Let w = \( \begin{pmatrix} 2 \\ -1 \end{pmatrix}\). There exists a \(2 \times 2\) matrix \({P}\) such that \(\text{proj}_{{w}} {v} = {P} {v}\) for all 2-dimensional vectors \({v}\). Find \({P}\).
I'm not really sure where to start for this problem. Should I plug w into the projection formula?
