So, for the first part, the orthogonal complement would just be all f(x) where by ∫f(x) = 0 over the given interval [a,b]?
As for the second, I'm not quite sure what you mean. If I have those equations, and let x =[x_1, x_2, x_3, x_4] be my unknowns, I have:
[x_1,x_2,x_3,x_4] = x_3[-i...