Question

线性代数.求向量组是否线性相关并求秩9题的第一小题

Answer 1

9 (1) A=(a1,a2,a3,a4)=

[1 1 1 1]

[3 3 -2 -4]

[5 2 1 1]

[-4 -2 -1 1]

[0 1 -1 -1]

行初等变换为

[1 1 1 1]

[0 0 -5 -7]

[0 -3 -4 -4]

[0 2 3 5]

[0 1 -1 -1]

行初等变换为

[1 1 1 1]

[0 1 -1 -1]

[0 -3 -4 -4]

[0 2 3 5]

[0 0 -5 -7]

行初等变换为

[1 1 1 1]

[0 1 -1 -1]

[0 0 -7 -7]

[0 0 5 7]

[0 0 -5 -7]

行初等变换为

[1 1 1 1]

[0 1 -1 -1]

[0 0 1 1]

[0 0 0 2]

[0 0 0 0]

r(a1,a2,a3,a4) = 4, 则 a1,a2,a3,a4 线性无关.