向量组的线性相关性

Question

向量组的线性相关性加急加急

Answer 1

Answer 2

设出k1,k2,k3根根据线性无关性解出

Answer 3

若a1, a2 ,a3......,an线性相关，则存在不全为0的k1,k2,k3......kn满足k1*a1+k2*a2+ k3*a3......+kn*an=0 或者若存在不全为0的k1,k2,k3......kn满足k1*a1+k2*a2+ k3*a3......+kn*an=0，则a1, a2 ,a3......,an线性相关，否则a1, a2 ,a3......,an线性无关本回答被网友采纳

Answer 4

a1, a2, a3 线性无关，则 r(a1, a2, a3) = 3.
(a1+a2, 3a2+2a3, a1-2a2+a3) = (a1, a2, a3)P, 其中 P =
[1 0 1]
[1 3 -2]
[0 2 1]
初等行变换为
[1 0 1]
[0 3 -3]
[0 2 1]
显然 r(P) = 3, 则 r(a1+a2, 3a2+2a3, a1-2a2+a3) = 3，
则 a1+a2, 3a2+2a3, a1-2a2+a3 线性无关。

Answer 5