14. Let nonzero vectors ü,ỷ,wER' be linearly independent. Show that there does not exist a nonzero vector x, such that X-ủ = xv = x•w = 0
14. Let nonzero vectors ü,ỷ,wER' be linearly independent. Show that there does not exist a nonzero vector x, such that X-ủ = xv = x•w = 0
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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![14. Let nonzero vectors \( \vec{u}, \vec{v}, \vec{w} \in \mathbb{R}^3 \) be linearly independent. Show that there does not exist a nonzero vector \( \vec{x} \), such that
\[
\vec{x} \cdot \vec{u} = \vec{x} \cdot \vec{v} = \vec{x} \cdot \vec{w} = 0
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20fbb71c-9fd5-4b59-9900-a3864652c523%2F6c0ec037-ffee-4f33-ba53-c1de6dc7843f%2F735h1sb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:14. Let nonzero vectors \( \vec{u}, \vec{v}, \vec{w} \in \mathbb{R}^3 \) be linearly independent. Show that there does not exist a nonzero vector \( \vec{x} \), such that
\[
\vec{x} \cdot \vec{u} = \vec{x} \cdot \vec{v} = \vec{x} \cdot \vec{w} = 0
\]
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