• 2022-06-08
    判断矩阵[tex=7.643x3.643]jyVOORWehIbTNQvvtYroWoGNXAqhwZEepcy9qfmUbiWDJnvaw1HUbQJlFz+L49mtT9iDWk27vO2YRwDxh+BISkluY5BVmrMtR5s/G5H9KZrslL5g7D0e2NZAJythvdiY[/tex]是否与对角矩阵相似;若与对角矩阵相似,求一个可逆矩阵 [tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex],使[tex=3.357x1.286]QehgMsIi+Hsdet9OihqiWQ==[/tex]为对角矩阵。
  • 解 [tex=0.786x1.286]pi/GsQ3apuRt43V3XQq/tA==[/tex]的特征多项式[tex=13.643x3.929]vAGON7+JxTsi8RkBcCBNjOdWSD1avKTKahYRgaf+lGU7rubxJpyGzDco4aUnxHWcIRLOlE/y+DSkydlaPSyrcGhivp2fPwFwMBvkBIJY9qOOd8Fk2t8b5LF1Ui9rsx/s8vwMNHltjEc1n5ah3sFKL8fvmHM9zC0+4W54vzxiFVM=[/tex][tex=18.5x3.929]9FriVQZ0SHvrVqwV6C3CcS/Qe/pblz3CBsQHxgrhQk7SD9sHq737u0TO8rL1UHjgKw0IBl+1a/In6CS6CbIBrGhqn+QQRaluzqlDwwOosuaP5y+7mF2QdhuEs3FnSMjY1Fl95Tjm3NeaSBqXI+fKMjVTy6R9SVpGC24PqFof49NnxprXZ9QCh8ew+w08ZjvP6/6cBt+uoKDBJ/7Hq5mBqIR3HCxfRgjhOx+9zmIeE8+fqA1mOG4R20UXda+W3uIG[/tex],则[tex=0.786x1.286]pi/GsQ3apuRt43V3XQq/tA==[/tex]的特征值为[tex=3.429x1.286]JjUvEVviPupZHWIJEKQ81I7ITZV5SOlj8equn5QT42I=[/tex],[tex=2.857x1.286]2knAlYuRhXMS6H+UKdX/pn7x7h2jbE/1/jdQmxsRa2A=[/tex] 。当[tex=3.429x1.286]JjUvEVviPupZHWIJEKQ81I7ITZV5SOlj8equn5QT42I=[/tex]时,解方程组[tex=6.643x1.286]z/zS1eZmZ6AuHi9K9/u2sWYvwvXSba1qTXQPlzB9fvw=[/tex]。 由[tex=19.786x3.643]8VFrrbmhLK6lbU3zpdbswflo/gX3WBBKZRbKTykn28e5iX/DqhWX4SU9j+mGzbTwG2eBno2OZhx8mprdNMJDtnN11fEP38Ncj8/H3NOHvNQqgeffKuuFDaKeGpNa88E9Y9jwCRUSFoTGIMu3EN59lxu4QasF8A3D5IqH5PoqYaTKDzCLv3zK28BVVPNegh/Neq0E7NBDM6kMoaBfhP1yxAdgdD/f6wjZagaiQjAgzWiMWbPLeF1IYx1cWDB5/pv6gmpt2EuorcfNEbs0ZeNCuQ==[/tex],得[tex=8.214x1.286]4lVZcdj5/wxnIqd+snGobzPbOV28Yc/SPaCAJ5o+kC8=[/tex], 所以[tex=0.786x1.286]pi/GsQ3apuRt43V3XQq/tA==[/tex]不能与对角矩阵相似。

    举一反三

    内容

    • 0

      下列矩阵是否与对角矩阵相似?若相似于对角矩阵, 求 [tex=0.714x1.286]BMKsEVFNvpiLV0UsqDFXCw==[/tex] 使 [tex=3.214x1.286]1sFdXzzqHCc4qLXdM8ki4Toicy90dsQBVNzF4LK8JX8=[/tex] 为对角矩阵.[p=align:center][tex=4.5x2.786]jcCMHflCR8OS9TosV6N5vEh2mkwOQPgJaMjhXUUvt/u/aDMg7Joull2yzyzjRLUkka8hhHVAcdjyppjElztjEA==[/tex]

    • 1

      下列矩阵是否与对角矩阵相似?若相似于对角矩阵, 求 [tex=0.714x1.286]BMKsEVFNvpiLV0UsqDFXCw==[/tex] 使 [tex=3.214x1.286]1sFdXzzqHCc4qLXdM8ki4Toicy90dsQBVNzF4LK8JX8=[/tex] 为对角矩阵.[p=align:center][tex=6.929x3.643]jcCMHflCR8OS9TosV6N5vAsRiX0HRDF6deVm1P3ZNbcryL/4z1YRStI9T1RLH8oBSlyEGqOTzkzDCbMq0bIIXVYueNkOeT26F02GTHQKQUW3/9zfT6cXZLWR2NMKEfA3[/tex]

    • 2

      下列矩阵是否与对角矩阵相似?若相似于对角矩阵, 求 [tex=0.714x1.286]BMKsEVFNvpiLV0UsqDFXCw==[/tex] 使 [tex=3.214x1.286]1sFdXzzqHCc4qLXdM8ki4Toicy90dsQBVNzF4LK8JX8=[/tex] 为对角矩阵.[p=align:center][tex=6.143x3.5]jcCMHflCR8OS9TosV6N5vBd033QJVVKN8Pu/Wce/RY+4F9/ZEYCNLpGGCW95mbfQVIkZ3V/nk34FVk/TFVprQr5n0GJXqwW3N/OKYy3Z7PY=[/tex]

    • 3

      对下列实对称矩阵[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 求正交矩阵[tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex], 使得[tex=3.357x1.286]TvRsUv5t/3lJOPEdcGcONfuVM4C/bLaP8ZJtWRinRXA=[/tex]为对角矩阵:[tex=6.214x2.786]sSXBpxJWudVpH1R35o4LnE0bLZnSPEoDNmtl5XLvZQ81q6AbPwVhJ0ckZM/g2nUxqJrc7JTIzM2sUXDRpC7mKQ==[/tex]

    • 4

      如果矩阵[tex=9.357x3.643]3BT1BgBZQ5uJXxD5dg+w25oxXRH9+KEjMiNSxk6AZG+PsFZwXRxPIBN6s44j902W5vNNmOjVBXquMCKEgf/BNJ5SSXfj6kONTH2cuTJkBPIBOYobCdzUTg1N8KvXoIB3[/tex]与对角矩阵相似,则写出相似对角矩阵[tex=0.929x1.0]tfHTq5YB6eq76zMfF9z56Q==[/tex] 及 [tex=0.786x1.0]6J6pLBwELDvuZYB9vl6pdg==[/tex].解: