Exercise 3.1.21

A combination of the columns of $C$ is also a combination of the columns of $A$. Then $C=\left[\begin{array}{cc}1\hfill & 3\hfill \\ 2\hfill & 6\hfill \end{array}\right]$and $A=\left[\begin{array}{cc}1\hfill & 2\hfill \\ 2\hfill & 4\hfill \end{array}\right]$have the same column space. $B=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 3\hfill & \hfill 6\hfill \end{array}\right]$ has a different column space. The key word is "space".