Exercise 3.5.22

$A=\left[\begin{array}{cc}u\hfill & w\hfill \end{array}\right]\left[\begin{array}{c}{v}^T\hfill \\ z^T\hfill \end{array}\right]=\left[\begin{array}{cc}1\hfill & 2\hfill \\ 2\hfill & 2\hfill \\ 4\hfill & 1\hfill \end{array}\right]\left[\begin{array}{cc}1\hfill & 0\hfill \\ 1\hfill & 1\hfill \end{array}\right]=\left[\begin{array}{cc}3\hfill & 2\hfill \\ 4\hfill & 2\hfill \\ 5\hfill & 1\hfill \end{array}\right]\begin{array}{ccc}\hfill & u,w\text{ span column space; }\hfill & \hfill \\ \hfill & v,z\text{ span row space }\hfill \end{array}$