Suppose u, v E V. Prove that (u, v) = 0 if and only if ||u|| ≤ ||u + av|| for all a € F.
Suppose u, v E V. Prove that (u, v) = 0 if and only if ||u|| ≤ ||u + av|| for all a € F.
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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![Suppose \( u, v \in V \). Prove that \(\langle u, v \rangle = 0\) if and only if
\[
\| u \| \leq \| u + av \|
\]
for all \( a \in \mathbb{F} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15ed467-90ec-4e60-afef-3d3f6119f74d%2Ffb2d9c2e-fd18-4741-996b-c74507efbd14%2Fqsnypoo_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose \( u, v \in V \). Prove that \(\langle u, v \rangle = 0\) if and only if
\[
\| u \| \leq \| u + av \|
\]
for all \( a \in \mathbb{F} \).
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