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1. Let X = {r1, X2, X3, X4} and let b: X x X → [0, ∞) be symmetric with %3D b(x1, T2) = 3, b(x2, T3) = 1, b(x2, x4) = 2. %3D %3D %3D Let c = 0 and let m(x) = deg(x). Let f, g E C(X) be functions defined by %3D f(x1) = 1, f(x2) = 2, ƒ(x3) = 3, f(x4) = 4, g(x1) = 0, g(x2) = -3, g(r3) = 4, g(x4) = –1. and %3D %3D Ma) Calculate the inner product (f,g), and norms || f|| and ||9g|| in l²(X,m) X(b) Find || f – g||- c) Show that ||h|| = 0 for a function h E C(X) if and only if h = 0. %3D

1. Let X = {r1, X2, X3, X4} and let b: X x X → [0, ∞) be symmetric with %3D b(x1, T2) = 3, b(x2, T3) = 1, b(x2, x4) = 2. %3D %3D %3D Let c = 0 and let m(x) = deg(x). Let f, g E C(X) be functions defined by %3D f(x1) = 1, f(x2) = 2, ƒ(x3) = 3, f(x4) = 4, g(x1) = 0, g(x2) = -3, g(r3) = 4, g(x4) = –1. and %3D %3D Ma) Calculate the inner product (f,g), and norms || f|| and ||9g|| in l²(X,m) X(b) Find || f – g||- c) Show that ||h|| = 0 for a function h E C(X) if and only if h = 0. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi, Please have a look at the image, I need only the solution of part (c)

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1. Let X = {r1, 2, X3, 14} and let b: X x X [0, 00) be symmetric with b(x1, 2) = 3, 6(x2, T3) = 1, b(x2, x4) = 2. Let c =0 and let m(x) = deg(x). Let f, g E C(X) be functions defined by f(x1) = 1, f(x2) = 2, f(x3) = 3, f(x4) = 4, g(r1) = 0, g(x2) = -3, g(r3) = 4, g(x4) = –1. and Ha) Calculate the inner product (f, g), and norms || f|| and ||g|| in l²(X,m). X(b) Find || f – g|| - c) Show that ||h|| = 0 for a function h E C(X) if and only if h = 0. %3D
Transcribed Image Text:1. Let X = {r1, 2, X3, 14} and let b: X x X [0, 00) be symmetric with b(x1, 2) = 3, 6(x2, T3) = 1, b(x2, x4) = 2. Let c =0 and let m(x) = deg(x). Let f, g E C(X) be functions defined by f(x1) = 1, f(x2) = 2, f(x3) = 3, f(x4) = 4, g(r1) = 0, g(x2) = -3, g(r3) = 4, g(x4) = –1. and Ha) Calculate the inner product (f, g), and norms || f|| and ||g|| in l²(X,m). X(b) Find || f – g|| - c) Show that ||h|| = 0 for a function h E C(X) if and only if h = 0. %3D
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