一、题目
设 $\boldsymbol{\alpha}_{1}=\left[\begin{array}{l}0 \\ 0 \\ c_{1}\end{array}\right]$, $\boldsymbol{\alpha}_{2}=\left[\begin{array}{l}0 \\ 1 \\ c_{2}\end{array}\right]$, $\boldsymbol{\alpha}_{3}=\left[\begin{array}{c}1 \\ -1 \\ c_{3}\end{array}\right]$, $\boldsymbol{\alpha}_{4}=\left[\begin{array}{c}-1 \\ 1 \\ c_{4}\end{array}\right]$, 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哪个?
(A) $\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \boldsymbol{\alpha}_{3}$
(B) $\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \boldsymbol{\alpha}_{4}$
(C) $\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{3}, \boldsymbol{\alpha}_{4}$
(D) $\boldsymbol{\alpha}_{2}, \boldsymbol{\alpha}_{3}, \boldsymbol{\alpha}_{4}$
难度评级:
继续阅读“只要行列式有两行或者两列成比例,则组成该行列式的行或者列向量之间都是线性相关的”