判断向量组[tex=5.429x2.071]DhkZQ6U+YNvBth9C/XILFMuyTkrIFxkmeUNyW8fUmDY=[/tex]，[tex=5.357x2.071]lenZbrFoHxv5kjVjiyqqVkBnaXSxxjf2Y4MOogWnen0=[/tex]，[tex=7.643x1.714]ei6OOqz7fGydc/UBHxpRORo0UsTlIJKOh405MJwDBh7wNWleXkHDl9kl22+udwbzaegR3z0RLjWPPRnQOjl2tw==[/tex]，[tex=7.643x1.714]IbghfoX/HIVbusiB7s7zXOzC9mhpiMjRn7MQBGbgH/S/V/jMHitEMCg+sLOOTANzpcGDLWXlkfaz50RJSeWUWg==[/tex].线性相关还是线性无关，要求说明理由(其中[tex=0.571x0.786]7G1MINzwputr5mgALyjQfA==[/tex], [tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex], [tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex], [tex=0.571x1.0]1GNMN/euvQoeKc/ZwvRQhg==[/tex]为互异的数)

2022-06-10

判断向量组[tex=5.429x2.071]DhkZQ6U+YNvBth9C/XILFMuyTkrIFxkmeUNyW8fUmDY=[/tex]，[tex=5.357x2.071]lenZbrFoHxv5kjVjiyqqVkBnaXSxxjf2Y4MOogWnen0=[/tex]，[tex=7.643x1.714]ei6OOqz7fGydc/UBHxpRORo0UsTlIJKOh405MJwDBh7wNWleXkHDl9kl22+udwbzaegR3z0RLjWPPRnQOjl2tw==[/tex]，[tex=7.643x1.714]IbghfoX/HIVbusiB7s7zXOzC9mhpiMjRn7MQBGbgH/S/V/jMHitEMCg+sLOOTANzpcGDLWXlkfaz50RJSeWUWg==[/tex].线性相关还是线性无关，要求说明理由(其中[tex=0.571x0.786]7G1MINzwputr5mgALyjQfA==[/tex], [tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex], [tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex], [tex=0.571x1.0]1GNMN/euvQoeKc/ZwvRQhg==[/tex]为互异的数)

答案：

解  计算矩阵[tex=7.786x1.357]ZYa3nSAfkeMO9ZXBQC7rDlh2u26hE4Ff0dz9qoF0kMQlOT27uBqAKzyteDrLS/tZwy3j+cq8VbxcRBBP1zmmeKOHCj8kzmEDDDtk0NiJ+g4H0JEoP3hHmdv8CnA3ZaVD[/tex]的秩，因为[tex=10.286x1.357]lzQA79ac5kFYKCdOtG3ykkW4s/xCBVtNCcpguF7k61I3hwQHPnh2eayoaPRMRY3r9+j1rDZzCwIypFpoEJv1R08yjdcw+2zBMYwpZkJw84vtfwROIL8S48cZrLgRKpeJ+VQHZksB6SmEJKWN8X0sc/nYozihC4jBcnStDEH+p+M=[/tex][tex=10.571x2.429]U7Z5/G5cWSezcBiznLmVQpRJMUQLFa7RPDqVRrOY1egc6NLz5ONZTMRUeZwpGRw81vuBDDLO21POtKU++PVpHUiOPKPq5nBXP8KwPsoax/zpPV1GOwhzubU25p0qtOsYuAF64O81yt1OIDxNazjRiYBJWnh1p8ReyBIdpSixWMsy3UumhHrq/fW95cHTsdN1[/tex]，而[tex=9.929x1.571]U7Z5/G5cWSezcBiznLmVQgGbYziaBQdNasn5X5YAGvkDk0cr1UngQsKONp6syBEgyA2yPZ5AKIKC8KBVQJyw8WrTsQoT035IZom1+iyPNX01FHivuhtLNsbNPpMc02ye3CUcKe505ct4ji9DEwtBx+73cBdKL/bW9fIOW+otVB0=[/tex]是一个范德蒙德行列式，由于[tex=0.571x0.786]7G1MINzwputr5mgALyjQfA==[/tex], [tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex], [tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex], [tex=0.571x1.0]1GNMN/euvQoeKc/ZwvRQhg==[/tex]为互异的数，所以 [tex=11.714x2.214]lzQA79ac5kFYKCdOtG3ykn7MYIJPjf1sr/nHTR9cOY/oLVkAyzznSUXSaXoPMWWUpq5JI6ZyGvWe1XGQ0WcwcIWYp56N4JOPK5LowuUzGjep7zL7b4UB0x9wpgcCecmOxztJduO6xjKTRJCro+bcuLI3L6wXsGmJEG5O0nbbvlk=[/tex]。因此[tex=11.143x1.357]lzQA79ac5kFYKCdOtG3ykkW4s/xCBVtNCcpguF7k61I3hwQHPnh2eayoaPRMRY3r9+j1rDZzCwIypFpoEJv1R08yjdcw+2zBMYwpZkJw84vtfwROIL8S48cZrLgRKpeJ+VQHZksB6SmEJKWN8X0sc4XAnQBmQrh8koJwMD5ZskQ=[/tex]，据此可知[tex=9.0x2.214]IfEG3NsBfGhtbCalasoF/yFRn5lKwvktB9rhaHlsHlnDbVvxMgd8n3+pr/rk1mB/HAlGVnnSQTCX5Yd3zLQSv6fB4ph3/9UfjjPfwgCkew7iqs5vEtAQRWe/WyxR5A/WrAVVxg6jxMp8mSUOdy/ZnqGeKF8HgJUu73iEe/CW1AU=[/tex]是满秩的，即秩为 4，与言量个数相同，所以该向量组线性无关.

举一反三

内容

0
设[tex=12.929x3.429]CdfBpM+Ix2U8w1X/V6+RxnoDks5x812g8rsoEHy7/dnkXO2vkzq0jWmXkZZlv7xRyQoGOhdccJTLUK1X6uC3cw==[/tex]求[tex=0.571x0.786]7G1MINzwputr5mgALyjQfA==[/tex]，[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]，[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]，[tex=0.571x1.0]TcM6B5Wrs5vy9dWrxRPSdg==[/tex].
1
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 。
2
设随机变量(X,Y)的概率分布列为[img=345x154]178ab1c9ce3bc1b.png[/img]求[tex=1.571x1.0]JUrGU6ftUjxQCIr6CyfDwQ==[/tex],[tex=1.357x1.0]yL/7/hhyqgwzAX8jnIq3OQ==[/tex],[tex=4.357x1.357]LN0xwhQHSOeLwBClUlpHQw==[/tex].
3
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]
4
如图所示为[tex=2.857x1.214]XYsoOkU08IOARqv6dBCvJw==[/tex]氧气的循环过程，此循环过程由两个等体过程和两个等温过程组成试求：(1) 循环的效率;(2) 若[tex=0.571x0.786]7G1MINzwputr5mgALyjQfA==[/tex]、[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]、[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]、[tex=0.571x1.0]1GNMN/euvQoeKc/ZwvRQhg==[/tex]各状态的压强分别是[tex=0.929x1.0]tzYCqfQDSNBdcaN7/TUOtg==[/tex]、[tex=0.857x1.0]hCPXKZWXIjExHsqcKoENZQ==[/tex]、[tex=0.857x1.0]8YF2LywM+p2QLOb8WxWTeA==[/tex]、[tex=0.929x1.0]YHUq/+DWfpLqDhGvpN/BFQ==[/tex]，证明：[tex=4.143x1.0]PfKy32YxGdhGGGmojFmeR+Mke+nTHKmdi4qm8S1MIQg=[/tex]。