线性代数方面,a1=(1,1,3,1),a2=(4,1,-3,2),a3=(1,0,-1,2),证

2025-05-08 02:23:57
推荐回答(1个)
回答1:

A = (a1, a2, a3) =
[1 4 1]
[1 1 0]
[3 -3 -1]
[1 2 2]
行初等变换为
[1 1 0]
[0 3 1]
[0 -6 -1]
[0 1 2]
行初等变换为
[1 1 0]
[0 1 2]
[0 0 -5]
[0 0 11]
行初等变换为
[1 1 0]
[0 1 2]
[0 0 1]
[0 0 0]
r(a1, a2, a3) = 3
故 a1, a2, a3 线性无关。