Consider the projection matrix P that satisfies Pv = Projection of v onto \(\begin{pmatrix} 4 \\ 1 \end{pmatrix}\).
Find 3 vectors with integer components and magnitude no greater than 8 that satisfy Pv = \(\begin{pmatrix} 4 \\ 1 \end{pmatrix}\).
Use this to help you find \(P^{-1}\begin{pmatrix} 4 \\ 1 \end{pmatrix}\) .
