Question

Let u=  (-1,3) and w =(2,4) Find the resulting vector of 2u-4w  in component form..

Answer 1

Very simple. You just use the vectors as normal numbers, and multiply the coordinates with 2 and 4 like this: 

2*u = 2* (2,4) = (4,8)
4*w = 4* (-1,3) = (-4,12)

(4,8) - (-4,12) = (8,-4)

So the vector has the coordinates (8,-4)

Answer 2

$\bf \begin{cases} u= (-1,3)\\ w =(2,4)\\ ----------\\ \textit{scalar multiplication}\\ 2u\implies 2(-1,3)\implies 2\cdot -1,2\cdot 3\\ \qquad -2,6\\ 4w\implies 4(2,4)\implies 4\cdot 2,4\cdot 4\\ \qquad 8,16\\ ----------\\ 2u-4w\\ (-2,6)-(8,16)\implies (-2-8\ ,\ 6-16) \end{cases}$