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下列向量判斷是線性獨立或線性相依
Aug 27th 2014, 05:24

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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