设 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 均为 $n$ 维列向量， $\boldsymbol{A}$ 是 $m \times n$ 矩阵，下列选项正确的是（ ）．
A
若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性相关，则 $\boldsymbol{A} \boldsymbol{\alpha}_1, \boldsymbol{A} \boldsymbol{\alpha}_2, \cdots, \boldsymbol{A} \boldsymbol{\alpha}_s$ 线性相关
B
若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性相关，则 $\boldsymbol{A} \boldsymbol{\alpha}_1, \boldsymbol{A} \boldsymbol{\alpha}_2, \cdots, \boldsymbol{A} \boldsymbol{\alpha}_s$ 线性无关
C
若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性无关，则 $\boldsymbol{A} \boldsymbol{\alpha}_1, \boldsymbol{A} \boldsymbol{\alpha}_2, \cdots, \boldsymbol{A} \boldsymbol{\alpha}_s$ 线性相关
D
若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性无关，则 $\boldsymbol{A} \boldsymbol{\alpha}_1, \boldsymbol{A} \boldsymbol{\alpha}_2, \cdots, \boldsymbol{A} \boldsymbol{\alpha}_s$ 线性无关
E
F