(a) Prove the inner product axioms for the weighted inner product (3.15), assuming w(x) 0 for...
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(b) Explain why it does not define an inner product if w is continuous and w(xo) < 0 for some x0 ∈ [a.b],
(c) If w(.v) ≥ 0 for a ≤ x ≤ b. does (3.15) define an inner product? Hint: Your answer may depend upon w(x).
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a To prove the first bilinearity condition The second has a similar proof or ...View the full answer
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