问题详情

设向量组α1,α2,α3线性无关,则线性无关的向量组是()。


A、&alpha;<sub>1</sub>-&alpha;<sub>2</sub>,&alpha;<sub>3</sub>-&alpha;<sub>1</sub>,&alpha;<sub>2</sub>-&alpha;<sub>3</sub>

B、&alpha;<sub>1</sub>-&alpha;<sub>2</sub>,2&alpha;<sub>2</sub>+3&alpha;<sub>3</sub>,&alpha;<sub>1</sub>+&alpha;<sub>3</sub>

C、&alpha;<sub>1</sub>-&alpha;<sub>2</sub>,2&alpha;<sub>2</sub>+&alpha;<sub>3</sub>,&alpha;<sub>1</sub>+&alpha;<sub>2</sub>+&alpha;<sub>3</sub>

D、&alpha;<sub>1</sub>-&alpha;<sub>2</sub>+&alpha;<sub>3</sub>,2&alpha;<sub>1</sub>+&alpha;<sub>2</sub>-3&alpha;<sub>3</sub>,8&alpha;<sub>1</sub>+&alpha;<sub>2</sub>-7&alpha;<sub>3</sub>

时间:2022-01-09 23:35 关键词: 在职攻读硕士联考

答案解析

B
[解析] 对选项A,(α1-α2)+(α3-α1)+(α2-α3)=0对选项C,(α1-α2)+(2α2+α3)-(α1+α2+α3)=0利用观察法,通过简单地加减,可知A、C均线性相关,可排除。对选项D,有故正确答案为B。