求下列矩阵的特征值和特征向量.[tex=7.643x3.643]075gCzZzsMRb6HYXYk9X9yD1hAmtvBJ6+FZJhinzU/YixR0pcINNPybaF0HKSAvA4/uRV7cNaIQJgmJa5d4NHDPGy09MeSc7R9NDjrit2apCBP1F59aSzcXeFx8fTMft[/tex]并问它们不同特征值的特征向量是否两两正交? 它们是否可以相似对角化?

2022-06-29

求下列矩阵的特征值和特征向量.[tex=7.643x3.643]075gCzZzsMRb6HYXYk9X9yD1hAmtvBJ6+FZJhinzU/YixR0pcINNPybaF0HKSAvA4/uRV7cNaIQJgmJa5d4NHDPGy09MeSc7R9NDjrit2apCBP1F59aSzcXeFx8fTMft[/tex]并问它们不同特征值的特征向量是否两两正交? 它们是否可以相似对角化?

答案：

由[tex=13.071x3.929]VpkzC0JbsLi+VOXFvrxHvqGIhkgknrE4SdBAZL4DJaL29Cg+rDXGHYZf4fv4SC7I4LHkQ+pZvz/1fjzvuw3AFn7uzJAC/ekwuJ9vHXxUQv4+OeedNz22FoJMDj0wYK6Mw49zhHhbYObmoF5N5e/SivEbBBAcISoliz4k4wHXCiI=[/tex][tex=2.643x1.429]QVlyyKGYC5Kg3PIPSVM2SQRt0qYPSMgjNKcykf2mBWA3s2X6omxDkBBxilCRYY3D[/tex][tex=21.143x3.929]Uyz5s0rmQIddjb5Jc2T/YReFItGfxnwGtg1lNK/V7Xl+ch1JSDN+i2A+cyzDFpqUzXSkJPpulI6CabIhrL8g2z06xcaY8jbK6y5BsXt9DKadqallnR4285EdZ/WAH/K0TdRfI+mh6L6/E2GTCKn3sde1zCX8kBQJ2znm5k9+XrvpLfwNo99hUKdctwAFiuDk0nHSYH7ZN1hCG7UwzDNr1nmff2fYRVFMEpSggAqyYMkAqnC9BohtXmWeFCsAVgnHPm9n9gxMVHsyHV+yLZFEJ8UbcQWnrbBEe+KqlOR8lzA=[/tex][tex=2.643x1.429]QVlyyKGYC5Kg3PIPSVM2SaSUHX8xi4nl4Ti16RCnRhnah3axCG6wkPFcUvI/OtwY[/tex][tex=25.214x3.929]RY4nsV4JiVnLy74vFzSxajkz7paikvO+zICsm7e+whThwCF8iYDpr6fvUrtaTSWUoTnprvrfUIdg2tYPF9l/7bs9+QRZIKkyPfByqT9QvoOLsj0wGCowHqgEJYtbaTIQmg2Z2hJRtTQysUxMwiOYWyohALM+UqSZcdzVKnadrxBa2qGWH6FTqbBU9dcgLTT9zN/XNzmx7j1xzsUXBRc26reL3H27E6zKVfFTGbbykbhXiBA/FasyUdDZ4YDkAH6tlJb512ktg1p1TJc9CNVCv/A4/0a7w7HR45SwzbqIT4Y=[/tex]则[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的特征值为 [tex=5.643x1.214]6CzHpBoEVdfGanuoycm4yCAjQHLAtZAbYZ4L//1d0jmTw1U+1At9b7n8jSPIMkXT[/tex]( 三重根). 对于特征值[tex=1.929x1.0]n+JpmAy1Ht3b6A/spGmyBg==[/tex]，解齐次线性方程组 [tex=10.429x1.357]mKVNJsiyow8GVoVavy9eF/2QAt3kDWo0PWrs8bjUDcYC5ZkR96Q/Wj5+FsMirOJP[/tex]，因为[tex=12.357x3.929]IVNWSxfZqWr3ernBI/y6SMzQbpt5BGnnfV/6yKfv7D/CUPDVbgWzAPusBLOH/elbPHAsHNfMwhTrRiDC3IWvX0C0wZVLav8vw4TOnDxt2E+fck0GbgMsH7iLGuvh3dAT[/tex][tex=4.143x1.643]Ie5doAZSahPyurce3Tx3MfbYgL/2vjLig4EITOEwv884o41AhFFSOCGpuCSO25XkJwfhp4L+xFew5eBm/la5M0NVBm548FeYQaT1a18xJZgP0lURvqhHQTcmTGBp/RicyAiOzybVOEkmwO+ZL3zcFcQp5YnDMovNfWdovFP5WDk=[/tex][tex=8.643x3.929]jcCMHflCR8OS9TosV6N5vJNyIP83+Tb+gbe85j7Z7X2bTwp+V0GLlwK8Wsp4xncrAJB+sQ9M94eQM0rjzeHN11RJLAAwW1fLjsaYDGtol6yKLk4T++GIPFYqjUL+7hoa[/tex][tex=4.143x2.857]Ie5doAZSahPyurce3Tx3MfbYgL/2vjLig4EITOEwv884o41AhFFSOCGpuCSO25XkJwfhp4L+xFew5eBm/la5M0NVBm548FeYQaT1a18xJZjQkPb5nZELPV0LRxqG/aKADjRrmjV9TYJNyIg/OnuQT2gGfO63ri+ZgVgJ+7KX3z0dllBrctoKWxIkAY2Ww1ko[/tex][tex=6.929x3.643]jcCMHflCR8OS9TosV6N5vJNyIP83+Tb+gbe85j7Z7X3x9b2jrTh+JQyXH+x2UFrNwcoODnCjDNexbQA17CfHhskZ04AUQjXRMR7TG3+Xkqa3i7pnvLbLwR/T/EmxPwF4[/tex]得基础解系[tex=5.714x3.643]p6s2gbDpHNG1bw7iD9wGIFLTh5gaYpPc1vAuRFDsMqZyLcY1RculXyjIUlwS70hVoQcyp6ST2BERHl7xTnR3nQ==[/tex]，[tex=4.929x3.5]i/mx3B4d+9VJ4yMzJ9jF4RrDt6NKPjdX7mar2o5fMBnLbf64aR4b5A+arYUA823Efea+2ohgebaKNMT8M50bGw==[/tex]于是对应于[tex=5.643x1.214]6CzHpBoEVdfGanuoycm4yCAjQHLAtZAbYZ4L//1d0jngFJa/cAiIugbgY7TRQWbK[/tex]的全部特征向量为[tex=4.286x1.214]VKIHFGmakHa74Evu2bb7UcEbkp8rkEW4tr520rj9VPo=[/tex]([tex=0.929x1.214]k+EsmtQEg+wpx+CCfSE+Ew==[/tex]， [tex=0.929x1.214]PJJ5dgU9/nwHiHFQ3+EuQw==[/tex]不全为0) .因为该矩阵为三阶的，而其线性无关的特征向量不足 3 个，故不能相似对角化.

举一反三

内容

0
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3
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4
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