Question

Let u = <-6, 1>, v = <-5, 2>. Find -4u + 2v

Answer 1

This is a very simple addition problem. Why are you struggling with it?

If u = <-6,1>, then 2u = <2(-6),2(1)> = <-12,2>
If u = <-6,1> and v = <-5,2>, then u + v = <-6-5,1+2> = <-11,3>

Use these principles.

Answer 2

\(\large\color{black}{ \displaystyle u=\langle a,\quad b \rangle \\ v=\langle c,\quad d \rangle}\)

\(\large\color{black}{ \displaystyle \color{red}{\rm x}u + \color{red}{\rm y}v=\\ \color{red}{\rm x}\langle a,\quad b \rangle + \color{red}{\rm y}\langle c,\quad d \rangle= \\ \langle \color{red}{\rm x}a,\quad \color{red}{\rm x}b \rangle + \langle \color{red}{\rm y}c,\quad \color{red}{\rm y}d \rangle= \\ \langle \color{red}{\rm x}a+\color{red}{\rm y}c,\quad \color{red}{\rm x}b+\color{red}{\rm y}d \rangle. }\)