Finding the matrix of projection Find the matrix A of the orthogonal projection onto the line L in R2 that consists of all scalar multiples of the vector $\begin{pmatrix} 2 \\ 3 \ \end{pmatrix}$. How do I begin to solve this? Any help would be appreciated.

Hint:
The orthogonal projection of vector $v$ onto the mine directed by vector $u$ is given by
$$p_u(v)=\frac{\langle v,u\rangle}{\langle u,u\rangle}\,u$$
Hence all you have to do is to calculate the projections of the vectors of the basis onto the vector $\begin{pmatrix}2\\3\end{pmatrix}$.
