Question

Let u = <-6, -2>, v = <-2, 3>. Find -3u + 2v

Answer 1

multiply, and add ... seems basic enough

Answer 2

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

Answer 3

u = <-6, -2> can be written as -6x-2y

v = <-2, 3> can be written as -2x+3y

what do we get with:

-3(-6x-2y) + 2(-2x+3y)

Answer 4

@amistre64 so we plug the other x and y values into the equation

Answer 5

no, the xy parts are simply visual cues, they could be called ij or rs or whatever, but the simply tell us that the coefficient is an x component or a y componet

Answer 6

we simply need to expand, collect like terms, and see what the coefficients turn out to be

Answer 7

so you get 14 ?

Answer 8

-3(-6x-2y) + 2(-2x+3y)

18x+6y -4x +6y

18x - 4x +6y +6y

(18- 4)x +(6+6)y

14x +12y

putting it back in component form we get: (14,12)

Answer 9

oh okay i see now, thank you so much @amistre64

Answer 10

good luck ;)