### Instruction: Find the matrix that corresponds to projecting onto the vector $\begin{pmatrix} 2 \\ -3 \end{pmatrix}.$.### Response: So let's call the vector we're projecting onto $\begin{pmatrix} 2 \\ -3 \end{pmatrix}$ $v$.
Okay. So the projection matrix is going to be $\frac{vv^T}{v^Tv}$.
Right. So $v^T$ is $\begin{pmatrix} 2 & -3 \end{pmatrix}$.
And $v^Tv$ is $4+9=13$.