设向量组[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.143x1.286]PZ3wc82RrbgX5KwVcyJcmA==[/tex]，[tex=0.929x1.286]Ff8PJr0vif92Cy4pi5zjsXNsBLAtsgBLgvGGr1gK+KY=[/tex]与向量组[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.143x1.286]PZ3wc82RrbgX5KwVcyJcmA==[/tex]，[tex=0.929x1.286]Ff8PJr0vif92Cy4pi5zjsXNsBLAtsgBLgvGGr1gK+KY=[/tex]，[tex=1.857x1.286]BfplC3qdmMIuR9ktapG5oimLVgqI3Q2kb4TqtCnVJ9k=[/tex]，[tex=1.143x1.286]PZ3wc82RrbgX5KwVcyJcmA==[/tex]，[tex=1.0x1.286]K7Gmg5Cgo+HS/qEv7bZhTFh2fUxkbcP/SryOO1HoJnA=[/tex]有相同的秩，证明：[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.143x1.286]PZ3wc82RrbgX5KwVcyJcmA==[/tex]，[tex=0.929x1.286]Ff8PJr0vif92Cy4pi5zjsXNsBLAtsgBLgvGGr1gK+KY=[/tex]与[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.143x1.286]PZ3wc82RrbgX5KwVcyJcmA==[/tex]，[tex=0.929x1.286]Ff8PJr0vif92Cy4pi5zjsXNsBLAtsgBLgvGGr1gK+KY=[/tex]，[tex=1.857x1.286]BfplC3qdmMIuR9ktapG5oimLVgqI3Q2kb4TqtCnVJ9k=[/tex]，[tex=1.143x1.286]PZ3wc82RrbgX5KwVcyJcmA==[/tex]，[tex=1.0x1.286]K7Gmg5Cgo+HS/qEv7bZhTFh2fUxkbcP/SryOO1HoJnA=[/tex]等价．
举一反三
- 已知向量组(Ⅰ)：[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.071x1.286]UXqxuREAJBGsvAILiAPouak3R42ZYLRYRDS+UrrM1J0=[/tex]；(Ⅱ)：[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.071x1.286]UXqxuREAJBGsvAILiAPouak3R42ZYLRYRDS+UrrM1J0=[/tex]，[tex=1.071x1.286]aYbv6eCiEgc2XuIKnpB58n0Z5WWyWfmZ3+2BaOGtS2M=[/tex]；和(Ⅲ)：[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.071x1.286]UXqxuREAJBGsvAILiAPouak3R42ZYLRYRDS+UrrM1J0=[/tex]，[tex=1.071x1.286]EKM5dkWdu/Omh1L14pE1cUwDjbxI7m7Xu3SyQ45qSw0=[/tex]．如果各向量组的秩分别为秩(Ⅱ)[tex=0.786x1.286]rj6W22mVYNX/YbwkMquVUw==[/tex]秩(Ⅱ)[tex=1.571x1.286]xPxHspfEVLiX53VbgCuNSA==[/tex]，秩(Ⅲ)[tex=1.571x1.286]kkHQLqaVxc3ZtQo9JAFiEA==[/tex]，证明：向量组[tex=1.071x1.286]pWE6wju4u8fPNU7ACnOUQHLeZNVAdSH/I6vNZLZGzWg=[/tex]，[tex=1.071x1.286]JGq/5/Kh4u/M938ZQm31Chbw+GLwp2eDbQ5S+yzPRr0=[/tex]，[tex=1.071x1.286]UXqxuREAJBGsvAILiAPouak3R42ZYLRYRDS+UrrM1J0=[/tex]，[tex=3.286x1.286]GZGPt+7Y5RJqODKSxp8Zkv/URzsl+ajWKjSTqTXlfrs=[/tex]的秩为4
- 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 。
- 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}
- 对 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]的不同值，分别求出循环群[tex=1.143x1.214]StMMJ6qThnpokZJIPGrdFyP3vrLnUdltYxmLxjw8za8=[/tex]的所有生成元和所有子群。(1) 7; (2) 8; (3)10 ;(4) 14 ; (5) 15 (6) 18 。
- 判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]