Posted by **Anonymous** on Wednesday, February 13, 2008 at 2:38pm.

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**, Wednesday, February 13, 2008 at 3:24pm
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**, Wednesday, February 13, 2008 at 5:06pm
What? I don't understand what you did. . .

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