0158《 高等代数》西南大学20春在线作业
0158 高等代数1.[判断题]设多项式f(x)|g(x)，c是一个非零常数，则cf(x)|g(x)。
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A.正确
B.错误
2.[判断题]一个齐次线性方程组的两个解向量的和仍是该方程组的一个解向量。
A.正确
B.错误
3.[判断题]设A是n阶矩阵，若非齐次线性方程组AX=B无解，则|A|=0。
A.正确
B.错误
4.[判断题]设A是可逆矩阵，交换A的第一行和第二行得矩阵B，则B也是可逆矩阵。
A.正确
B.错误
5.[判断题]设<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572446077367048801.png" title="201910301572446077367048801.png" alt="图片25.png"/>是线性空间V的两个子空间，若<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572446165366050516.png" title="201910301572446165366050516.png" alt="图片26.png"/>。
A.正确
B.错误
6.[判断题]设W是线性空间V的子空间，<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572445973978088146.png" title="201910301572445973978088146.png" alt="图片24.png"/>。
A.正确
B.错误
7.[判断题]设A是n阶矩阵，|A|=0，E是n阶单位矩阵，则|A+E|=1。
A.正确
B.错误
8.[判断题]若多项式g(x)|f(x)，则g(x)为f(x)与g(x)的一个最大公因式。
A.正确
B.错误
9.[判断题]如果一个向量组线性相关，那么它的任一部分组也线性相关。
A.正确
B.错误
10.[判断题]设<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572445694215040909.png" title="201910301572445694215040909.png" alt="图片22.png"/>为一个向量组，由于<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572445741577091057.png" title="201910301572445741577091057.png" alt="图片23.png"/>，所以<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572445756256079083.png" title="201910301572445756256079083.png" alt="图片19.png"/>线性无关。
A.正确
B.错误
11.[判断题]如果一个二次型是正定的，那么它的函数值恒大于零。
A.正确
B.错误
12.[判断题]数域P上两个不可约多项式的积一定是可约多项式。
A.正确
B.错误
13.[判断题]如果两个n阶矩阵的秩相同，那么它们一定合同。
A.正确
B.错误
14.[判断题]设<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572446632675069492.png" title="201910301572446632675069492.png" alt="图片19.png"/>为一个向量组，若<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572446740732007286.png" title="201910301572446740732007286.png" alt="图片27.png"/>，则<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572446754168089235.png" title="201910301572446754168089235.png" alt="图片19.png"/>线性相关。
A.正确
B.错误
15.[判断题]若A，B为n阶对角形矩阵，则AB=BA。
A.正确
B.错误
16.[主观填空题]6级排列654213的逆序数等于 。 奥鹏作业答案 Q 7 61 296 021
A.
17.[主观填空题]设A为<img class="kfformula" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAAsCAYAAADl06/eAAADTUlEQVRoQ+3YS8hVVRjG8Z8JVkY4iBQHoWEZERQhQQPBSeQgFAykQWZQUWB0cVAgIYnkLY2KcCBUWiRlBpGF0U2NCBrUJAhqkJiBNUijxKSbxQvrxOl0LpvDt18x14Zv8p2117PWfz/rXc9ak9QnhcCkFJUqooJOMkEFXUEnEUiSqY6uoJMIJMlUR1fQSQSSZKqjK+gkAkky1dEVdBKBJJnq6P8h6HOwAIvxA87HFXgFb+HXluZ8EZ7GXryNH4v2dViGx3C4Je1/us1ydOjcjW/wDv4qI7gMO/AR1rQEO0DvxMIemK9iFQ62DTn6zwI9C8/hPTzVBTT0Hy0fYRE+a2HSAfpBvIzp+B1f4ljXB29B9t9dZoGeUZz7LVbiRNcwVuMh3IhPWphxgF6BLTjZQv+NuswCPWgwU0v9nI3l+K6nYSz3a/DMCEgX4xE8j897+qigcRV240k822cpB8An8DUeHwB7VJuzHvSF2FhcHDAHLethIEdBDnMH6PvwKebgK1yNn/BSTxlrVAbGaZRdOqJU3ITLcS1eL46ODWrY0w9oE8gd0LEBx19ns41534+5eDgDdjbobpihHbk6ausG7B+RArrBbi/5d1hJ6WhFfj8Pv/R8ycjwu7C5xL9xjNr4ndMJuhMv7yqwb8eHI0Ye6SU2xvnYNqRuNwEwrewLUbLuxfEmL43b5nSDjnHPw5vYU6LfsAg2kaDjZBqbcDj7VhwZF2KT9zJAT8YDuAP34OMBS/j7MuGjAwbeXTpeKG7+YoSrL8FaHMCLPaWpA/p63FI2ySbMxmqTAXpKSRc3F5C9oCMBvIZ9Qxzdb+PruHsY7ID4bjmsrMOfXZQi9Wwt9x5RviKFtPZkgI7BL8EpvNFnJneWJXzbgN+HpYtRsGeWaBcx8ucBKylg98vwEwo9C/QF5QInNrsPCvSYyJWIBBH/W98nZjWJcKNgL8Wl5QTauSEMN2/Cb2Uj7r4SmFDAnc6yQIfeubih1MNDJXJFDY3buwD9R58ZTsQRPOYY5SluD8PVkdkjx8dh5f2Wbgz/M5VM0K045UzptIJO+lIVdAWdRCBJpjq6gk4ikCRTHV1BJxFIkqmOrqCTCCTJVEdX0EkEkmSqoyvoJAJJMn8DZHa4La1dYmwAAAAASUVORK5CYII=" data-latex="3\times 5"/>矩阵，B为<img class="kfformula" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAArCAYAAAD41p9mAAACr0lEQVRoQ+3YXajNWRjH8c8pecndRNHcIJPcuKK8lFDcEFcuxlsRNUpK3CkSIS93IpQrYkoKKZELoqamJE0zV/KW8pJCZkQyemqd2u3O3nPOyXma/taqfbPPav3O892//+951r9HXSkEelJUqogKOskEFXQFnUQgSaY6uoJOIpAkUx1dQScRSJKpjq6gkwgkyVRHV9BJBJJkMh39M2bjBP7CF4zDSrzHsaSaQybqXo93+DVDNxN0AD3dVtRj7MQ5fMwouGhMxVkcxJkM3WzQb/ASo/ECD/Apo9AWjVHYh3XY2FTQj3AnGWy73GJMLNHRWEcPBPRwbMVdXMO/XX6gmViOXSV3O239sey7XpxcQRdSs3AIe3C1A+z+7InjhmEzLmBEaYKNBf0B4/G6ZHM4MZrR/S6O7Qayv5AD9DyMwXlMaTroyTiAAB5rAo5jL252iYa+gA4E8tjS/I7g76aDHonP5dPLNKae7ZiBDWUi6cS7FezbMpp1i5RWjTj7t/LkxPeNdnQngEtxEYsQTarbmoujJW+3dMnt1jOmISLqZEs8fZeg5+A2fikx8i1Bx7y+CafwquXgRoKOeFhTmtEOPG0j2Qs6/ra7nzn9T4mOuFV2mkbiqJiZV+Fe27k/YDVu4A9EFMWtNV4FDMnKuBlGNh9GAF2BP9sqWVjm5GW41KHKvhpfxEiMfv8Fu68jG+noKHQtnhWgrYX3NsMFxWGxp311my4GC7uxoGO8iltbNLJ4VGMF5PnYj224NUDIvdsHAzsaZMzT8T817qVSNKbIy+l4iEl4Xl6bPukD8lBcwX8qV/B4Spbgd1wu1/wrQxLOLa4ayvPr2RV0rgcypo7civ6nahV00g9TQVfQSQSSZKqjK+gkAkky1dEVdBKBJJnq6Ao6iUCSTHV0BZ1EIEnmK5iHqSxPAm81AAAAAElFTkSuQmCC" data-latex="5\times 4"/>矩阵，则AB的列数等于<span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
18.[主观填空题]在向量组<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572443587752099405.png" title="201910301572443587752099405.png" alt="图片19.png"/>中，<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572443702259051093.png" title="201910301572443702259051093.png" alt="图片20.png"/>，则<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572443716984061091.png" title="201910301572443716984061091.png" alt="图片19.png"/>的秩等于<span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
19.[主观填空题]设A为3阶矩阵，A的特征值为2，0，-5，则A的秩等于 。
A.
20.[主观填空题]若2为f(x)的根，且2是<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/24/201910241571925269718074577.png" title="201910241571925269718074577.png" alt="图片10.png"/>的5重根，则2为f(x)的<span style="text-decoration: underline;"> </span><span style="text-decoration: none;">重根。</span>
A.
21.[主观填空题]设<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572438468911007973.png" title="201910301572438468911007973.png" alt="图片8.png"/>，则f(x)的所有系数的和等于<span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
22.[主观填空题]若<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/29/201910291572350129457051704.png" title="201910291572350129457051704.png" alt="图片1.png"/>，则c=<span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
23.[主观填空题]设<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/25/201910251571970044803001646.png" title="201910251571970044803001646.png" alt="图片4.png"/>为对称矩阵，则a=<span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
24.[主观填空题]若矩阵<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/24/201910241571923842777062000.png" title="201910241571923842777062000.png" alt="图片8.png"/>不可逆，则a=<span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
25.[主观填空题]3阶行列式<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs2018/2019/10/30/201910301572449847072038120.png" title="201910301572449847072038120.png" alt="图片36.png"/><span style="text-decoration: underline;"> </span><span style="text-decoration: none;">。</span>
A.
26.[问答题]<img style="vertical-align: middle; margin-right: 2px;" src="http://zuoye.eduwest.com/ueditor/dialogs/attachment/fileTypeImages/icon_doc.gif"/><a style="font-size:12px; color:#0066cc;" href="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/attachFiles2018/2020/03/09/202003091583765496691074385.doc" title="计算题.doc">计算题.doc</a>
A.
27.[问答题]<img style="vertical-align: middle; margin-right: 2px;" src="http://zuoye.eduwest.com/ueditor/dialogs/attachment/fileTypeImages/icon_doc.gif"/><a style="font-size:12px; color:#0066cc;" href="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/attachFiles2018/2020/03/09/202003091583765598274073038.doc" title="证明题.doc">证明题.doc</a>
A.
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