easy calc - Express vector w as...?

Question

i know this is supposed to be a really easy question but i can't get to the right answer!! i know you're supposed to find a/b by elimination then sub but i keep getting the wrong answer...

heres the question:
Given the vectors u = [2,1] and v= [-1,3]:
a) Express the vector w = [12, -1] as a linear combination of vector u and v.

ANSWER: 5u - 2v

can someone explain / show work of how to do this please!!!

PS. all the letters have the little vector sign on them, just dunno how to do it on the computer lol.

Answer 1

Solve for w in terms of u and v.

u = 2i + j
v = -i + 3j
w = 12i - j

Solve for a and b.

w = au + bv

2a - b = 12
a + 3b = -1

Add three times the first equation to the second.

7a = 35
a = 5

Plug into the first equation and solve for b.

2a - b = 12
2*5 - b = 12
10 - b = 12
-b = 2
b = -2

Therefore

w = au + bv
w = 5u - 2v

Answer 2

Check out this page for the answer (I'm able to render graphics on this page)



http://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.99659.html