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  3. show that the la b inner product satisfies the following...

Question: show that the la b inner product satisfies the following...

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Show that the L[a, b] inner product satisfies the following properties. . The L2 inner product is conjugate-symmetric (i.e., 〈f, g〉 = 〈g, Ó),homo- geneous, and bilinear (these properties are listed in Definition 0.1) . Show that the L inner product satisfies positivity on the space of contin uous functions on [a, b] by using the following outline. (a) We want to show that if JD Ifa)2 dt -0, then f o all a s (b) Suppose, by contradiction, that If (to)| > 0; then use the definition of continuity to show that |f(t)| > If(to)l1/2 on an interval of the fornm (c) Then show If (to)12 4 -128] 〉 0,

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