题目
11.填空题已知alpha_(1)=[1,1,2,2,1],alpha_(2)=[0,2,1,5,-1],alpha_(3)=[2,0,3,-1,3],alpha_(4)=[1,1,0,4,-1]线性相关,则alpha_(1)=[1,1,2],alpha_(2)=[0,2,1],alpha_(3)=[2,0,3],alpha_(4)=[1,1,0]线性____.
11.填空题
已知$\alpha_{1}=[1,1,2,2,1],\alpha_{2}=[0,2,1,5,-1],\alpha_{3}=[2,0,3,-1,3],\alpha_{4}=[1,1,0,4,-1]$线性相关,
则$\alpha_{1}=[1,1,2],\alpha_{2}=[0,2,1],\alpha_{3}=[2,0,3],\alpha_{4}=[1,1,0]$线性____.
题目解答
答案
已知向量 $\alpha_1 = [1, 1, 2, 2, 1]$,$\alpha_2 = [0, 2, 1, 5, -1]$,$\alpha_3 = [2, 0, 3, -1, 3]$,$\alpha_4 = [1, 1, 0, 4, -1]$ 线性相关。考虑向量 $\alpha_1' = [1, 1, 2]$,$\alpha_2' = [0, 2, 1]$,$\alpha_3' = [2, 0, 3]$,$\alpha_4' = [1, 1, 0]$,它们是三维空间中的四个向量。根据线性代数基本定理,三维空间中任何四个向量必线性相关。
因此,答案为 $\boxed{\text{相关}}$。