Solve the following pair of equations for the vectors u and v. Assume i = and j = . 8u +7v = i , u - v = j u = ( )i + ( )j v = ( )i + ( )j Can someone explain to me how to solve this?

Question

Solve the following pair of equations for the vectors u and v. Assume i = <1,0> and j = <0,1>. 8u +7v = i , u - v = j u = ( )i + ( )j v = ( )i + ( )j Can someone explain to me how to solve this?

amistre64 · Answer

setup the equations ...
let u = (xu, yu)  and v=(xv,yv)

8u = (8xu, 8yu)  and 7v=(7xv,7yv)
1u = (xu, yu)      and -1v = (-xv, -yv)

then its just a matter of adding the parts and addressing the system of equations that resutls

amistre64 · Answer

8u = (8xu, 8yu)
+7v =  (7xv,7yv)
----------------
                  1  ,  0


  1u = ( xu,   yu)
-1v = (-xv, -yv)
---------------
                0  ,   1

anonymous · Answer

Forgive me, but I'm not following...