设[tex=7.214x1.286]itM1zREauh9F4ZvfS14M1+Dof2Y51unHLcn0d2QfLNY=[/tex]，证明：（1）存在[tex=2.571x1.286]HZJWSsoyOzmWbT8BjkQzO0Y+WbST060CkrxPGWjRfYE=[/tex]，[tex=2.286x1.286]41F2pSd/QgGL6d94b04phkb07ZU3sNCbaTxJsnurITU=[/tex]，[tex=8.071x1.286]ozLlBKUTqqDA8mX+nPWlvBf6UcZe0eqnaNOa0C+Qdug=[/tex]，使[tex=3.643x1.286]JyBS1UhiO/VAkWcj8RxcQg==[/tex]；（2）存在[tex=2.786x1.286]UwypD1JPgqzihZlNywIRJn/k5aVwjlqpoe8Cb8ZBkqQ=[/tex]，[tex=2.429x1.286]30bunvIBg8TG5uBos0A5zJO/3ZelnsKJoL0rx/D/N+M=[/tex]，[tex=8.071x1.286]u5MByEykxsWQao9jXqP0hEgKNCcFij8AfXSEQTgOWdw=[/tex]，使[tex=3.643x1.286]HJVyndwSRhtEgFk7GAA0Qg==[/tex]；（3）存在[tex=2.429x1.286]1fkiac3zIxSRaIJAeBiMef7WLW3h1+DjumE5ucuxBIY=[/tex]，[tex=2.071x1.286]3a9DU4t/74kipFp+fCK0bklmiy+WdJMA2BvzuBAxIBE=[/tex]，[tex=7.929x1.286]qY8HAwm7jZsMi2WUMoBdc4h9V3cLIh+tIfviCPqzFW8=[/tex]，使[tex=3.429x1.286]eLmQ1SJ6zHm4LEtQwlqEhg==[/tex].

2022-06-08

设[tex=7.214x1.286]itM1zREauh9F4ZvfS14M1+Dof2Y51unHLcn0d2QfLNY=[/tex]，证明：（1）存在[tex=2.571x1.286]HZJWSsoyOzmWbT8BjkQzO0Y+WbST060CkrxPGWjRfYE=[/tex]，[tex=2.286x1.286]41F2pSd/QgGL6d94b04phkb07ZU3sNCbaTxJsnurITU=[/tex]，[tex=8.071x1.286]ozLlBKUTqqDA8mX+nPWlvBf6UcZe0eqnaNOa0C+Qdug=[/tex]，使[tex=3.643x1.286]JyBS1UhiO/VAkWcj8RxcQg==[/tex]；（2）存在[tex=2.786x1.286]UwypD1JPgqzihZlNywIRJn/k5aVwjlqpoe8Cb8ZBkqQ=[/tex]，[tex=2.429x1.286]30bunvIBg8TG5uBos0A5zJO/3ZelnsKJoL0rx/D/N+M=[/tex]，[tex=8.071x1.286]u5MByEykxsWQao9jXqP0hEgKNCcFij8AfXSEQTgOWdw=[/tex]，使[tex=3.643x1.286]HJVyndwSRhtEgFk7GAA0Qg==[/tex]；（3）存在[tex=2.429x1.286]1fkiac3zIxSRaIJAeBiMef7WLW3h1+DjumE5ucuxBIY=[/tex]，[tex=2.071x1.286]3a9DU4t/74kipFp+fCK0bklmiy+WdJMA2BvzuBAxIBE=[/tex]，[tex=7.929x1.286]qY8HAwm7jZsMi2WUMoBdc4h9V3cLIh+tIfviCPqzFW8=[/tex]，使[tex=3.429x1.286]eLmQ1SJ6zHm4LEtQwlqEhg==[/tex].

答案：

（1）因为[tex=6.071x1.286]l6KiMuJszw/NiYNc9MgMY4x3i0xaiTN3Z6+2tdFtP/8=[/tex]，所以[tex=0.786x1.286]pi/GsQ3apuRt43V3XQq/tA==[/tex]与[tex=6.5x2.857]De166nmeTkb4C/83+ZZH202/QbV8Y6Xk7v27/WBUYkjBsYPBHE7NHOVK/E1QfD6lKgDvt94OlnMU9eAf1GYr66Ud1MV7z0xGq7mQNNpRXvNA+GNfNzCR+t/Ly1z7QTyu[/tex]等价，即存在两个可逆矩阵[tex=2.643x1.286]yBZ/LqB/AZC7VqtlB/tyL5Kmotis3ZvgbIpErK9nZCY=[/tex]，[tex=2.357x1.286]M2Sv9ryEODSLKW4r+lIDBZC8dYuSPUHXcQ5ugsX8jfA=[/tex]使得[tex=13.5x2.857]RDJhm5pzJFAsQfjNdGow78RlI0yeeDt2UnR3NPfVbsxRqkyigLMccv58fJlXVRC5iUnOC9ENQRkmMnAz/Tr7zf0HQcAZ3l+dWT5D+bogJRPU97+r19ByUoCVpsEU3ybPdnQnwvfHOcHNKfq34gUD/A==[/tex]，令[tex=11.143x2.857]IMX6lHFT9Rneg6GbARSbnTvT872gTbxF8QXCHolCunFkjp8F4eDvreDnJQI75m2DfYVB7LbVzgYP5TqbIh6iTLJPHYIuGmh4jNWvKnrVlqNOluRg1QohI8vMc4DcDQ+zP0McjF3l5j3cbTmp6fQR+g==[/tex]，[tex=10.714x2.857]AXhunoPO/ZvW3RGc9/eBKxUQh65AJrTMJscLLgDNnUBpgofB53c6FqDRG980NLVozG1hJgJUCVrCecd8p31DWkMzb2q6TOK0GfHa4Ot7QYt3vNCAJivRIHp32fWHmZLu[/tex]，因为[tex=2.643x1.286]yBZ/LqB/AZC7VqtlB/tyL5Kmotis3ZvgbIpErK9nZCY=[/tex]，[tex=2.357x1.286]M2Sv9ryEODSLKW4r+lIDBZC8dYuSPUHXcQ5ugsX8jfA=[/tex]是可逆的而[tex=6.5x2.857]De166nmeTkb4C/83+ZZH202/QbV8Y6Xk7v27/WBUYkiBDzYU7nEg9UVCTRIIhqIeT6rVWqE8jIs7hF1LlAwwCVYeT6/5MFSmsXWi1bIwurg=[/tex]，[tex=6.286x2.857]De166nmeTkb4C/83+ZZH202/QbV8Y6Xk7v27/WBUYkiBDzYU7nEg9UVCTRIIhqIeT6rVWqE8jIs7hF1LlAwwCSRupCb6Yf4BKPi7BK9jSgk=[/tex]的秩都为[tex=0.5x1.286]/r3Eij8VRNC5JxYjlQuXEQ==[/tex]，所以[tex=8.071x1.286]ozLlBKUTqqDA8mX+nPWlvBf6UcZe0eqnaNOa0C+Qdug=[/tex]，并且[tex=0.786x1.286]q1djlrfSWHAqH21hBgtrSw==[/tex]是[tex=2.643x1.286]yu9Fqc429BTsCWKDfgGy8g==[/tex]的，[tex=0.786x1.286]TKU5UzNEMzEJwORo6mbEYA==[/tex]是[tex=2.357x1.286]ieJ4oBuAdnQNHF888Qy4pA==[/tex]的。而且计算可得[tex=2.571x1.0]KMdO1deQSBcMSbsM9XcX8Q==[/tex][tex=18.857x2.857]jbJ/mROLWS6ndk4G8jLUWM6EbXHdZhFE7RL5Zp3Wlhxd0TwsablVAaNVlhyk7GzA3ykq3u87VPe9kJvMiAedQCXcVkWwQcJSStjnDkmhTeNLf+ces0xlaAaHo//kTQh8EsJ3CGJjq1CwWuzs0GbDQzbVOT7R7K4kcBon2xKfY9u1FkUbFIdQ8InuVsFg5wUeix415go4+zDveMUHGMxpzalrHPVT5dV5OgQhA6pdrWZM+f8n0xqPCWhat6djPV1G[/tex][tex=13.5x2.857]QU3j1rcBGJPFS3ETfua8E1HjvZr70AL5uojIIqF6FwWiXB+/GpTc5TGVAI9p6PmEgT0gRZLjiLhR1ZbKCycqFKxmFh0FTQJZ+inodpkS0nsvzSNQmEuvXd+jwDXrIb3SwBphdf5D1/v2QYPOLbeEBQ==[/tex]；（2）只需令[tex=11.429x2.857]ul79qfA64XMb/7hpI9lbG2abWmixy0opbTgTJ7mu1CXeCJy8OwlHKU5nvv33JSl9adz26i9OVY1H0f8dNT+gr8fq749+8z4yotQWORrDxXDFB3Le3QNCvT5JQbqNgzqgQqIDuUJjhFTWKh/aRJY0pA==[/tex]，[tex=10.786x2.857]FqgMW7tDCnuqMkErPaLMAyHzzPmxOpXbHPlIgjMIUO1GroXTmFHAA3A/kW4SAwhWxovLwsUEMh3JCB7QryDf10QPi6ZgUNrxFAx5CHdlMfxMXwPTavc1JZURWgQlBOGG[/tex]，同（1）分析可知这样构造得到的[tex=2.786x1.286]UwypD1JPgqzihZlNywIRJn/k5aVwjlqpoe8Cb8ZBkqQ=[/tex]，[tex=2.429x1.286]30bunvIBg8TG5uBos0A5zJO/3ZelnsKJoL0rx/D/N+M=[/tex]即为所需的两个矩阵；（3）只需令[tex=9.286x2.857]euNgL+pw5vNC7EzYkAHBTPcz89SktH8qzGB4hCBWOf7Y6bA6vPpatOzq/VP0wDXtpIY1/1AK+qfcNV2cMilveEQsx0zWtq6aAi1F67jDTRShDdzGoHYzNHjOY26ONHb6[/tex]，[tex=10.286x1.643]g47rcimAzhAVL+vJcEpK+4VxxfII06+hRHW44YqoUSGiVdiGQbHYnRsuMRcS/TCGWm55drtlZgUjCro39AzZ3YeNRDFp28cW3otGdDlyFBk0VjBkymTw2QuB4RKtDVN3[/tex]，同（1）分析可知这样构造得到的[tex=2.429x1.286]1fkiac3zIxSRaIJAeBiMef7WLW3h1+DjumE5ucuxBIY=[/tex]，[tex=2.071x1.286]3a9DU4t/74kipFp+fCK0bklmiy+WdJMA2BvzuBAxIBE=[/tex]即为所需的两个矩阵。

举一反三

内容

0
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 。
1
【单选题】设X为连续型随机变量, 其概率密度: f(x)=Ax2, x∈(0,2); 其它为0. 求(1)A=(); (2) 分布函数F(x)=(); (3) P{1<X<2} (10.0分) A. （1）3/8；（2）x<0, F(x)=0; 0≤x<2, F(x)=1/8x³; x≥2, F(x)=1; （3） 7/8 B. （1）5/8；（2）x<0, F(x)=0; 0≤x<2, F(x)=1/8x³; x≥2, F(x)=0 （3） 1/8
2
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]
3
设二维离散随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的可能值为(0, 0)，(−1, 1)，(−1, 2)，(1, 0)，且取这些值的概率依次为1/6, 1/3, 1/12, 5/12，试求[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]与[tex=0.643x1.0]O+viFNA0oHTwnBtQyi80Zw==[/tex] 各自的边际分布列．
4
设f(x)在[0,a]上连续，在(0,a)内可导，且f(a)=0，证明至少存在一点[tex=3.643x1.357]lTsOOhJ85nTn3mrT2Mx0lw==[/tex]使[tex=6.286x1.429]JZ8spbP5y8lrG0FgeChLIS7LPAFOZNl0MwLjGUb1ZoE=[/tex]