Given the vectors:

Question

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?

Answer 1

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.

Answer 2

What? I don't understand what you did. . .