Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
1. Let V be an inner product space. Suppose f,g E V such that f - g Lg (a) Prove that 1l12= ||f- g|2 + ||9||2.
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Transcribed Image Text:1. Let V be an inner product space. Suppose f,g E V such that f - g Lg (a) Prove that 1l12= ||f- g|2 + ||9||2.
Expert Solution
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Step 1

Given:

The vectors f g are in V, an inner product space andf-glg -8| +|\g| To prove:
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Step 2

Proof:

Pythagorean theorem states that whenever a, b are in W and (a,b)0 then a lb or lalipla+b = Since f g are in V, f-g is also in V. As f-gg, then this implies f-g.g)0 Then + \S-8/+ -8+g|l s-l +
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