设矩阵[tex=9.429x3.643]sSXBpxJWudVpH1R35o4LnCGIOkycDZTkkPhY8mBIKIbwAeHt7Ug8XVMVGyxdxELbZmbQmzn0XHljZC59w/+iYhNL8ZZ7JVS/tNqKV85yGr7r9HJ13dVj/sx4hqJwWb6y[/tex]，已知存在正交矩阵[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]，使得[tex=4.857x1.286]qqZjVILGZVRAhgf21Vfsux42UL7UB5yw+5T8BXDq4/s=[/tex]为对角矩阵，且[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]的第一列为[tex=7.571x2.214]eeCanaQCFlwDWIBYI6oJvDhnQpfKKsvSO4a3BEPz5LPN32tKtDiz0O9vdZi30Kyz20Ut7MsCn6OCtyvgDBpjrQ==[/tex] . 求常数[tex=0.571x1.286]mRKL/orzOudCEARA8qn3Kw==[/tex]，矩阵[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]及[tex=0.714x1.286]6GaLCkpufqH4y+Zpjb+RIQ==[/tex] .

2022-06-09

设矩阵[tex=9.429x3.643]sSXBpxJWudVpH1R35o4LnCGIOkycDZTkkPhY8mBIKIbwAeHt7Ug8XVMVGyxdxELbZmbQmzn0XHljZC59w/+iYhNL8ZZ7JVS/tNqKV85yGr7r9HJ13dVj/sx4hqJwWb6y[/tex]，已知存在正交矩阵[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]，使得[tex=4.857x1.286]qqZjVILGZVRAhgf21Vfsux42UL7UB5yw+5T8BXDq4/s=[/tex]为对角矩阵，且[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]的第一列为[tex=7.571x2.214]eeCanaQCFlwDWIBYI6oJvDhnQpfKKsvSO4a3BEPz5LPN32tKtDiz0O9vdZi30Kyz20Ut7MsCn6OCtyvgDBpjrQ==[/tex] . 求常数[tex=0.571x1.286]mRKL/orzOudCEARA8qn3Kw==[/tex]，矩阵[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]及[tex=0.714x1.286]6GaLCkpufqH4y+Zpjb+RIQ==[/tex] .

答案：

[b]解[/b]     设[tex=1.0x1.0]E4FovvvmKFxHayApGHhrvg==[/tex]对应的特征值为[tex=1.0x1.214]Km/qUtFFKwzj+P2mZlKsTQ==[/tex]，则[tex=5.143x1.286]NLy3z1bAemr6IyKI32cr0eS+SqzkjoPOjvw9h6Y/XSxFlys/BeNPgc6wlk2tTYEf[/tex]，即[tex=9.5x3.643]NC4MtLlgpxebbMxqJ1lKmgimTGZfICQuZoE7zabSgg//43EQYBWwv+sikZvZdVR6aONRMqxxdVC7e+WAX1zXQQxc8z03waZg19KyLNxaxS8UQ80vH6wZzwmzQ14A4FYAEfDjln5nuWmzBanTYl5gxw==[/tex][tex=4.071x3.5]075gCzZzsMRb6HYXYk9X9xaIzHO3duphZRd+g1rZUuQt7BzcvHYqeVHEAC88QZnSVeizKhROJ5vlau2EN2VcSg==[/tex][tex=6.0x3.5]Sj2sZeWkGUxi5Q5GoAn2jeBxTrPmglm3MwSq8t8gK3Ox5AU4srVOhCRuV+wRI3V+0u1srg7w2bVJiwc3d0S0sa7LGbVT/iHgfSKSKBJrNEOlWgyofNWCdprPVXwAgPMU[/tex]，解得 [tex=5.286x1.214]UszqgJIxJOG1PqCzY9wZB4wMAcM6H7hU7kwbADESjbc=[/tex] . 故[tex=10.286x3.929]QN0fTQbn6M33pU3gx/S2sskwPlrKAzoJ8mdYiTYC7tEgZ1AaArgl09OrlcfsmPT0tQKiThSXvT56h5YmTlJ0k3SR68znwAS+CgwlrfdazDYQc/ohRudDENv/6Hq1y7qu[/tex] .  由[tex=4.214x1.357]iooNHBryO1CC7KxpW77T2/REV6koV6Lk3S/Y/ZRQSAE=[/tex][tex=9.214x1.357]d5BG7xBS/SrOcu4IouhRaCVrw9rY7xooyyj/RJVV40mrP/3kaleN8j5su1NELvVb[/tex]，得矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的特征值[tex=8.357x1.214]bIhyVuesdTVULtsOGUuMfontV7dcXcpSKpe1StXZL3PMpN7uZsa5eZ9fXK7J39+7[/tex] . 对[tex=2.214x1.214]M2UyJ2lvpWR2QtWgYqh8JQ==[/tex]，解[tex=5.714x1.357]nRk4xLTfQylA0hcfsYEFYfOfu0nrZeAN9NRpw2Une6s=[/tex]，得特征向量[tex=6.143x1.5]oXdRG9yshOb1NwMsyAiNGK7/VCLK3fFbIl25LYpPIWQ=[/tex] . 对[tex=3.0x1.214]+DQtHu+Y9OZI819l5uHhwg==[/tex]，解[tex=6.5x1.357]DXyMHJFWMX25BXBrQfANyAYiS4lvgozk83UgP6c19ck=[/tex]，得特征向量[tex=6.143x1.5]XxmSvvp+3myecRH7JBOp0F+SwRkWtgqssP8Gx2NBpB4=[/tex]  .  将[tex=2.286x1.214]yeVzZBBZCQfR+mjUDVHZBOBn0fO/PVIPD6aCYQYq1Ug=[/tex]单位化后分别作为矩阵[tex=0.857x1.214]to/MrMoO1ux8UhZHnpEvBg==[/tex]的第 2,3两列，可得所求矩阵为[tex=13.286x8.357]OwAEH/Gxn3EoUTp+oFenUYW/RXN6pxUcdBfy1WFWeNadGmJekOzRDGsB6LEXr7IinfQ9tdlQVeHY8M4Y7FGn7lSDWtwc8NkVMS5QzRf3UZbotIhkSQr7nFOae6Ld4CnY2pP1Zpf4wL4pNK1i9QCzbbc6Fg5UfOz+sf/u5CW7dM/bM9Yx1avfOBkuTR24knLMmqBUOvuxxXkg0Vjf+bG5dF06JQ4jbau35WpjnEFRB8XKO0Bj/j5FooX84LbTxw+FdF+8T5qfsag0nNTFjgLfmWmQuvDCMj5Fn/mDYEe6H98=[/tex]，[tex=8.5x3.643]wKwEfvVACmjDBjXmJ3arkUox8qpdkfywEROvqQMMm0bUQiJ/P4EIlvbee+GIltH9zCToAaJvMRDY7JtrBHA9EIk4OJOTLteI0iB6Skwf+VyNNTpnlOkgg5lRAzdIlpst[/tex] .

举一反三

内容

0
若矩阵[tex=7.857x3.5]sSXBpxJWudVpH1R35o4LnA4lIqpBf4gH8eIU2tIDFvHUTa28LnVAl1Ag/LVtmAu+dU0hsU1hhCpG5YGpQ8ul9X0YZiiEbfbYY4waQDC3uoZh/ueoInJj//6K313tBkPa[/tex]相似于对角矩阵[tex=0.714x1.286]6GaLCkpufqH4y+Zpjb+RIQ==[/tex]，试确定常数[tex=0.571x1.286]mRKL/orzOudCEARA8qn3Kw==[/tex]的值，并求可逆矩阵[tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]，使[tex=5.286x1.286]inWzbGHM3BuvW87VMI4x1zvT5gGl553eJez0aB4E+qw=[/tex] .
1
设[tex=2.643x1.286]yu9Fqc429BTsCWKDfgGy8g==[/tex]矩阵[tex=0.786x1.286]pi/GsQ3apuRt43V3XQq/tA==[/tex]的秩为[tex=0.5x1.286]/r3Eij8VRNC5JxYjlQuXEQ==[/tex]。证明：存在列满秩矩阵[tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]和行满秩矩阵[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]，使[tex=3.571x1.286]pSpT/0da3Zd5mno7ETYbCQ==[/tex]。
2
set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
3
6个顶点11条边的所有非同构的连通的简单非平面图有[tex=2.143x2.429]iP+B62/T05A6ZTM0eeaWiQ==[/tex]个，其中有[tex=2.143x2.429]ndZSw3zT0QTOVLVdoUto1Q==[/tex]个含子图[tex=1.786x1.286]J+vVZa2YaMpc6mJBbqVvWw==[/tex]，有[tex=2.143x2.429]lmhx48evnQMhi03NovPXig==[/tex]个含与[tex=1.214x1.214]kFXZ1uR8GjycbJx+Ts2kyQ==[/tex]同胚的子图。供选择的答案[tex=3.071x1.214]3KinXFh3SXhZ7nIe1y9KEV6aadxhhJWeEy6Dij1iObdMUZkY6ZA5J2dVVjPSuhEf[/tex]：(1) 1 ;(2) 2 ;(3) 3 ; (4) 4 ;(5) 5 ;(6) 6 ; (7) 7 ; (8) 8 。
4
【计算题】5 ×8= 6×4= 7×7= 9×5= 2×3= 9 ×2= 8×9= 7×8= 5×5= 4×3= 5+8= 6 ×6= 3×7= 4×8= 9×3= 1 ×2= 9×9= 6×8= 8×0= 4×7=