4.设向量组 (alpha )_(1)=(({a)_(11),(a)_(21),(a)_(31))}^r ,_(2)=(({a)_(12),(a)_(22),(a)_(32)) _(3)=-|||-(a13,a23,a33)T。向量组 (beta )_(1)=(({a)_(11),(a)_(21),(a)_(31),(a)_(41))}^r (beta )_(2)=((a)_(12),(a)_(22),-|||-_(32),(a)_(42))}^T, (beta )_(3)=(({a)_(13),(a)_(23),(a)_(33),(a)_(43)) 则有 () 。-|||-(1)若α1,a2,α3线性相关,则β1,β2,β3也线性相关-|||-(2)若α1,α2,α 3线性无关,则β1,β22,β3也线性无关-|||-(3)若β1,β2,β3线性无关,则a1,α2,a3也线性无关-|||-(4)若α1,α2,α 3线性无关的充分必要条件是β1,β2,β3线-|||-性无关

参考答案与解析:

相关试题

设向量组(Ⅰ):α1=(a11,a21,a31)T,α2=(a12,a22,a32)T,α3=(a13,a23,a33)T,向量组(Ⅱ):β1=(a11,a21,a31,a41)T,β2=(a12,a

[单选题]设向量组(Ⅰ):α1=(a11,a21,a31)T,α2=(a12,a22,a32)T,α3=(a13,a23,a33)T,向量组(Ⅱ):β1=(a1

  • 查看答案
  • 设向量组(Ⅰ):α1=(a11,a21,a31)T,α2=(a12,a22,a32)T,α3=(a13,a23,a33)T,向量组(Ⅱ):β1=(a11,a21,a31,a41)T,β2=(a12,a

    [单选题]设向量组(Ⅰ):α1=(a11,a21,a31)T,α2=(a12,a22,a32)T,α3=(a13,a23,a33)T,向量组(Ⅱ):β1=(a1

  • 查看答案
  • 设向量组(Ⅰ):α1=(a11,a21,a31)T,α2=(a12,a22,a32)T,α3=(a13,a23,a33)T,向量组(Ⅱ):β1=(a11,a21,a31,a41)T,β2=(a12,a

    [单选题]设向量组(Ⅰ):α1=(a11,a21,a31)T,α2=(a12,a22,a32)T,α3=(a13,a23,a33)T,向量组(Ⅱ):β1=(a1

  • 查看答案
  • 设向量组(alpha )_(1),(alpha )_(2),(alpha )_(3) 线性无关, (alpha )_(1),(alpha )_(2),(alpha )_(3) 证明:向量组 (alph

    设向量组(alpha )_(1),(alpha )_(2),(alpha )_(3) 线性无关, (alpha )_(1),(alpha )_(2),(alph

  • 查看答案
  • 4.设向量组beta_(1)=alpha_(1)+2alpha_(2)-alpha_(3),beta_(2)=alpha_(1)+2alpha_(2)+2alpha_(3),beta_(3)=alph

    4.设向量组beta_(1)=alpha_(1)+2alpha_(2)-alpha_(3),beta_(2)=alpha_(1)+2alpha_(2)+2alp

  • 查看答案
  • 设向量组alpha_1, alpha_2, alpha_3, alpha_4线性无关,则()。

    设向量组alpha_1, alpha_2, alpha_3, alpha_4线性无关,则()。设向量组$\alpha_1, \alpha_2, \alpha_3

  • 查看答案
  • 9.设向量组α1,α 2,α3与向量组β1 β2,β3有如下关系:-|||-(beta )_(1)=(alpha )_(2)+(alpha )_(3) (beta )_(2)=(alpha )_(1)

    9.设向量组α1,α 2,α3与向量组β1 β2,β3有如下关系:-|||-(beta )_(1)=(alpha )_(2)+(alpha )_(3) (bet

  • 查看答案
  • 已知向量 a_1, a_2, a_3, a_4, a_5,且有 r(alpha _1, alpha _2, alpha _3, alpha _4)= 3,r(alpha _1, alpha _2, a

    已知向量 a_1, a_2, a_3, a_4, a_5,且有 r(alpha _1, alpha _2, alpha _3, alpha _4)= 3,r(a

  • 查看答案
  • 4.求向量组alpha_(1)=(1,1,2,3),alpha_(2)=(1,-1,1,1),alpha_(3)=(1,3,3,5),alpha_(4)=(4,-2,5,6),alpha_(5)=(3

    4.求向量组alpha_(1)=(1,1,2,3),alpha_(2)=(1,-1,1,1),alpha_(3)=(1,3,3,5),alpha_(4)=(4,

  • 查看答案
  • 若向量组(alpha )_(1),(alpha )_(2),(alpha )_(3)线性无关,则向量组(alpha )_(1),(alpha )_(2),(alpha )_(3), (alpha )_

    若向量组(alpha )_(1),(alpha )_(2),(alpha )_(3)线性无关,则向量组(alpha )_(1),(alpha )_(2),(al

  • 查看答案