How do you find a=(3b+c)+5b given b=<6,3> and c=<-4,8>?

1 Answer
Aug 31, 2016

a= < 44, 32 >

Explanation:

We can simplify the given color(red)(a)=(3color(blue)(b)+color(green)(c))+5color(blue)(b) a bit as:
color(white)("XXX")color(red)(a)=8color(blue)(b)+color(green)(c)

Given that color(blue)(b)=color(blue)(< 6,3>)
then
color(white)("XXX")color(blue)(8b)=< 6*8,3*8 > = color(blue)(< 48,24>)

and given that color(green)(c)=color(green)( < -4, 8 >

we have
color(white)("XXX")color(red)(a)=color(blue)(< 48, 24 >) + color(green)( < -4,8 >)

color(white)("XXXX")= < color(blue)48color(green)(-4), color(blue)(24)color(green)(+8) >

color(white)("XXXX")= < 44, 32 >