若数字矩阵$A$的初等因子是$lambda,lambda^{2},lambda^{3},lambda-2,(lambda-2)^{2},lambda+2,(lambda+2)^{2}$,则$A$的不变因子组是()。
若向量组$alpha_{1},alpha_{2},alpha_{3},alpha_{4}$线性无关,则向量组$alpha_{1}-alpha_{2},alpha_{2}-alpha_{3},alpha_{3}-alpha_{4},alpha_{4}-alpha_{1}$也线性无关.
因为$(alpha_{1}-alpha_{2})+(alpha_{2}-alpha_{3})+(alpha_{3}-alpha_{4})+(alpha_{4}-alpha_{1})=0$,所以$alpha_{1}-alpha_{2},alp...
设$alpha_{1},alpha_{2},alpha_{3}$是某齐次线性方程组的基础解系,下面向量组中可作为该方程组基础解系的是()。
(B),(D)中向量组线性相关,不能作为基础解系;(C)中向量组尽管线性无关,但与$alpha_{1},alpha_{2},alpha_{3}$不等价,也不能作为基础解系。