Question

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

<34, -8>
<14, 0>
<14, 3>
<44, -12>

Answer 1

\(\bf \square <a,b>\implies <\square \cdot a,\square \cdot b>
\\ \quad \\
<a,b>+<c,d>\implies <a+c,b+d>\)

thus do the scalar multiplication and then add the resulting vectors

Answer 2

Umm how do I do Scalar multiplication?

Answer 3

\(\bf \square <a,b>\implies <\square \cdot a,\square \cdot b>\leftarrow {\color{brown}{ \textit{scalar multiplication}}}
\\ \quad \\
<a,b>+<c,d>\implies <a+c,b+d>\)

Answer 4

My browser isn't showing what the little boxes in front of <a.b> or <?*a,?*b> are...

Answer 5

is just a box, thus, just means any value

Answer 6

I'm sorry I don't know what goes there. i'm assuming a=-6, b= 1, c=-5 and d=2 but I don't know what to do with the boxes.

Answer 7

\(\large u = <-6, 1>\qquad v = <-5, 2>
\begin{array}{llll}
{\color{brown}{ -4}}u\implies <{\color{brown}{ \square }}\cdot -6,{\color{brown}{ \square }}\cdot1>
\\ \quad \\
{\color{olive}{ 2}}v\implies <{\color{olive}{ \square }}\cdot -5,{\color{olive}{ \square }}\cdot2>
\end{array}\)

Answer 8

what would you get for that?

Answer 9

Is it <-4*-6*u*1> and <2*-5*v*2> ?

Answer 10

yeap

Answer 11

hmmm wait.. a sec

Answer 12

how did the "u" and "v" get there?

Answer 13

Ummmm -4u<-- and 2v<---?

Answer 14

so you just distribute the "scalar number" inside the vector, that's a scalar multiplication

Answer 15

is it 24,-20 ????

Answer 16

hmmm what did you get for -4u and 2v?

Answer 17

I don't know anymore :( I thought i had distributed them into the vector but then you were confused as to where I got the variables from!

Answer 18

well... you had
Is it <-4*-6*u*1> and <2*-5*v*2>
? ?

also a scalar multiplication gives you a vector back anyhow

Answer 19

<-8, 30, uv, 2>?

Answer 20

https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/multiplying-vector-by-scalar <--- may want to review it a bit

Answer 21

http://www.youtube.com/watch?v=pNMrYACjHXQ <--- this one works better I think