$u_1 = (1, -1)'$ and $u_2 = (1, 1)'$ are two vector of $R^2$. Endow $R^2$ with an inner product such that $||u_1|| = 1$ and $||u_2|| = 1$.
Well, honestly, I don't completely understand what the problem asks. Endow $R^2$ with inner product? Then I tried the inner product of $u_1$ $u_2$. So, $<u_1,u_2> $ $= (1,-1)*(1,1)=0$. Then two vectors are orthogonal. But I don't know to how to proceed. Do i have show that $||u_1|| = 1 $ and $||u_2|| = 1 $? if so, what theorem or formula should I use?
Thanks in advance!