Let P be the matrix that projects onto j that is, we want P to satisfy
\(\mathbf{P} \mathbf{v} = \text{The projection of $\mathbf{v}$ onto } \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} \) for all vectors v.
Use the pictures below to calculate \(\mathbf{P}\mathbf{i}, \mathbf{P} \mathbf{j}, \mathbf{P}\mathbf{k} \).
Calculate the matrix P that projects onto j.
