* Let X be the vector space of continuous real valued functions in [-1, 1]. Define (·, ·) : X×X → R as (x, y) = | x(1) y(1) dt. (a) Show that (-, ·) is a inner product. (b) Let Y c X be the set of even continuous real valued functions in [-1, 1]. That is, y € Y y(1) = y(-1) Vt e [-1,1]. Let Zc X be the set of odd continuous real valued functions in [-1,1]. That is, ze Z z(t) = -z(-1) VtE [-1,1]. Show that Y IZ.

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