选项
A.
A.向量组 $alpha_{1}＋alpha_{2},alpha_{2}＋alpha_{3}，alpha_{3}＋alpha_{1}$ 线性无关；
B.
B.向量组 $alpha_{1},２alpha_{2},３alpha_{3}$ 线性无关；
C.
C.向量组 $alpha_{1}＋alpha_{2},alpha_{2}＋alpha_{3}，alpha_{3}－alpha_{1}$ 线性无关；
D.
D.向量组 $alpha_{1}＋２alpha_{2},２alpha_{2}＋３alpha_{3}$ 线性无关。
正确答案：
名词解析
因为 $alpha_{3}－alpha_{1}＝（alpha_{2}＋alpha_{3}）－（alpha_{1}＋alpha_{2}）$ 线性无关，所以（Ｃ）错误。用定义验证其它都正确。