# How do you find a=-b+4c given b=<6,3> and c=<-4,8>?

Feb 8, 2017

$a = < - 22 , 29 >$

#### Explanation:

If

$b = < 6 , 3 >$

$c = < - 4 , 8 >$

and

$a = - b + 4 c$

$\iff$ substitute in

$a = \left(- 1\right) < 6 , 3 > + 4 < - 4 , 8 >$

Since if you take a scalar $c$ and multiply it by a vector $< a , b >$ you get $c < a , b > = < c a , c b >$ then we can multiply and get

$a = < - 6 , - 3 > + < - 16 , 32 >$

and since the addition of two vectors $a$ and $b$ makes a vector $a + b$

$a + b = < {x}_{a} + {x}_{b} , {y}_{a} + {y}_{b} >$

we can add the vectors algebraically

$a = < \left(- 6 - 16\right) , \left(- 3 + 32\right) > = < - 22 , 29 >$