题目
设向量组alpha_1,alpha_2,alpha_3线性无关，则下列向量组线性相关的是(）。A. alpha_1-alpha_2,alpha_2-alpha_3,alpha_3-alpha_1B. alpha_1+alpha_2,alpha_2+alpha_3,alpha_3+alpha_1C. alpha_1,alpha_1+alpha_2,alpha_1+alpha_2+alpha_3D. alpha_1+2alpha_2,alpha_2+2alpha_3,alpha_3+2alpha_1
设向量组$\alpha_1,\alpha_2,\alpha_3$线性无关，则下列向量组线性相关的是(）。
A. $\alpha_1-\alpha_2,\alpha_2-\alpha_3,\alpha_3-\alpha_1$
B. $\alpha_1+\alpha_2,\alpha_2+\alpha_3,\alpha_3+\alpha_1$
C. $\alpha_1,\alpha_1+\alpha_2,\alpha_1+\alpha_2+\alpha_3$
D. $\alpha_1+2\alpha_2,\alpha_2+2\alpha_3,\alpha_3+2\alpha_1$
题目解答
答案
A. $\alpha_1-\alpha_2,\alpha_2-\alpha_3,\alpha_3-\alpha_1$