### Instruction: Find the projection of the vector $\begin{pmatrix} 4 \\ 5 \end{pmatrix}$ onto the vector $\begin{pmatrix} 2 \\ 0 \end{pmatrix}.$.### Response: To find the projection of one vector onto another, I need to use the formula $\text{proj}_v u = \frac{u \cdot v}{v \cdot v} v$, where $u$ is the vector being projected and $v$ is the vector it is projected onto.
I can plug in the given values for $u$ and $v$ and simplify the expression.
The dot product of $u$ and $v$ is $u \cdot v = 4 \times 2 + 5 \times 0 = 8$.
The dot product of $v$ and itself is $v \cdot v = 2 \times 2 + 0 \times 0 = 4$.