Question

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

Answer 1

We add vectors simply by adding their corresponding components.

<a,b>+<c,d>=<a+c,b+d>

Let's simplify the problem by first finding -2u and 5v

-2u=-2*<5,6>=<-10,-12>

5v=5*<-2,-6>=-10,-30

Now let's add the vectors together.

<-10+(-10),-12+(-30)>=<-20,-42>

So our answer would be <-20,-42>

Double check my math; I'm prone to making arithmetic mistakes when explaining things.. .