超前自学网《线性代数》18春在线作业1-0001
<p>设A可逆，则下列说法<span>错误的是</span>（<span><span> </span>）。</span></p><p><span><img width=”498″ height=”58″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/4aae370c-3777-4d5c-ad8e-267d5d5aebaf/2016118152218836.jpg” /></span></p><p> </p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”621″ height=”85″ alt=”” src=”http://file.open.com.cn/ItemDB/2016118143148694.jpg” /></p>
A:-6
B:6
C:2
D:-2
<p>下列矩阵中不与对角矩阵相似的是（<span><span> </span>）。</span></p><p><span><img width=”522″ height=”109″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/549e9d4b-76e7-478d-973d-9cbc36bda257/201611814503704.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”350″ height=”75″ alt=”” src=”http://file.open.com.cn/ItemDB/201611814243296.jpg” /></p>
A:2
B:3
C:4
D:5
<p>如图：</p><p><img width=”476″ height=”177″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/84044e50-32bb-42c3-9830-b2362fe8a6ab/2016118153722603.jpg” /></p>
A:A
B:B
C:C
D:D
<p>对任意<em>n</em>阶方阵<strong><em>A</em></strong>、<strong><em>B</em></strong>总有（<span><span> </span>）。</span></p><p><span><img width=”333″ height=”46″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/fd414111-bc9b-4297-878a-58fa7bf65565/2016118152847221.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p><span>如图：</span></p><p><span><img width=”457″ height=”86″ alt=”” src=”http://file.open.com.cn/ItemDB/2016118143510956.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”504″ height=”88″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/4ff6cc63-5f83-48d2-afaf-d536473223ba/201611815214114.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”367″ height=”187″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/6adf6476-065a-4ab1-92df-c654f240ecaf/2016118152247728.jpg” /></p>
A:A
B:B
C:C
D:D
<p>设<em>k</em>为常数，<strong><em>A</em></strong>为<em>n</em>阶矩阵，则|<em>k<strong>A</strong></em>|=（<span><span> </span>）。</span></p><p><img width=”316″ height=”58″ alt=”” src=”http://file.open.com.cn/ItemDB/2016118153525121.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”517″ height=”143″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/7a90213d-5005-4a7d-a44f-295294f57842/2016118145526135.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”338″ height=”33″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/4aae370c-3777-4d5c-ad8e-267d5d5aebaf/2016118151938621.jpg” /></p>
A:-6
B:-2
C:2
D:6
<p>如图：</p><p><img width=”576″ height=”231″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/93719f40-7041-4a0c-9d66-9b6f95b1a4bb/2016118154243503.jpg” /></p>
A:A
B:B
C:C
D:D
<p>设<strong>A</strong>为任意<strong>n</strong>阶矩阵，下列矩阵中为反对称矩阵的是（<span><span> </span>）。</span></p><p><span><img width=”391″ height=”65″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/4b997f12-9386-441e-8663-dfff3d2cbe50/2016118152559446.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”392″ height=”270″ alt=”” src=”http://file.open.com.cn/ItemDB/2016118153343200.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”345″ height=”37″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/15510358-8cc7-4fb7-a41a-085986e07b1d/2016118152351876.jpg” /></p>
A:-4
B:-1
C:1
D:<p>4</p>
<p>如图：</p><p><img width=”470″ height=”99″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/1bd6b681-f39e-484a-b6c5-45da119509d6/2016118144156285.jpg” /></p>
A:A
B:B
C:C
D:D
如图：<p><span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: ‘Times New Roman'”><img width=”366″ height=”88″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/cdd5e1e8-4df1-48ef-bbcd-8d095af63882/2016118153310554.jpg” /></span></p>
A:A
B:B
C:C
D:D
如图：<p><span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: ‘Times New Roman'”><img width=”353″ height=”84″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/7e90fed4-b3fc-4d0b-963f-ad606a124fd6/2016118154358777.jpg” /></span></p>
A:2
B:1
C:0
D:-1
<p>如图：</p><p><img width=”556″ height=”230″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/75760680-2be1-47f7-a4be-cd7ab42aab9f/2016118143052878.jpg” /></p>
A:<p>A</p>
B:B
C:C
D:D
<p>如图：</p><p><img width=”561″ height=”222″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/ca13f49b-9d86-4ad9-b145-dac034992126/201611815013980.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”484″ height=”84″ alt=”” src=”http://file.open.com.cn/ItemDB/2016118142653679.jpg” /></p>
A:8M
B:2M
C:-2M
D:-8M
<p>如图：</p><p><img width=”403″ height=”179″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/1bd6b681-f39e-484a-b6c5-45da119509d6/2016118144116364.jpg” /></p>
A:A
B:B
C:C
D:D
<p>设n阶方阵<strong>A</strong>不可逆，则必有（<span><span> </span>）。</span></p><p><img width=”469″ height=”75″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/ef2e2def-d643-400f-bed4-d3c99e839cad/201611814593951.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”452″ height=”121″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/f085f5f2-742d-491a-825e-826086402c39/201611815944739.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”406″ height=”280″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/4ff6cc63-5f83-48d2-afaf-d536473223ba/2016118152014613.jpg” /></p>
A:A
B:B
C:C
D:D
<p>对任意同阶方阵<em>A,B</em>，下列说法正确的是（<span><span> </span>）。</span></p><p><span><img width=”378″ height=”82″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/55ad0c1a-9d00-4a49-bed3-a1a3c8f7b996/201611814299189.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>设A、B为同阶可逆矩阵，则以下结论正确的是（<span><span> </span>）。</span></p><p><span><img width=”462″ height=”60″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/d215e3a1-ee07-4d4c-b73a-d86f2f389ba1/2016118152134343.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>设<strong><em>A</em></strong><em>，<strong>B</strong></em>是同阶正交矩阵，则下列命题<span>错误的是</span>（<span><span> </span>）。</span></p><p><span><img width=”459″ height=”63″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/fd414111-bc9b-4297-878a-58fa7bf65565/2016118153947412.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”526″ height=”146″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/f085f5f2-742d-491a-825e-826086402c39/2016118145852965.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”488″ height=”204″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/7e90fed4-b3fc-4d0b-963f-ad606a124fd6/2016118154438402.jpg” /></p>
A:A
B:B
C:C
D:D
<p>下列矩阵中是正定矩阵的为（<span><span> </span>）。</span></p><p><span><img width=”326″ height=”149″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/ce1d1f04-a94d-4722-bd98-9be51007acd0/2016118151027950.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”521″ height=”165″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/3dd76c00-22c2-4ee1-8965-939ab9f16d09/201611815394600.jpg” /></p>
A:A
B:B
C:C
D:D
<p>设矩阵<strong>A</strong>的秩为r，则<strong>A</strong>中（<span><span> </span>）。</span></p>
A:所有r<span>-1</span>阶子式都不为0
B:所有r<span>-1</span>阶子式全为0
C:<p><span>至少有一个r阶子式不等于0</span></p>
D:至少有一个r阶子式不等于0
<p>如图：</p><p><img width=”525″ height=”122″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/7e774ebd-6571-42ce-aa02-5ec24ff20488/2016118142937909.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”516″ height=”86″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/18bb9e13-f528-45ef-87e2-dfe952ce65a6/2016118145557584.jpg” /></p>
A:A
B:B
C:<p>C</p>
D:D
<p>如图：</p><p><img width=”367″ height=”189″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/6adf6476-065a-4ab1-92df-c654f240ecaf/2016118152428320.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”546″ height=”61″ alt=”” src=”http://file.open.com.cn/ItemDB/2016118142515879.jpg” /></p>
A:<span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA”>m+n</span>
B:<span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-font-width: 200%”>-</span><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA”>(m+n)</span>
C:<p><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA”>n<span>-m</span></span></p>
D:m<span>-n</span>
<p>下列二次型中，秩为2的二次型是（<span><span> </span>）。</span></p><p><span><img width=”406″ height=”79″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/82a8d622-07ca-41f6-9a1a-3402e4efbf84/2016118154030316.jpg” /></span></p>
A:A
B:B
C:C
D:D
<p>设<strong>A</strong>是正交矩阵，则下列结论错误的是（<span><span> </span>）。</span></p><p><img width=”506″ height=”80″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/93e18e1c-de6f-41a3-947e-66facc0c4bc5/201611815850506.jpg” /></p>
A:A
B:B
C:C
D:D
<p>如图：</p><p><img width=”418″ height=”32″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/28e399e6-0434-4460-b6f2-910230c076ee/2016118154859410.jpg” /></p>
A:错误
B:正确
<span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>设</span><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>阶方阵</span><em><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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; mso-bidi-font-weight: bold”>A</span><span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman’; mso-bidi-font-weight: bold”>、</span><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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; mso-bidi-font-weight: bold”>B</span><span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman’; mso-bidi-font-weight: bold”>、</span><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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; mso-bidi-font-weight: bold”>C</span></em><span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>满足关系式</span><em><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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; mso-bidi-font-weight: bold”>ABC</span></em><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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”>=<strong><em>I</em></strong></span><span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>，则</span><em><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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; mso-bidi-font-weight: bold”>BCA</span></em><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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”>=<strong><em>I</em></strong></span><span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>一定成立。</span>
A:错误
B:正确
<p>如图：</p><p><img width=”289″ height=”35″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/c7f99031-3257-4cce-a422-23f1af99c682/2016118154824194.jpg” /></p>
A:错误
B:正确
<p>如图：</p><p><img width=”330″ height=”39″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/425ce003-6638-4935-94bf-dc04dd8ce2ad/2016118151511383.jpg” /></p>
A:错误
B:正确
<span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>若</span><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>正定，则</span><span lang=”EN-US” style=”FONT-SIZE: 12pt; FONT-FAMILY: ‘Times New Roman’,’serif’; 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: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>的特征值均为正。</span>
A:错误
B:正确
<p>如图：</p><p><img width=”424″ height=”32″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/7e90fed4-b3fc-4d0b-963f-ad606a124fd6/2016118154840612.jpg” /></p>
A:错误
B:正确
<span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>等价的两个矩阵，秩相等。</span>
A:错误
B:正确
<p>如图：</p><p><img width=”366″ height=”38″ alt=”” src=”http://file.open.com.cn/ItemDB/13352/dcdf7b84-b2d1-474e-a1dc-9732493eefb0/201611815175905.jpg” /></p>
A:错误
B:正确
<span style=”FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-ascii-font-family: ‘Times New Roman’; mso-hansi-font-family: ‘Times New Roman’; mso-bidi-font-family: ‘Times New Roman'”>向量组整体线性无关，则部分向量组也线性无关。</span>
A:错误
B:正确
<p><strong><em>A、B、C</em></strong>均为4阶方阵，且有<strong><em>AB=AC</em></strong>，则有<strong><em>B=C</em></strong>。</p>
A:错误
B:正确
