It's an easy question...
Let and
Show that is in Span{u,v} for all a and b. In other words = Span{u,v}
Directly from the definition: solve
for x and y. If you can then .
That is the same as solving x+ y= a, 2x- 2y= b. Multiply the first equation by 2 and add: 4x= 2a+ b so x= (2a+ b)/4. Multiply the first equation by 2 and subtract: 4y= 2a- b so y= (2a- b)/4. Those exist for all a and b.