Let and . Let be an inner product in such that :
Calculate and .
My attempt : I tried to figure out how is definied the inner product but I didn't find. After all I'm not even sure I should start the problem this way. If I should, then it's not an obvious thing to do... I need help on this.
Thanks a lot for your reply!
I must say it's hard for me to understand what you've done in some points.
You saidbut since then you don't use and . (but maybe I'll have to use them to finish the problem, so it's not a big deal).for any
But I have no idea of. I've tried to see it writing it in my sheet but I didn't success to understand.see that
We know that and that , so how do you multiply them? I then thought I'd have to substitute for the first coordonate of and for the second one... but this makes no sense.
So when I'll understand that part I'll try to go further and finish it alone.
By the way I didn't see Calculus III (multivariable calculus) but I guess it doesn't matter.
Today I could ask a helper at university... he told me a hint : and is a basis of .
So I could solve the problem. (Well I think I did it correctly!)
I wrote that any can be writen in the form and wrote something similar for . I ended with a not so beautiful expression (I had to deal with properties of inner product) as answer... but they don't ask it to be nice.