三向量 v1、v2、v3,三實數a、b、c
若 av1 + bv2 + cv3 = (0,0,0), 且a=b=c=0, 則v1、v2、v3為線性獨立。
可取三向量之行列式值,若為0則v1、v2、v3為線性相依,不為0線性獨立。
1. (1,-2,1),(2,3,1),(1,-1,3)
行列式
1 -2 1
2 3 1
1 -1 3
= (9-2-2)-(3-12-1) = 15 ---線性獨立
2.(5,-3,2),(2,4,-1),(1,-11,4)
行列式 = (80+3-44)-(8-24+55) = 0 --- 線性相依
3.(3,10,6),(6,8,7),(-3,12,4)
行列式 = 6(53-58) = -30 ---線性獨立
4.(-4,-3,4),(1,-2,3),(6,0,0)
行列式 = 6(-9+8) = -6 ---線性獨立
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