随机刷题

已知 ${\eta }_{1},{\eta }_{2}$ 是非齐次线性方程组 ${Ax} = b$ 的两个不同解， ${\xi }_{1}$， ${\xi }_{2}$ 是对应齐次线性方程组 ${Ax} = 0$ 的基础解系, ${k}_{1},{k}_{2}$ 为任意常数,则 ${Ax} = b$ 的通解为$\underline{\qquad}$.

A. ${k}_{1}{\xi }_{1} + {k}_{2}\left({{\xi }_{1} + {\xi }_{2}}\right) + \frac{{\eta }_{1} - {\eta }_{2}}{2}$
B. ${k}_{1}{\xi }_{1} + {k}_{2}\left({{\xi }_{1} - {\xi }_{2}}\right) + \frac{{\eta }_{1} + {\eta }_{2}}{2}$
C. ${k}_{1}{\xi }_{1} + {k}_{2}\left({{\eta }_{1} + {\eta }_{2}}\right) + \frac{{\eta }_{1} - {\eta }_{2}}{2}$
D. ${k}_{1}{\xi }_{1} + {k}_{2}\left({{\eta }_{1} - {\eta }_{2}}\right) + \frac{{\eta }_{1} + {\eta }_{2}}{2}$