设[tex=5.429x1.357]ipQZtUadSfa+xHYBxwXmT9skjdb0cz0qKrutu0egeYiy6oLUR1QuDS3hR017C7NF[/tex]，证(1) 存在[tex=2.357x1.214]BT7HQAy5GjfZdSgpd57PKnscrqcsJim9pOBv3EZlph0=[/tex]，[tex=2.143x1.214]fdR7t4oVJhV08CIhyFu4RA==[/tex]，[tex=7.286x1.357]I0S7YmfiBWOUIbXXy093ABTFrzmDlY2372t/BiRKmPk=[/tex]，[tex=1.5x1.0]9R1iO9EH8ROnKwEON0/V1w==[/tex]使[tex=3.071x1.0]FQxXCOTKMRfpdLQjm6tLqA==[/tex]；(2) 存在[tex=2.643x1.214]lm1bD7FNxYMRadaYfCaVaAhmNjQKET8XbNu5YWNqVSU=[/tex]，[tex=2.286x1.214]WHGElpapIUBQRqFA3Q4ZEw==[/tex]，[tex=7.0x1.357]+w5YNOhryr9OY/+Ai6Hyl8UuHsICosWk+P71jkSJjEE=[/tex]，使[tex=3.357x1.0]4ski73TDViKb4JBDVCGDmw==[/tex]；(3) 存在[tex=2.286x1.214]d7S1LcIgklK8UUaYKlZqXvaVXC4IWD9FMerwDsu+miA=[/tex]，[tex=1.929x1.214]VbplOwcj2mUxnMAxqFikLw==[/tex]，[tex=7.071x1.357]7non2cYltk1raU9C6EgNiIsvRJilD1bu0lrAI61bHXQ=[/tex]，[tex=1.429x1.0]fn35X1c7wWwy40cZYHFICA==[/tex]使[tex=2.929x1.0]294rYApfuLvKak9fzKAmSA==[/tex]。

2022-05-29

设[tex=5.429x1.357]ipQZtUadSfa+xHYBxwXmT9skjdb0cz0qKrutu0egeYiy6oLUR1QuDS3hR017C7NF[/tex]，证(1) 存在[tex=2.357x1.214]BT7HQAy5GjfZdSgpd57PKnscrqcsJim9pOBv3EZlph0=[/tex]，[tex=2.143x1.214]fdR7t4oVJhV08CIhyFu4RA==[/tex]，[tex=7.286x1.357]I0S7YmfiBWOUIbXXy093ABTFrzmDlY2372t/BiRKmPk=[/tex]，[tex=1.5x1.0]9R1iO9EH8ROnKwEON0/V1w==[/tex]使[tex=3.071x1.0]FQxXCOTKMRfpdLQjm6tLqA==[/tex]；(2) 存在[tex=2.643x1.214]lm1bD7FNxYMRadaYfCaVaAhmNjQKET8XbNu5YWNqVSU=[/tex]，[tex=2.286x1.214]WHGElpapIUBQRqFA3Q4ZEw==[/tex]，[tex=7.0x1.357]+w5YNOhryr9OY/+Ai6Hyl8UuHsICosWk+P71jkSJjEE=[/tex]，使[tex=3.357x1.0]4ski73TDViKb4JBDVCGDmw==[/tex]；(3) 存在[tex=2.286x1.214]d7S1LcIgklK8UUaYKlZqXvaVXC4IWD9FMerwDsu+miA=[/tex]，[tex=1.929x1.214]VbplOwcj2mUxnMAxqFikLw==[/tex]，[tex=7.071x1.357]7non2cYltk1raU9C6EgNiIsvRJilD1bu0lrAI61bHXQ=[/tex]，[tex=1.429x1.0]fn35X1c7wWwy40cZYHFICA==[/tex]使[tex=2.929x1.0]294rYApfuLvKak9fzKAmSA==[/tex]。

答案：

证明:(1) 因为[tex=5.429x1.357]ipQZtUadSfa+xHYBxwXmT9skjdb0cz0qKrutu0egeYiy6oLUR1QuDS3hR017C7NF[/tex]，所以[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]与[tex=6.929x2.857]jcCMHflCR8OS9TosV6N5vFA4o5KwCvcZw7OQuwp/Z3bYaK05rhwwntLlZUhWF7XYKriyG6eRtvH8X8o31JyGMZ/Y67FbhXtnUV99LFFS/Nk=[/tex]等价，即存在两个可逆矩阵[tex=2.429x1.214]/HVqmYz0axKhGYzcalhO+gJ8av6lKrqDWX2SFIXviWA=[/tex]，[tex=2.214x1.214]HJB1MrpQTymgVix9nM1WYTkjtnxcM0btPKmPrDcFM24=[/tex]使得[tex=13.357x2.857]BYzw5xMjCl4P+ivKl/fs26sezFrO7Ki0gUnPtI7ru9i47zp5M5oOjeZyIF1fS2kOU6eHChcG1asfnZkwAkb51TEk4UHasgRJMCHMSSZYcfXKnukor1Rj03Yg5nDrbzBdfIAIAaddV/YJzRAr1HcYHA==[/tex]，令[tex=11.0x2.857]qkP16fDx24FQNBphoHkJ8LAPgD7SwRJqf2lsthwxKkqT5+MAFPqgOSQtTU2H+QZDiUPIALhO1lxqvZMyGLeQ/t9hahPLPrEdP0BPB+VNSkWyenIDcJvE6usIGEFnBkln[/tex]，[tex=10.714x2.857]Nw/iCPiBfAazOGg7nvEajh7tquELrKfk9oUtjn7NG9KogL9RmNBfFhNAX9t+l9poz6/+D46E58+GlNFt0rebCWXVLMNdEzfBZXO3mg6jphLLu63I89yG8Tr6Fg1iALbq[/tex]，因为[tex=2.429x1.214]/HVqmYz0axKhGYzcalhO+gJ8av6lKrqDWX2SFIXviWA=[/tex]，[tex=2.214x1.214]VFJJ3d0VHPDNwfXtg5iaz99FARgqvFI6EDEdeA07IQM=[/tex]是可逆的而[tex=6.929x2.857]jcCMHflCR8OS9TosV6N5vFA4o5KwCvcZw7OQuwp/Z3bYaK05rhwwntLlZUhWF7XYKriyG6eRtvH8X8o31JyGMVparNPx6LMsZPUAdqih96Y=[/tex]，[tex=6.714x2.857]075gCzZzsMRb6HYXYk9X9xYTAnsYVafTdsPcWQqaNhcZCJ3XXRUMheNGa/+cADBlYowMVzEnPrYcQLYAl2zsCkvCTLi/fPs/Qy8ks3aLgVc=[/tex]，的秩都为[tex=0.5x0.786]51EIYuoXo3UTYashe96uEQ==[/tex]，所以[tex=6.571x1.357]ASPNbXL4S3TWthOfFETgH3hFXu7ZVgJdXIfCRYHZa4s=[/tex].并且[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]是[tex=2.714x1.071]Xa6YzCV9VTlW9p4lLOpktw==[/tex]的，[tex=0.714x1.0]9fIXCQOmrgOp2L5B47vYUQ==[/tex]是[tex=2.429x1.071]fYRl1cpBZV0k8ULAvI7FIg==[/tex]的.而且计算可得[tex=35.0x2.857]Xp8jpYvcvXftJyrrPz4fu3oTZd1bleyA02I47KS/LVJr8ybriC3bxlbmqpsufp2jLMHm2Q3wW7aOn7gtKXE9jcbIn7CULDc0mca90AfYYgcVo/GzYGsx9LZ/HTocIrLAk6GBaK4KND/o9YmdJTi1rE6QnraX5oV40X9fRW3IwSUU7hUImzjnj0h1zYqDNR47g9GqjawqYOoaYt1AhXGqqtDvP79CTcN+VjxQ7usQ65YtfLATdnUm0BhQQhHwo3U4d7DSNt3DCd/VHsj9ZOOvHtsZGkoh4J4EBVRBZcbYtmHiMwf0N8aTMF8kHrvZmXtYQgahW7mRA3hIUwdnKR6ISjFmZ9XGJdAxwYWYTNVGTrQyUbBXScgxaTaeWseYejT968udCGAluFrebF9W7UPnmg==[/tex](2) 只需令[tex=11.286x2.857]ajLKReZtRmFT6yGtLXJKAKuIjsdqeYqVoLebNZr8VpN03wKokkSPutIa9oePbgYRSp456gexFUGdybj5wgG0Pomgu2AObhlsNEoeWTRnCxjJIkhrUAbMp/8U7f6jbvIy[/tex]，[tex=10.857x2.857]5KkWR0/NxYE/C8lkSBm4pO3dZ13QthNOuP7aK0PL0f8HnbbR34+tCx4Ty30i8pz4rqitk1cPSNBZ37oI5TJfHMcPQocm4KUI9n8d8VJbxlaM6VSE4G0FpbP1mHgf1Zk5[/tex]，同(1)分析可知这样构造得到的[tex=2.643x1.214]lm1bD7FNxYMRadaYfCaVaAhmNjQKET8XbNu5YWNqVSU=[/tex]，[tex=2.286x1.214]FYyGaRzcsFPOp3Apviu4URjBr5ENI14wIxqKgeirq6o=[/tex] 即为所需的两个矩阵.(3) 只需令[tex=9.143x2.857]LSOlm+su56MJfVxQv2wj1ohWMHjPFc7ETpS3B+ENz5aZ2BLAT4SKISiVBsbb76M0vx3HTpakMzUW1fNdMJmiZpez7WGhCCvYYAqnFGUyDBdjEbKRn5IGZTLN3Ix/xKlc[/tex]，[tex=8.786x1.429]uY74pY8/bNizJM/QefDoDzaSisz8vyAcFppJwCVYpdQT9bgvFTCZ9RE8m4+e+acBmIAVF/CS/caFFw7wa87B+A==[/tex]同 (1) 分析可知这样构造得到的[tex=2.286x1.214]d7S1LcIgklK8UUaYKlZqXvaVXC4IWD9FMerwDsu+miA=[/tex]，[tex=1.929x1.214]SMuZNX4dUxK2T900+oXjZ15tzH5HO9oejeKdaL4Q3as=[/tex]即为所需的两个矩阵.

举一反三

内容

0
对于以下两种情形:(1)x为自变量,(2)x为中间变量,求函数[tex=2.214x1.214]sy9gaFRMGlrH59gm9bWSDg==[/tex]的[tex=1.5x1.429]5W5tOYbJ+LlsRP2dMsi4byxwtjvvL/3u7NEzPV5PWp0=[/tex]
1
[tex=2.214x1.0]Z8GWW72u+MH/mjafnp+83A==[/tex]丙酮酸经过丙酮酸脱氢酶系和柠檬酸循环产生[tex=4.0x1.214]EPDWVFNjIR8daNoozaWRDg==[/tex],生成的[tex=3.214x1.0]1AqDCKqjaAug6buHS5Z0tQ==[/tex]、[tex=3.429x1.214]HYAn2+I9AZQLWcA3ajoPaw==[/tex]和[tex=2.143x1.0]qQANfGnLx7pE5mcaEibuNg==[/tex](或[tex=2.071x1.0]YGdeb/NAM7yg+XY6SY16Fg==[/tex])的摩尔比是( )。未知类型：{'options': ['3:2:0', '4:2:1', '4:1:1', '3:1:1', '2: 2:2'], 'type': 102}
2
有容量分别为[tex=3.286x1.286]pCZ+fPe3X5XtlIcXCf6RGw==[/tex]和[tex=3.286x1.286]JjWMjbwalVPPThZBywJsLQ==[/tex]的独立随机样本得到下述观测结果，（X、 Y为观测值， f为频数）X 12.3 12.5 12.8 13.0 13.5 Y 12.2 12.3 13.0f 1 2 4 2 1 f 6 8 2现已知变量X、Y的总体均呈正态分布。请问在0.05的显著性水平下，可否认为这两个总体属同一分布？[tex=24.786x1.286]OVWwFMgiPzBDnRSqBYypUv4puOxaqZVbzeGoYhEt/ZwiQxP0kGgAAWuaJInyBhH09xLkSWqB6n3qd1WXaKpfvwUNfmmVSMJTzi4wz4IT6q4=[/tex][tex=8.429x1.286]AcUD6cTXhAghaQMem3GRbFMfFVpZHcyA3tP0z+S7RAk=[/tex] [tex=13.357x1.357]ZPe8nXNlBeMmW2cEA+D6DaqP/loFbcVH2QukDH1SMofLM6E74nDyl0WrH8imm/Ai[/tex]
3
判断半径大小并说明原因:(1)[tex=1.071x1.0]ZIxpATrL2EWTpYe3CKPlpg==[/tex]与 [tex=1.357x1.0]LO7mudz7++HOXb8YDQ1UtQ==[/tex](2) [tex=1.286x1.0]nOvFdt4hpTubfX23eRvSvg==[/tex]与[tex=1.071x1.0]Kr2c9X1cZ4El5JSNMoM0/w==[/tex](3) [tex=1.214x1.0]Q1mlMfKWwfAuQJLgzt2cVQ==[/tex]与[tex=1.357x1.0]ovKrdUm5wnQSTfl9He3wzA==[/tex](4)[tex=1.143x1.0]8nY7k4VEnlDIEx7o05iMhQ==[/tex]与[tex=1.357x1.214]in11+JirBe0MeyXDnVwAww==[/tex](5)[tex=1.643x1.214]cIgqspnlK9Ra13rNdyZhHQ==[/tex]与[tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex](6)[tex=1.929x1.143]CtrLAecFBVyCnMYbqB02Ag==[/tex]与[tex=2.0x1.214]2cEIifUWf5oYRzhjCpTV6A==[/tex](7)[tex=2.214x1.214]OdTls2gllRl/Z1zy0+35/g==[/tex]与[tex=2.071x1.214]YDXlUgl4Yvd6QFjcd0Ns2Q==[/tex](8)[tex=2.071x1.214]QvCjZKA7OQkNYccCl0MVgQ==[/tex]与[tex=1.929x1.214]GDfkuEdqfBLP2oRgr+Wojw==[/tex]
4
求下列函数的导函数：(1) [tex=5.0x2.357]X/CieCDGJ7iPQ3YFWuscHxHrcIE/dPFa9tFyiJXze8A=[/tex](2)[tex=6.643x1.714]Oj74y/L+OxY81QME5JWMcl+7PZ2FGQswwvjgVhjq1Dmb6dBU0oAjZBW7eFBVjqo6[/tex]