Question

If 2u+2v=4w-3v+2u, then w is a linear combination of u and u+v.
True or False?

Answer 1

What is a linear combination?

Answer 2

well try to solve for w and see what happens. your goal is to have
w = au + b(u+v) for some a,b in R

Answer 3

If you don't understand some part of the definition of linear combination then we can help. But we can't know what you don't know unless you make some kind of attempt so that we can fix it. Being wrong is probably the most important thing you can do right now for us @nicolemakucheff

Answer 4

so we have,
4w = 5v = -5u + 5u + 5v = -5u + 5(u+v)

so yes, it's true

Answer 5

@xxferrocixx Why are you just giving away this answer with no good reasoning? You've said "the goal is to have yadda yadda..." Why? This is not good enough.

Answer 6

@Kainui I was assuming the asker knows what linear combination is. Maybe I shouldn't have assumed so?

Answer 7

If the asker understood it then I don't think this question would be asked.

Answer 8

The question is about proving linear combinations, the concept must be understood to answer. @Kainui is correct the question would not be asked if they understood. The purpose of Open Study is help understand and guide so that the next time they attempt a similar problem they may have learned how to solve. Giving the answer is robbing the user of their education.

Answer 9

thanks @xxferocixx I was having trouble understanding the concept