Let A =$ \left[\begin{array}{cccc}2 & 3 & 2 & 3 \\ 3 & 4 & -1 & 1 \\ 1 & 1 & -3 & -2\end{array}\right] $
and $f: R^4 → R^3$ the linear map given by f(x) = Ax. Determine one base for each B of $R^4$ and a base C of $R^3$, so that the matrix of $f$ has the shape $ \phi_{C}^{B}(f) $ = $ \left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right] $
now what i have done is finding kernel base for A which was {(11,8,1,0),(9,-7,0,1)} and the image base will be 1st two column. usually in our tasks we were given A and base B and base C and we need to calculate the last matrix $\phi_{C}^{B}(f)$ , but now we were only given A and $ \phi_{C}^{B}(f) $ , so i don't know how to get the base B and C