUtcyWZ0oIiBDSbCUt286XqfpC4WfIhkSpqcWHrcuyzeozbX8QXGpX5xWKDwhm3OMZH5T5a3E1q0YsDcHRjYF/9f4eaOYIjVSA9G7xjqyTEB+DruAUKjPf0MVsdEWExe/6FsZUeJ1w1wvDFZ/dLLYuKzJwI7AwI6YG/hHNp1LLO7sCZwoo54ApWko/k7vwXJKZpBEkt/qMHc6OEkoDUg26wm6P3EsDXh+A==[/tex]令 [tex=4.929x1.357]Ld41YouFXqd2n+lAjQyRIdTTvT/pyghQ23x/Y1VIONNi0/X6TQSMYpSczc4oNr8M[/tex]，得矩阵 的特征值[tex=8.929x1.214]6CzHpBoEVdfGanuoycm4yFUSj/2JzS5zP1FYOPXS6mkNH/3D2gHr8HxbubeUGmFB6rOWTa3ST+1tC0JYhuSaIg==[/tex]。对于 [tex=3.929x1.214]6CzHpBoEVdfGanuoycm4yAWZu2OgO1dKTmQSQi26Nfc=[/tex]，解齐次线性方程组 [tex=5.286x1.357]gudbqgCftubGGIHOy6IcjZIRKZHNfuPUz7Laj7C/drA/ltncBS2ECIKv5LCnXl60sZ6OJ3eo0jlTbrW4G20Ftw==[/tex]，得对应的特征向量 [tex=18.929x1.5]spsZ+rMIOMiqBxP/ZoH2F9iNWsaEegqh8ld8GRxvVZ5Wxc/yKXpRjOCoXAenu0sKGmgpm5B+QxxeMHcZjRZE+ifu0keU9j9ywB65UsPfOQqLT8tKYaCreU2LkGXO55oOBmPub68AT+rXw3xgFmTkRdz8qO8WMFsZEt8q7ikFjENz6hlGXeeFBddc8yj8NSyc[/tex]已是正交向量组，只需将其单位化：[tex=14.643x3.0]Bon++APCFFqGDVhoG+r8OZ8HGhv4G64apDOcUVicxMg0N4WhXETspH0XYRuoiBYvB8C8ePiEoEQQdnaXIXQAkr/E53PpngSrHJXDF3cxvLObU7gCznSibZkunIkguQ0QmDRMtfUtziFHecGrOmXW6AEh1f2xifMYHl9o7UggZ7mV60xxPjjiU1w5Hsp44qvoEZZVqDUL9HdFhEW6u0JELcSecsaJB7X3QSR9mWHnmPA=[/tex][tex=15.357x3.0]Bon++APCFFqGDVhoG+r8OQMYIT+Sy4e273D5soUtmn/CEMKtMS3+zjYkxLpbZFKn/PEx6i8549Wa4zEabOfViyv0mtoIwgRu+u5k3jUG5gzDNxZGD0b4ODYkmvNoM+92QrK1tdJCFpBYn1LioaPqUnYk11qhh3U+/tlfNE7j9Cb0hOX5XT5bcLPXUyB/P075ZKZm9p+qaPxjiNpaL5AXn/ydlo4JYmwSZsJ1qjKc6TE=[/tex]对于 [tex=4.714x1.214]hlw99zLkibQTyxSi+YMaPSjoesoLXAiQMydxEl6kS9s=[/tex]，解齐次线性方程组[tex=6.071x1.357]DSfO7+3gKzynuGrodSOpYZ2Kyb1+zm4JXubkveeuh6z6TMyw7kfKn95NWoGuKWwVJ4gGU2kl4/iDACzFTiXLnw==[/tex]，得对应的特征向量 [tex=17.786x1.5]spsZ+rMIOMiqBxP/ZoH2F1icWoF63w1Oy/VO1tqItj7RIORampk9CKDQutxr/eVlDw5ZxvW6u3ul62RqxOvwOHyUlAO+5opdBQMJ742GHMSWKgZQkJGeH/Xcl0e3aKUrcvd7uStvHlTDN0znHil0l2Ca+HIZ9JckPdnRd291xtofkWams+J607qt31pLlmKTF909RpcvS7uuffVvq86+uA==[/tex]已是正交向量组，将其单位化：[tex=15.571x3.0]Bon++APCFFqGDVhoG+r8OeEZoAIDfmb/oxl26IyJHyAqzQPpIZoKTMsatTKaS7u//lALCT6Kvz5MfuRcfcqfxBkoaZvnMoqDaoDyuHzQON2KrdL07LY5NLeKyzI2d7L+K23qgX25//Hn/mnKM3pTDwADO0QO0Q9xt0QCdv+nyewqO1GAmrDS2Agt9w8spYIPwGerx1ynB86b9w4iM5nn2PgbdUIDnjfkaNF/XLN/BCI=[/tex][tex=14.571x3.0]Bon++APCFFqGDVhoG+r8OY3n+h099RfWcsp/uXBSJG2+EORfu7AOTRfC99YV3VRFh7Zaeb7P8wUa45LpcB/pEnHVjQc0nb+m3Se8H7d1vIEArlbQ3zk8J1m+Wjsn8sRjKqHG24DA6snnSD2wAr11IhIBUjqK9n4JoSach8kcxgpX2dXOlYClvOoRzzy96HJEVnf47bVchCyF7g+DFXOCNTyBy0tCtnvnmNaH3HFVOJg=[/tex]令矩阵[tex=16.0x11.214]VkSKvERjO0bCkxWdZ6+azBPhmKteK2uXwkUs4ICEZEohNrciXANzyiRbb/xgrznX+Ti77/pLzGhtKDWiV3MAqBi0smMOsy28bqd29tTEKE3cJjDiw/5cCtRBAKQTHx3atk78pxk26jy+Aw6AQ0BFplZak2vxdIqaOdZdrQuxcHStK2ga8Y88uEYfNhRP7HHuGyhBfh7eDWWA51K0hvlQXiEdSi9Qr9mHjSggwMMo+2K2PfjMj51byJZ9EqstvIG+aX0r6omNGgnAw+QZ+dpSDb+8zPwr4BXnw6+vgpKTebPJk9N2R9uhrABZ6G10BPNrWH1vvWvpB7v/wdw+nihqsDBezIAMbwZy6c9bTfKrGww=[/tex]则 [tex=0.929x1.214]aZ8kNpbAQnnvrf8BYsEIVQ==[/tex] 为正交矩阵，作正交变换[tex=3.071x1.214]Uw2aCIvC8lToOmPfAZoh2w==[/tex]，则原二次型化为标准形 [tex=7.286x1.5]BHMc3KoVWVo2i/CdAvYg+ctIXKc0X9dVHI78gnqSxL8UMSOVpc8sKOj5y2S7MRQF[/tex]。
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    • 0

      设二次型[tex=6.357x1.286]azJPYkBkJ0OlxSfK5H+BIROFyCNgO/PulWrQz//9Zh4Uqg3a16SbLoGCRUwpQWcE[/tex][tex=8.643x1.286]XPNDI7csNHnqWQ92RQ5arPw9OFoyPFtmyUJjZWkyPU+tFEMK5stYnoeVEB6pkpUE[/tex][tex=5.571x1.286]O7LwsPxSbKNzsUaYdcaFWygs220DvTXPD9EOEt3wCzV5gBm79JVKY16MwSAmvcvZ[/tex][tex=2.929x1.286]vedobJ7KUaWclGusUFos9g==[/tex]的矩阵[tex=0.786x1.286]pi/GsQ3apuRt43V3XQq/tA==[/tex]的特征值之和为1，特征值之积为-12 . （1）求[tex=1.429x1.286]+fmtub6g+tF54Tl5ap2zBg==[/tex]的值；（2）利用正交变换将二次型[tex=0.643x1.286]+RQz+inOZSqc5WvKyEpD0Q==[/tex]化为标准形，并写出所用的正交变换和对应的正交矩阵 . 

    • 1

      用正交变换法将二次型 [tex=11.214x1.357]AkjIkUm3A8xTId+eQbup8tBtUstP8XF2BFVnl1O/4vpR85uyUDxH81wUsRNPTWnzJnoXWI67Bzg91aC1cPLSGtwNhMTGkzKY3bWD+IQO8Io=[/tex] 化为标准形, 并写出所作的可逆线性变换.

    • 2

      用动态规划策略求解矩阵连乘问题1 2 3 4 M*M*M*M，其中1M（20*5）、2M（5*35）、3M（35*4）和4M（4*25），则最优的计算次序为（）。 A: 1 2 3 4 ((M*M)*M)*M B: 1 2 3 4 (M*M)*(M *M ) C: 1 2 3 4 (M*(M *M))*M D: 1 2 3 4 M*(M *(M *M ))

    • 3

      有六组量子数： (1) n＝3，l＝1，m＝－1；(2) n＝3，l＝0，m＝0；(3) n＝2，l＝2，m＝－1；(4) n＝2，l＝1，m＝0；(5) n＝2，l＝0，m＝－1；(6) n＝2，l＝3，m＝2 其中正确的是( )。 A: (1)(3)(5) B: (2)(4)(6) C: (1)(2)(4) D: (1)(2)(3)

    • 4

      已知实二次型[tex=8.429x1.5]CKlOGn/4oc+CIjd/NrEXYL4dkmrBlW2GCC51Nn4jxKDKCw4XacjR6Wkq7aCfgBox[/tex]经正交变换[tex=2.857x1.0]NGl8c6nTOCjuPJKs2cOxRw==[/tex]可化为标准形[tex=5.571x1.5]BxX+JKGKByN8807bHgu+T1pktokv0l3dVZx8FO3ro+VWSdtzbyfx30MD7Apuy3Zt[/tex],则矩阵[tex=4.0x1.357]EBNDcMm1xMDWg08FZWWY1Q==[/tex][input=type:blank,size:6][/input].