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