科数网
题号:10858    题型:单选题    来源:李永乐武忠祥考研数学冲刺模拟试卷5
设 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 是 $n$ 维列向量, 则下列命题中正确的是
$\text{A.}$ 若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 中任意 $s-1$ 个向量都线性无关,则向量组 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 必线性无关. $\text{B.}$ 若 $\boldsymbol{\alpha}_s$ 不能由 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_{s-1}$ 线性表示, 则向量组 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 必线性无关. $\text{C.}$ 若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性无关, 则 $\left(\begin{array}{l}\boldsymbol{\alpha}_1 \\ \boldsymbol{\alpha}_s\end{array}\right),\left(\begin{array}{l}\boldsymbol{\alpha}_2 \\ \boldsymbol{\alpha}_s\end{array}\right), \cdots,\left(\begin{array}{c}\boldsymbol{\alpha}_{s-1} \\ \boldsymbol{\alpha}_s\end{array}\right)$ 必线性无关. $\text{D.}$ 若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性无关, 则 $\boldsymbol{\alpha}_1+\boldsymbol{\alpha}_2, \boldsymbol{\alpha}_2+\boldsymbol{\alpha}_3, \cdots, \boldsymbol{\alpha}_{s-1}+\boldsymbol{\alpha}_s, \boldsymbol{\alpha}_s+\boldsymbol{\alpha}_1$ 必线性无关.
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