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 \(\mathbf{P} \mathbf{v} = \begin{pmatrix} 4 \\1 \end{pmatrix}.\)
