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试题ID 38683    所属试卷 考研《线性代数》试题严选

试题
已知 $n$ 维向量 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots \boldsymbol{\alpha}_s, \boldsymbol{\beta}_1, \boldsymbol{\beta}_2, \cdots, \boldsymbol{\beta}_{5-1}$ .如果秩 $r\left(\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s, \boldsymbol{\beta}_1, \boldsymbol{\beta}_2, \cdots, \boldsymbol{\beta}_{5-1}\right)= r\left(\boldsymbol{\beta}_1, \boldsymbol{\beta}_2, \cdots, \boldsymbol{\beta}_{s-1}\right)$ ,则必有
$\text{A.}$ $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性相关. $\text{B.}$ $\boldsymbol{\beta}_1, \boldsymbol{\beta}_2, \cdots, \boldsymbol{\beta}_{5-1}$ 线性相关. $\text{C.}$ $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \cdots, \boldsymbol{\alpha}_s$ 线性无关. $\text{D.}$ $\boldsymbol{\beta}_1, \boldsymbol{\beta}_2, \cdots, \boldsymbol{\beta}_{5-1}$ 线性无关. $\text{E.}$ $\text{F.}$

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