I feel sorry to ask help for this problem, since I believe it's a simple one. But I go nowhere when I think alone.

The problem states :

Let be one of the following scalar product in the space of polynomials with real coefficients of degree .

a) , with different from when different from .

b) .

Prove that { }is notan orthogonal set if .

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First : I don't know how to start. Second : in the item a), I don't understand why there is the condition of the "i", if it isn't even in the equation. Maybe an error of text, so it should be ? Third : About what I must prove. It says, an orthogonal set, wouldn't it be an orthogonal basis? But even having said that, I still don't understand at all what they ask me to do. Please help me!