Posted by Anonymous on .
Given the vectors:
u = [3, 0]
v = [1, 2]
a) Express the vector w = [2, 8] as a linear combination of vectors u and v.
How do I do this?

Math  Algebraic Vectors 
Reiny,
let [2,8] = a[3,0] + b[1,2]
so you get 3a  b = 2
and 2b = 8
from the second equation b = 4, subbing that back in to the first...
3a  4 = 2
a = 2
check to see if [2,8] = 2[3,0] + 4[1,2]
sure does!
We were lucky that in the second equation one of the variables dropped out, normally you would end up solving 2 equations in 2 unknowns. 
Math  Algebraic Vectors 
Anonymous,
What? I don't understand what you did. . .