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
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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

\[
\vec{x} \cdot \vec{u} = \vec{x} \cdot \vec{v} = \vec{x} \cdot \vec{w} = 0
\]
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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