设alpha_(1),alpha_(2),alpha_(3)是四元非齐次线性方程组Ax=b的三个解向量，且A的秩R

设$\alpha_{1},\alpha_{2},\alpha_{3}$是四元非齐次线性方程组$Ax=b$的三个解向量，且$A$的秩$R

A. =3$，$\alpha_{1}=(1,2,3,4)^{T}$，$\alpha_{2}+\alpha_{3}=(0,1,2,3)^{T}$，$k$为任意常数，则线性方程组$Ax=b$的通解为（）。
A. $x=k(1,1,1,1)^{T}+\alpha_{1}$
B. $x=k(0,1,2,3)^{T}+\alpha_{1}$
C. $x=k(2,3,4,5)^{T}+\alpha_{1}$
D. $x=k(3,4,5,6)^{T}+\alpha_{1}$

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