设向量组 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \boldsymbol{\alpha}_3$ 是三维线性空间 $V$ 的基，则（ ）也是 $V$ 的基．
A
$\boldsymbol{\beta}_1=\boldsymbol{\alpha}_1+\boldsymbol{\alpha}_2, \boldsymbol{\beta}_2=\boldsymbol{\alpha}_1+\boldsymbol{\alpha}_3, \boldsymbol{\beta}_3=2 \boldsymbol{\alpha}_1+\boldsymbol{\alpha}_2+\boldsymbol{\alpha}_3 ;$
B
$\boldsymbol{\beta}_1=\boldsymbol{\alpha}_1, \boldsymbol{\beta}_2=\boldsymbol{\alpha}_1+\boldsymbol{\alpha}_2, \boldsymbol{\beta}_3=\boldsymbol{\alpha}_1-2 \boldsymbol{\alpha}_2$ ；
C
$\boldsymbol{\beta}_1=\boldsymbol{\alpha}_1+2 \boldsymbol{\alpha}_2, \boldsymbol{\beta}_2=\boldsymbol{\alpha}_2+\boldsymbol{\alpha}_3, \boldsymbol{\beta}_3=\boldsymbol{\alpha}_1+3 \boldsymbol{\alpha}_2+\boldsymbol{\alpha}_3$ ；
D
$\boldsymbol{\beta}_1=\boldsymbol{\alpha}_1-\boldsymbol{\alpha}_2, \boldsymbol{\beta}_2=\boldsymbol{\alpha}_2-\boldsymbol{\alpha}_3, \boldsymbol{\beta}_3=\boldsymbol{\alpha}_1+\boldsymbol{\alpha}_2+\boldsymbol{\alpha}_3$ ．
E
F