Find a basis for the column space of A=(123245122)A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 1 & 2 & 2 \end{pmatrix}A=121242352.
{(121),(242),(352)}\left\{\begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}, \begin{pmatrix} 2 \\ 4 \\ 2 \end{pmatrix}, \begin{pmatrix} 3 \\ 5 \\ 2 \end{pmatrix}\right\}⎩⎨⎧121,242,352⎭⎬⎫
{(121)}\left\{\begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}\right\}⎩⎨⎧121⎭⎬⎫
{(121),(242)}\left\{\begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}, \begin{pmatrix} 2 \\ 4 \\ 2 \end{pmatrix}\right\}⎩⎨⎧121,242⎭⎬⎫
{(121),(352)}\left\{\begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}, \begin{pmatrix} 3 \\ 5 \\ 2 \end{pmatrix}\right\}⎩⎨⎧121,352⎭⎬⎫