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福师《高等代数选讲》在线作业二-0003

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发表于 2020-8-8 18:51:20 | 显示全部楼层 |阅读模式
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n阶方阵A,有|kA|=k|A|,k为一正整数
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060525/3021e209.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/f6149d48.JPG"></IMG>
A:错误
B:正确

两个对称矩阵不一定相似。
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/65c864f6.JPG"></IMG>
A:错误
B:正确

两个等价的向量组,一定包含相同个数的向量。
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/f1cf9a9d.JPG"></IMG>
A:错误
B:正确

若排列abcd为奇排列,则排列badc为偶排列.
A:错误
B:正确

若f(x), g(x), u(x), v(x) 都是F[x] 中的多项式, 且 u(x)f(x) + v(x)g(x) = 1,则 (f(x), g(x)) = 1.
A:错误
B:正确

若n阶方阵A可对角化,则A有n个线性无关的特征向量
A:错误
B:正确

双射既是单射也是满射
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/8fb902fd.JPG"></IMG>
A:错误
B:正确

<p>试题如图<img height="51" width="236" alt="" src="http://file.open.com.cn/ItemDB/9367/ec52c06f-b050-4019-af36-72dbe4c04098/20081016115622600.jpg" /></p>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/0f2d9fd7.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/6bc08e0e.JPG"></IMG>
A:错误
B:正确

<p>试题如图<img height="24" width="510" alt="" src="http://file.open.com.cn/ItemDB/9367/f2a61474-d62c-4382-af6e-8cdb8a7f321e/20081016115654288.jpg" /></p>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/d4aa6386.JPG"></IMG>
A:错误
B:正确

交换行列式的两列,行列式的值不变
A:错误
B:正确

对于同阶矩阵A、B,秩(A+B)≤秩(A)+秩(B)
A:错误
B:正确

只有可逆矩阵,才存在伴随矩阵
A:错误
B:正确

两个有限维向量空间同构的充要条件是维数相同.
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/6b4d6d38.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060528/253093de.JPG"></IMG>
A:错误
B:正确

<font face="Arial">&nbsp;在全部n(n&gt;1)级排列中,奇排列的个数为n!/2. </font>
A:错误
B:正确

设V是一个n维向量空间,W是V的一个子空间,则dimW≤n
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060525/be135cb9.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/9bc37c04.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060528/5cba88a2.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/6204266d.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060528/0a42edce.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060525/08ea0588.JPG"></IMG>
A:错误
B:正确

(1,1,0), (1,0,1), (0,1,1)构成为3维向量空间的一个基
A:错误
B:正确

n阶实对称矩阵属于不同特征根的特征向量彼此正交
A:错误
B:正确

n维向量空间中选出n+1个向量一定线性无关.
A:错误
B:正确

有理数域是最小的数域
A:错误
B:正确

欧氏空间中的正交向量组一定线性无关
A:错误
B:正确

<span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: Arial; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">若</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;,&quot;serif&quot;; mso-hansi-font-family: Arial; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-fareast-font-family: 宋体">n</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: Arial; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">阶方阵</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;,&quot;serif&quot;; mso-hansi-font-family: Arial; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-fareast-font-family: 宋体">A</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: Arial; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">的行列式等于</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;,&quot;serif&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-fareast-font-family: 宋体">0</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: Arial; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">,则</span><span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: &quot;Times New Roman&quot;,&quot;serif&quot;; mso-hansi-font-family: Arial; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-fareast-font-family: 宋体">A</span><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: Arial; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">的行向量是线性相关的</span>
A:错误
B:正确

<font face="Arial">设Am&times;n为实矩阵,则线性方程组Ax=0只有零解是矩阵A&rsquo;A为正定矩阵的充要条件</font>
A:错误
B:正确

设A为n阶正交矩阵,则A的实特征值是1或-1.
A:错误
B:正确

有理数域上任意次不可约多项式都存在
A:错误
B:正确

矩阵的乘法不满足交换律,也不满足消去律。
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/d1a264e2.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/ce37ffcb.JPG"></IMG>
A:错误
B:正确

在矩阵的初等变换下行列式的值不变
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060528/7ee8c5ab.JPG"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/b0d56310.JPG"></IMG>
A:错误
B:正确

正交矩阵的行列式等于1或-1
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/shuxfxfs/20060526/fc47ecb4.JPG"></IMG>
A:错误
B:正确

两个矩阵A与B,若A*B=0则一定有A=0或者B=0
A:错误
B:正确

矩阵A的行列式不等于零,那么A的行向量组线性相关。
A:错误
B:正确

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