【判断题】【消耗次数:1】
设n阶方阵A与B相似,则|A|=|B|.
正确
错误
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相关题目
【单选题】 设A和B皆为n阶方阵,则下面论断错误的是()。
①  A与B等价的充要条件是rank(A)=rank(B)
②  若A与B等价,则|A|=|B|
③  A与B等价的充要条件是存在可逆阵P、Q,使A=PBQ
④  A可逆的充要条件是A等价于E<SUB>n</SUB>
【单选题】 设A和B皆为n阶实方阵,则下面论断错误的是()。
①  <SPANstyle="FONT-SIZE:10.5pt;FONT-FAMILY:宋体;mso-bidi-font-size:12.0pt;mso-font-kerning:1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:AR-SA;mso-ascii-font-family:TimesNewRoman;mso-hansi-font-family:TimesNewRoman;mso-bidi-font-family:TimesNewRoman">A与B</SPAN><SPANlang=EN-USstyle="FONT-SIZE:10.5pt;FONT-FAMILY:TimesNewRoman;mso-bidi-font-size:12.0pt;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"><SPANstyle="POSITION:relative;TOP:2pt;mso-text-raise:-2.0pt"></SPAN></SPAN><SPANstyle="FONT-SIZE:10.5pt;FONT-FAMILY:宋体;mso-bidi-font-size:12.0pt;mso-font-kerning:1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:AR-SA;mso-ascii-font-family:TimesNewRoman;mso-hansi-font-family:TimesNewRoman;mso-bidi-font-family:TimesNewRoman">相似的充要条件是存在可逆阵P</SPAN><SPANstyle="FONT-SIZE:10.5pt;FONT-FAMILY:宋体;mso-bidi-font-size:12.0pt;mso-font-kerning:1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:AR-SA;mso-ascii-font-family:TimesNewRoman;mso-hansi-font-family:TimesNewRoman;mso-bidi-font-family:TimesNewRoman">,使得A=P<SUP>-1</SUP>BP</SPAN>
②  若A是反对称矩阵,则A<SUP>T</SUP>=-A</P>
③  若A可逆,则A可以表示成若干个初等矩阵的乘积
④  若A是正交矩阵,则|A|=1
【判断题】 设A,B是n阶方阵,且秩(A) =秩(B),则秩(A+B) = 2秩(A)
①  正确
②  错误
【判断题】 A,B是同阶相似方阵,则A与B有相同的特征值.
①  正确
②  错误
【判断题】 若A,B皆为n阶方阵,则行列式 |AB|=|A||B|
①  正确
②  错误
【单选题】 对于n阶方阵A,B,下列结论错误的是( )
①  <img class=jc-formula data-tex=\left| { A }^{ T } \right| =|A| src=https://huaweicloudobs.ahjxjy.cn/699487E936328DA81367E10C602C35DD.png style=vertical-align: middle;/>
②  <img class=jc-formula data-tex=\left| \lambda A \right| =\lambda |A| src=https://huaweicloudobs.ahjxjy.cn/FCE18330BD784DE410607DF890719394.png style=vertical-align: middle;/>
③  <img class=jc-formula data-tex=\left| \lambda A \right| ={ \lambda }^{ n }|A| src=https://huaweicloudobs.ahjxjy.cn/593C83C883A879AAC361EF5F343C3758.png style=vertical-align: middle;/>
④  |AB|=|A||B|
【单选题】 设4阶方阵 A与B的秩满足R(A)=1,R(B)=4,则R(BAB)=[填空].
①  1
②  4
③  2
【判断题】 设A,B都是n阶矩阵,若A,B都可逆,则AB可逆。
①  正确
②  错误
【单选题】 设<img class=jc-formula data-tex=n src=https://huaweicloudobs.ahjxjy.cn/6593C84B94B8062EB35F270378D7D9B6.png style=vertical-align: middle;/>阶方阵A与B相似,下列结论错误的是
①  A和B有相同的特征多项式,从而有相同的特征值
②  R(A)=R(B)
③  |A|=|B|
④  A与B等价,但当它们可逆时,它们的逆矩阵不相似
【单选题】 设,AB为n阶方阵,满足等式AB=O,则必有( )
①  A=O且B=O
②  A+B=O
③  A=O 或B=O
④  A-B=O
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①  innovation
②  selection
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①  condition
②  situation
③  state
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①  which is
②  which it is
③  it is
④  where it is
【单选题】 —Can you take the day off tomorrow? —Well, I’ll have to get ____ from my boss.
①  permission
②  permit
③  allowance
④  possession
【单选题】 The house is made of wood and straw, and____to collapse in a heavy storm.
①  reliable
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【单选题】 ____ the water left in the kettle, the doctor put several things he unwrapped from a handkerchief.
①  At
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①  it
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①  proportion
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①  arbitrary
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