数学试题讲解

(I) {\begin{array}{cc} a_{11} x_{1} + a_{12} x_{2} + \dots + a_{12 n} x_{2 n} & = 0 \\ a_{21} x_{1} + a_{22} x_{2} + \dots + a_{22 n} x_{2 n} & = 0 \\ ⋮ \\ a_{n 1} x_{1} + a_{n 2} x_{2} + \dots + a_{n 2 n} x_{2 n} & = 0 \end{array}

的一个基础解系为

{(b_{11}, b_{12}, \dots, b_{12 n})}^{T}, {(b_{21}, b_{22}, \dots, b_{22 n})}^{T}, \dots, (b_{n 1}, b_{n 2}, \dots

，

{b_{n, 2 n})}^{T}

，

试写出线性方程组
（ II ）

{\begin{array}{lc} b_{11} y_{1} + b_{12} y_{2} + \dots + b_{12 n} y_{2 n} & = 0 \\ b_{21} y_{1} + b_{22} y_{2} + \dots + b_{22 n} y_{2 n} & = 0 \\ ⋮ \\ b_{n 1} y_{1} + b_{n 2} y_{2} + \dots + b_{n 2 n} y_{2 n} & = 0 \end{array}

的通解，并说明理由．