Hey everyone,
My teacher gave a problem to show that p = 1 + x and q = 1 - x are orthogonal, but he says let <p,q> = a0b0 + a1b1 be the inner product. How do I do this with out integrating? I'm a little confused.
Thanks
What are $\displaystyle a_{0}, b_{0}, a_{1}, b_{1}?$ I would assume you have something like $\displaystyle p(x)=a_{0}+a_{1}x,$ and $\displaystyle q(x)=b_{0}+b_{1}x.$ If that's so, then the inner product $\displaystyle \langle p,q\rangle=a_{0}b_{0}+a_{1}b_{1}$ will definitely give you orthogonality of those two polynomials. Do you see how?