设a<sub>1</sub>,a<sub>2</sub>...a<sub>s</sub>是s个n维向量,下列论断正确的是().
A.a,不能由a<sub>1</sub>,a<sub>2</sub>...a<sub>s-1</sub>线性表出,则向量组a<sub>1</sub>,a<sub>2</sub>...a<sub>s</sub>线性无关
B.已知存在不全为零的数k<sub>1</sub>,k<sub>2</sub>.....k<sub>s-1</sub>使得<img src='https://img2.soutiyun.com/ask/2021-03-04/983720401819059.png' />则a<sub>s</sub>不能由a<sub>1</sub>,a<sub>2</sub>...a<sub>s-1</sub>线性表出
C.a<sub>1</sub>,a<sub>2</sub>...a<sub>s</sub>线性相关,则任一向量均可由其余向量线性表出
D.a<sub>1</sub>,a<sub>2</sub>...a<sub>s</sub>线性相关,as不能由a<sub>1</sub>,a<sub>2</sub>...a<sub>s-1</sub>线性表出,则a<sub>1</sub>,a<sub>2</sub>...a<sub>s-1</sub>线性相关
时间:2024-07-01 17:08:56
-
设集合U={-2,-1,1,3,5},集合A={-1,3},那么C<sub>U</sub>A=()
A.{-2,1}
B.{-2,-1,5}
C.{-2,1,5}
D.{-1,3}
-
设论述域是{a<sub>0</sub>,a<sub>1</sub>,a<sub>2</sub>···a<sub>n</sub>}试证明下列关系式:
<img src='https://img2.soutiyun.com/ask/2021-01-28/980687024369602.png' />
-
设S={a<sub>1</sub>,a<sub>2</sub>,...,a<sub>8</sub>},B,悬S的子集,由Br;和B:所表达的子集是什么?应如何规定子集{a<sub>1</sub>,a<sub>2</sub>,...,a<sub>7</sub>}和{a<sub>1</sub>,a<sub>8</sub>}.
-
设α,β,γ<sub>1</sub>,γ<sub>2</sub>均为3维行向量,矩阵已知|A|=18,|B|=2,求|A-B|。
设α,β,γ<sub>1</sub>,γ<sub>2</sub>均为3维行向量,矩阵<img src='https://img2.soutiyun.com/ask/2020-10-22/972229266040196.png' />已知|A|=18,|B|=2,求|A-B|。
-
设A<sub>j</sub>表示四阶行列式 的第j列(j=1,2,3, 4),已知|a<sub>ij</sub>|=-2,那么
A.A.3
B.B.6
C.C.-6
D.D.-2
-
设A为n阶矩阵,β<sub>1</sub>,β<sub>2</sub>,···,β<sub>n</sub>为A的列子块,试用β<sub>1</sub>,β<sub>2</sub>,···,β<sub>n</sub>表示A<sup>T</sup>A。
-
设全集U={-2,-1,0,1,2},集合A={1,2},B={-2,1,2},则A∪(<sub>U</sub>B)等于()
A.?
B.{1}
C.{1,2}
D.{-1,0,1,2}
-
设a<sub>1</sub>>b<sub>1</sub>>0,记n=2,3,···证明:数列{a<sub>n</sub>}与{b<sub>n</sub>}的极限都存在且等于
设a<sub>1</sub>>b<sub>1</sub>>0,记<img src='https://img2.soutiyun.com/ask/2021-02-03/981198184073394.png' />n=2,3,···
证明:数列{a<sub>n</sub>}与{b<sub>n</sub>}的极限都存在且等于<img src='https://img2.soutiyun.com/ask/2021-02-03/981198207491733.png' />
-
设(A<sub>1</sub>,A<sub>2</sub>,…,A<sub>n</sub>)是集合的非空搜集,对n作归纳证明下述推广的德·摩根定律:
设(A<sub>1</sub>,A<sub>2</sub>,…,A<sub>n</sub>)是集合的非空搜集,对n作归纳证明下述推广的德·摩根定律:
<img src='https://img2.soutiyun.com/ask/2021-01-28/980696909231985.png' />
-
设a<sub>1</sub>=(5,-8,-1,2)<sup>T</sup>,a<sub>2</sub>=(2,-1,4,-3)<sup>T</sup>,a<sub>3</sub>=(-3,2,-5,4)<sup>T</sup>,从方程a≇
设a<sub>1</sub>=(5,-8,-1,2)<sup>T</sup>,a<sub>2</sub>=(2,-1,4,-3)<sup>T</sup>,a<sub>3</sub>=(-3,2,-5,4)<sup>T</sup>,从方程a<sub>1</sub>+2a<sub>2</sub>+3a<sub>3<img src='https://img2.soutiyun.com/ask/2020-11-26/97526278028527.png' /></sub>
-
设向量组A:a<sub>1</sub>,a<sub>2</sub>;B:a<sub>1</sub>,a<sub>2</sub>,a<sub>3</sub>;C:a<sub>1</sub>,a<sub>2</sub>,a<sub>4</sub>的秩为R<sub>A</sub>=R<sub>B⌘
设向量组A:a<sub>1</sub>,a<sub>2</sub>;B:a<sub>1</sub>,a<sub>2</sub>,a<sub>3</sub>;C:a<sub>1</sub>,a<sub>2</sub>,a<sub>4</sub>的秩为R<sub>A</sub>=R<sub>B</sub>=2,R<sub>c</sub>= 3,求向量组D:a<sub>1</sub>,a<sub>2</sub>.2a<sub>3</sub>- 3a<sub>4</sub>的秩.
-
设a∈R<sup>n</sup>,a=(a<sub>1</sub>,a<sub>2</sub>,...,a<sub>n</sub>)<sup>T</sup>≠0 求证: 是正交矩阵。
设a∈R<sup>n</sup>,a=(a<sub>1</sub>,a<sub>2</sub>,...,a<sub>n</sub>)<sup>T</sup>≠0
求证:
<img src='https://img2.soutiyun.com/ask/2020-08-16/966461113345045.png' />
是正交矩阵。
-
设A为n阶矩阵,证明:当k<sub>1</sub>≠0,k<sub>2</sub>≠0时,k<sub>1</sub>ξ<sub>1</sub>=k<sub>2</sub>ξ<sub>2</sub>不是A的特征向量.
设A为n阶矩阵,<img src='https://img2.soutiyun.com/ask/2021-03-05/983793334730841.png' />证明:当k<sub>1</sub>≠0,k<sub>2</sub>≠0时,k<sub>1</sub>ξ<sub>1</sub>=k<sub>2</sub>ξ<sub>2</sub>不是A的特征向量.
-
设X~N(μ,36),Y~N(u,64),记P<sub>1</sub>=P{X≤μ-6},P<sub>2</sub>=P{Y≥μ+8},则对任何实数μ都有[].(A)P<sub>1</sub>=P<sub>2</sub>;(B)P<sub>1</sub>>P<sub>2</sub>;(C)p<sub>1</sub><p<sub>2</sub>;(d)p<sub>1</sub>≠p<su
-
设A={1,2,3,4},A<sub>1</sub>={1,2},A<sub>2</sub>={1},A<sub>3</sub>=∅,求A<sub>1</sub>,A<sub>2</sub>,A<sub>3</sub>和A的特征函数X<sub>A1</sub>,X<sub>A2</sub>,X<sub>A3</sub>和X<sub>A</sub>。
-
设a<sub>1</sub>,a<sub>2</sub>,…,a<sub>n</sub>为互不相同的效,F(x)=(x-a<sub>1</sub>)(x-a<sub>2</sub>)…(x-a<sub>n</sub>)。证明:任何多
设a<sub>1</sub>,a<sub>2</sub>,…,a<sub>n</sub>为互不相同的效,F(x)=(x-a<sub>1</sub>)(x-a<sub>2</sub>)…(x-a<sub>n</sub>)。证明:任何多项式f(x)用F(x)除所得的余式为
<img src='https://img2.soutiyun.com/ask/2020-07-30/964972727738352.png' />
-
设a<sub>1</sub>=(1,1,0),a<sub>2</sub>=(0,1,1),a<sub>3</sub>=(3,4,0),求a<sub>1</sub>-a<sub>2</sub>及3a<sub>1</sub>+2a<sub>2</sub>-a<sub>3</sub>。
-
设向量组B:b<sub>1</sub>,b<sub>2</sub>,…,b<sub>r</sub>能由向量组A:a<sub>1</sub>,a<sub>2</sub>,…a<sub>r</sub>线性表示为(b<sub>1</sub>,b<sub>2⌘
设向量组B:b<sub>1</sub>,b<sub>2</sub>,…,b<sub>r</sub>能由向量组A:a<sub>1</sub>,a<sub>2</sub>,…a<sub>r</sub>线性表示为(b<sub>1</sub>,b<sub>2</sub>,…,b<sub>r</sub>)=(a<sub>1</sub>,a<sub>2</sub>,…,a<sub>r</sub>)K,其中K为s×r矩阵,且A组线性无关。证明B组线性无关的充要条件是矩阵K的秩R(K)=r。
-
设n≥2.f<sub>1</sub>(x),f<sub>2</sub>(x),..,f<sub>n-2</sub>(x)是关于次数小于或等于n-2的多项式,a<sub>1</sub>,a<sub>2</sub>,..
设n≥2.f<sub>1</sub>(x),f<sub>2</sub>(x),..,f<sub>n-2</sub>(x)是关于次数小于或等于n-2的多项式,a<sub>1</sub>,a<sub>2</sub>,...,a<sub>n</sub>为任意数,证明:行列式
<img src='https://img2.soutiyun.com/ask/2021-01-17/979772528327203.png' />
并举例说明条件“次数≤n-2”是不可缺少的.
-
设R<sub>1</sub>和R<sub>2</sub>是集合A=(a,b,c,d)上的关系,这里
设R<sub>1</sub>和R<sub>2</sub>是集合A=(a,b,c,d)上的关系,这里
<img src='https://img2.soutiyun.com/ask/2021-01-29/980786433537646.png' />
-
设λ<sub>1</sub>,λ<sub>2</sub>都是n阶矩阵A的特征值,λ<sub>1</sub>≠λ<sub>2</sub>,,且a<sub>1</sub>与a<sub>2</sub>分别是A的对应于λ<sub>1</sub>与λ<sub>2</sub>的特征向量,则().
A.c<sub>1</sub>=0且c<sub>2</sub>=0时,a=c<sub>1</sub>a<sub>1</sub>+c<sub>2</sub>a<sub>2</sub>必是A的特征向量
B.c<sub>1</sub>≠0且c<sub>2</sub>≠0时,a=c<sub>1</sub>a<sub>1</sub>+c<sub>2</sub>a<sub>2</sub>必是A的特征向量
C.c<sub>1</sub>,c<sub>2</sub>=0时,a<sub>1</sub>=c<sub>1</sub>a<sub>1</sub>+c<sub>2</sub>a<sub>2</sub>必是A的特征向量
D.c<sub>1</sub>≠0而c<sub>2</sub>=0时,a=c<sub>1</sub>a<sub>1</sub>+c<sub>2</sub>a<sub>2</sub>必是A的特征向量
-
设3(a<sub>1</sub>-a)+2(a<sub>2</sub>+a)=5(a<sub>3</sub>+a),其中a=(2,5,1,3)<sup>T</sup>,a<sub>2</sub>=(10,1,5,10)<sup>T</sup>,a<sub>3</sub>=(4,1,-1,1)<sup>T</sup>.求a向量由另外三个向量的线性表示.
-
设a<sub>1</sub>,a<sub>2</sub>,a<sub>3</sub>为正数1>2>3.证明:方程在区间(1,2)与(2,3)内各有一根.
设a<sub>1</sub>,a<sub>2</sub>,a<sub>3</sub>为正数<img src='https://img2.soutiyun.com/ask/2020-11-28/975436278461242.png' />1><img src='https://img2.soutiyun.com/ask/2020-11-28/975436278461242.png' />2><img src='https://img2.soutiyun.com/ask/2020-11-28/975436278461242.png' />3.证明:方程
<img src='https://img2.soutiyun.com/ask/2020-11-28/975436328089081.png' />
在区间(<img src='https://img2.soutiyun.com/ask/2020-11-28/975436278461242.png' />1,<img src='https://img2.soutiyun.com/ask/2020-11-28/975436278461242.png' />2)与(<img src='https://img2.soutiyun.com/ask/2020-11-28/975436278461242.png' />2,<img src='https://img2.soutiyun.com/ask/2020-11-28/975436278461242.png' />3)内各有一根.
-
求证四直线a<sub>1</sub>x<sup>2</sup>+2h<sub>1</sub>xy+b<sub>1</sub>y<sup>2</sup>=0a<sub>2</sub>x<sup>2</sup>+2h<sub>2</sub>xy+b<sub>2</sub>y<sup>2</sup>=0成调和线束的充要条件是a<sub>1</sub>b<sub>2</sub>+a<sub>2</sub>