13.【线性代数】——复习课

问题1

$已知A_{3\ast 3}{x}_{3\ast 1}=\left[\begin{array}{c}2\\ 4\\ 2\end{array}\right]的解，x=\left[\begin{array}{c}2\\ 0\\ 0\end{array}\right]+c\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right]+d\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]$

1. 求行向量生成的空间维数
2. 求矩阵A
3. Ax=b有解，b的值

问题2

$已知B=\left[\begin{array}{ccc}1& 1& 0\\ 0& 1& 0\\ 1& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& -1& 2\\ 0& 1& 1& -1\\ 0& 0& 0& 0\end{array}\right]$
1.求矩阵B的零空间的基
2.求$Bx=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]通解$