Question

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

Answer 1

`\bf \begin{cases} u = \ \textless \ 5, 6\ \textgreater \ \qquad &-2u\to -2\ \textless \ 5,6\ \textgreater \ \\ &\qquad \boxed{\ \textless \ -10,-12\ \textgreater \ }\\ v = \ \textless \ -2, -6\ \textgreater \ \qquad &5v\to 5\ \textless \ -2,-6\ \textgreater \ \\ &\qquad \boxed{\ \textless \ -10,-30\ \textgreater \ } \end{cases}`

scalar multiplication, now, add them up

Answer 2

<-20 , -42>

Explanation:

u = <5, 6>, v = <-2, -6>

To find -2u + 5v, we use scalar multiplication

Multiply -2 with vector u

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

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

Now we do -2u + 5v

Add both the vectors we got

<-10, -12> + <-10, -30>

<-10+-10, -12-30>

<-20 , -42>