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