Let \(\mathbf{P}\) be the \(2\times 2\) matrix that projects vectors onto \(\mathbf{u} = \begin{pmatrix}2\\ -1 \end{pmatrix}\). That is,
\(\mathbf{P}{v} = \operatorname{proj}_{{u}} ({v}) = \text{Projection of $\mathbf{v}$ onto $\mathbf{u}$}\)
Use the picture below to find
\(\mathbf{P} \begin{pmatrix}2 \\ -1 \end{pmatrix} \text{ and } \mathbf{P} \begin{pmatrix}1 \\ 2 \end{pmatrix}\)
using the geometric meaning of the matrix. Enter the answers as columns in the order above.
