# Question #f4b5b

Jan 9, 2017

$2 v - 4 u = \left(\begin{matrix}- 24 \\ 0\end{matrix}\right)$

#### Explanation:

$2 v - 4 u = 2 \left(\begin{matrix}2 \\ 4\end{matrix}\right) - 4 \left(\begin{matrix}7 \\ 2\end{matrix}\right)$

Each of the x and y components can be multiplied by the scalar quantity.

$\Rightarrow \textcolor{red}{2} \left(\begin{matrix}2 \\ 4\end{matrix}\right) - \textcolor{red}{4} \left(\begin{matrix}7 \\ 2\end{matrix}\right)$

$= \left(\begin{matrix}\textcolor{red}{2} \times 2 \\ \textcolor{red}{2} \times 4\end{matrix}\right) - \left(\begin{matrix}\textcolor{red}{4} \times 7 \\ \textcolor{red}{4} \times 2\end{matrix}\right) = \left(\begin{matrix}4 \\ 8\end{matrix}\right) - \left(\begin{matrix}28 \\ 8\end{matrix}\right)$

Similarly, subtract corresponding x and y components.

$\Rightarrow \left(\begin{matrix}4 \\ 8\end{matrix}\right) - \left(\begin{matrix}28 \\ 8\end{matrix}\right) = \left(\begin{matrix}4 - 28 \\ 8 - 8\end{matrix}\right) = \left(\begin{matrix}- 24 \\ 0\end{matrix}\right)$