4,問A取何值時,下列向量組線性相關?a1=(a,1,1),a2=(1,a,-1)T,a3=(1,-1,a)T

4,問A取何值時,下列向量組線性相關?a1=(a,1,1),a2=(1,a,-1)T,a3=(1,-1,a)T


det(a1,a2,a3)=0
a 1 1
1 a -1
1 -1 a
=> a^3-1-1-(a+a+a)=0
a^3-3a-2 =0
(a+1)(a^2-a-2)=0
(a+1)^2(a-2)=0
a=-1 or 2



線性代數、設a1,a2,a3均為三維列向量,且|a1 a2 a3|=1,那麼|a3 a2 a1-2a2|=


|a3,a2,a1-2a2|
c3+2c2
=|a3,a2,a1|
c1c3
=- |a1,a2,a3 |
=-1.



線性代數設向量組a1a2 a3線性無關證明向量組a1-a2 a2-a3 a3-a1線性相關