Question

**Calc 2 Help** let u∠ = 2i∠ + 3j∠ , and v∠ = 8i∠ - 13j∠ , and w∠ = -i∠ + j∠ . Find real numbers a and b so that u∠ =av∠ + bw∠ .

Answer 1

The "∠ " is mean to be over the preceeding character.

Answer 2

its best just to write it out in component form ...

u=<2,3>
v = <8,-13>
w=<-1,1>

Answer 3

the rest of it just amounts to distractors

Answer 4

this is also a matrix solution ....

Answer 5

should I do something like this..
<2,3> = a<8,-13> + b<-1,1>?

Answer 6

A x = v
| 8 -1| |a| = |2|
|-13 1 | |b| |3|

Answer 7

yes

Answer 8

8a -b = 2
-13a +b = 3

which defines a system of equation

Answer 9

@m.f.h sorry I wasn't sure how to type the notation.

Answer 10

would it be <2,3> = <8a,-13a> + <-b,b>?

Answer 11

i know ∠ mean the angle you can find this notation in calculator

Answer 12

yes, it would amount to that

Answer 13

add up the parts and compare them to the results your looking to get

Answer 14

<8a,-13a>
+ <-b, b >
-------------
<8a-b,-13a+b>
=
<2 , 3 >

Answer 15

8a -b = 2
-13a +b = 3

defines a system of equation which shouldve been lerant back in algebra classes

Answer 16

I solved for b
8a -2 =b, b = 3 +13a
8a-2 = 3 +13a
-5 = 5a
a = -1

Answer 17

is that not how I should do it?

Answer 18

as a dbl chk when your ready

rref{{8,-1,2},{-13,1,3}}

http://www.wolframalpha.com/input/?i=rref%7B%7B8%2C-1%2C2%7D%2C%7B-13%2C1%2C3%7D%7D

a does = -1, good job so far

Answer 19

if your comfortable with substitution, then by all means use it; its fine to go that route

Answer 20

ok b = -10