设有任意两个 $n$ 维向量组 $\alpha_1, \alpha_2, \cdots, \alpha_m$ 和 $\beta_1, \beta_2, \cdots, \beta_m$ ，若存在两组不全为零的 $\lambda_1, \lambda_2, \cdots, \lambda_m$ 和 $k_1, k_2, \cdots, k_m$ ，使 $\left(\lambda_1+k_1\right) \alpha_1+\cdots+\left(\lambda_m+k_m\right) \alpha_m$ $+\left(\lambda_1-k_1\right) \beta_1+\cdots+\left(\lambda_m-k_m\right) \beta_m=0$ ，则
$\text{A.}$ $\alpha_1, \alpha_2, \cdots, \alpha_m$ 和 $\beta_1, \beta_2, \cdots, \beta_m$ 都线性相关
$\text{B.}$ $\alpha_1, \alpha_2, \cdots, \alpha_m$ 和 $\beta_1, \beta_2, \cdots, \beta_m$ 都线性无关
$\text{C.}$ $\alpha_1+\beta_1, \alpha_2+\beta_2, \cdots, \alpha_m+\beta_m, \alpha_1-\beta_1, \alpha_2-\beta_2$,$\cdots, \alpha_m-\beta_m$ 线性无关
$\text{D.}$ $\alpha_1+\beta_1, \alpha_2+\beta_2, \cdots, \alpha_m+\beta_m, \alpha_1-\beta_1, \alpha_2-\beta_2$,$\cdots, \alpha_m-\beta_m$ 线性相关