单选题 （共 6 题 ），每题只有一个选项正确
设 $\alpha_1=\left(\begin{array}{l}0 \\ 0 \\ c_1\end{array}\right), \alpha_2=\left(\begin{array}{c}0 \\ 1 \\ c_2\end{array}\right), \alpha_3=\left(\begin{array}{c}1 \\ -1 \\ c_3\end{array}\right), \alpha_4=\left(\begin{array}{c}-1 \\ 1 \\ c_1\end{array}\right)$ ，其中 $c_1, c_2, c_3, c_4$ 为任意常数，则下列向量组线性相关的是
$\text{A.}$ $\alpha_1, \alpha_2, \alpha_3$
$\text{B.}$ $\alpha_1, \alpha_2, \alpha_4$
$\text{C.}$ $\alpha_1, \alpha_3, \alpha_4$
$\text{D.}$ $\alpha_2, \alpha_3, \alpha_4$
设 $\alpha_1=\left(\begin{array}{l}0 \\ 0 \\ c_1\end{array}\right), \alpha_2=\left(\begin{array}{l}0 \\ 1 \\ c_2\end{array}\right), \alpha_3=\left(\begin{array}{c}1 \\ -1 \\ c_3\end{array}\right), \alpha_4=\left(\begin{array}{c}-1 \\ 1 \\ c_4\end{array}\right)$ ，其中 $c_1, c_2, c_3, c_4$ 为任意常数，则下列向量组线性相关的是
$\text{A.}$ $\alpha_1, \alpha_2, \alpha_3$
$\text{B.}$ $\alpha_1, \alpha_2, \alpha_4$
$\text{C.}$ $\alpha_1, \alpha_3, \alpha_4$
$\text{D.}$ $\alpha_2, \alpha_3, \alpha_4$
设 $A$ 为 3 阶矩阵， $P$ 为 3 阶可逆矩阵，且
$$
P^{-1} A P=\left(\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 2
\end{array}\right),
$$
若 $P=\left(\alpha_1, \alpha_2, \alpha_3\right) ， Q=\left(\alpha_1+\alpha_2, \alpha_2, \alpha_3\right)$ ，则 $Q^{-1} A Q=$
$\text{A.}$ $\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1\end{array}\right)$
$\text{B.}$ $\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right)$
$\text{C.}$ $\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right)$
$\text{D.}$ $\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1\end{array}\right)$
设 $\alpha_1=\left(\begin{array}{l}0 \\ 0 \\ c_1\end{array}\right), \alpha_2=\left(\begin{array}{l}0 \\ 1 \\ c_2\end{array}\right), \alpha_3=\left(\begin{array}{c}1 \\ -1 \\ c_3\end{array}\right), \alpha_4=\left(\begin{array}{c}-1 \\ 1 \\ c_4\end{array}\right)$, 其中 $c_1, c_2, c_3, c_4$ 为任意常数，则下列向量组线性相关的是
$\text{A.}$ $\alpha_1, \alpha_2, \alpha_3$
$\text{B.}$ $\alpha_1, \alpha_2, \alpha_4$
$\text{C.}$ $\alpha_1, \alpha_3, \alpha_4$
$\text{D.}$ $\alpha_2, \alpha_3, \alpha_4$
设 $A$ 为 3 阶矩阵， $P$ 为 3 阶可逆矩阵，且
$$
P^{-1} A P=\left(\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 2
\end{array}\right) \text { ，若 } P=\left(\alpha_1, \alpha_2, \alpha_3\right) \text { ， }
$$
$Q=\left(\alpha_1+\alpha_2, \alpha_2, \alpha_3\right)$ ，则 $Q^{-1} A Q=$
$\text{A.}$ $\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1\end{array}\right)$
$\text{B.}$ $\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right)$
$\text{C.}$ $\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right)$
$\text{D.}$ $\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1\end{array}\right)$
设 $A, B, C$ 均为 $n$ 阶矩阵，若 $A B=C$ ，且 $B$ 可逆，则
$\text{A.}$ 矩阵 $\boldsymbol{C}$ 的行向量组与矩阵 $\boldsymbol{A}$ 的行向量组等价
$\text{B.}$ 矩阵 $\boldsymbol{C}$ 的列向量组与矩阵 $\boldsymbol{A}$ 的列向量组等价
$\text{C.}$ 矩阵 $C$ 的行向量组与矩阵 $B$ 的行向量组等价
$\text{D.}$ 矩阵 $\boldsymbol{C}$ 的列向量组与矩阵 $\boldsymbol{B}$ 的列向量组等价