Hi, there--

YOUR PROBLEM:
Given the vectors
u = (2,7) and
v = (3,1)

Find 2u-3v, u+v, and 3u-4v

SOLUTION:
To work add and subtract vectors, you work with the x-components and y-components separately.

(a) 2u-3v
Multiply the x-component and the y-component of vector u by 2 to get the vector 2u. 
2u = (2*2,2*7) = (4,14)

Multiply both components of vector v by 3 to get vector 3v.
3v = (3*3,3*1) = (9,3)

Now subtract the x- and y-compnents of  3v from those of 2u to get the components of 2u-3v.
2u - 3v = (4-9,14-3) = (-5,11)


(b) u+v
Add the x- and y-components of u and v separately to give the components of u+v.
(u+v) = (2+3,7+1) = (5,8)

(c) 3u-4v
3u = (3*2,3*7) = (6,21)
4v = (4*3,4*1) = (12,4)

3u-4v = (6-12,21-4) = (-6,17)

I hope this helps. Feel free to email if you have questions about the explanation.

Mrs. Figgy
math.in.the.vortex@gmail.com