线性相关，线性代数题目
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k1.α1+k2.α2+k3.α3=0
2k1+k2+3k3=0 (1)
-k1+4k2-6k3=0 (2)
7k1+11k2+3k3=0 (3)
3k1-2k2+8k3=0 (4)
consider (1) , (2), (3)
(3)-(1)
5k1+10k2 =0 (5)
2(3)+(2)
13k1+26k2=0 (6)
from (5) and (6)
k1=k2 =0
from (3)
k3=0
from (1) and (2) and (3)
k1=k2=k3=0 满足 (4)
ie
k1.α1+k2.α2+k3.α3=0
=>k1=k2=k3=0
α1,α2,α3 线性无关
2k1+k2+3k3=0 (1)
-k1+4k2-6k3=0 (2)
7k1+11k2+3k3=0 (3)
3k1-2k2+8k3=0 (4)
consider (1) , (2), (3)
(3)-(1)
5k1+10k2 =0 (5)
2(3)+(2)
13k1+26k2=0 (6)
from (5) and (6)
k1=k2 =0
from (3)
k3=0
from (1) and (2) and (3)
k1=k2=k3=0 满足 (4)
ie
k1.α1+k2.α2+k3.α3=0
=>k1=k2=k3=0
α1,α2,α3 线性无关
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