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Let ů,v,,v2,,v, be nonzero real valued vectors in R', such that ū is orthogonal to each v. Show that ü is orthogonal to each vector in the SPAN{ V,,v,,, v, }. p

Let ů,v,,v2,,v, be nonzero real valued vectors in R', such that ū is orthogonal to each v. Show that ü is orthogonal to each vector in the SPAN{ V,,v,,, v, }. p

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let \(\vec{u}, \vec{v}_1, \vec{v}_2, \ldots, \vec{v}_p\) be nonzero real valued vectors in \(\mathbb{R}^5\), such that \(\vec{u}\) is orthogonal to each \(\vec{v}_k\). Show that \(\vec{u}\) is orthogonal to each vector in the \(\text{SPAN}\{\vec{v}_1, \vec{v}_2, \ldots, \vec{v}_p\}\).
Transcribed Image Text:Let \(\vec{u}, \vec{v}_1, \vec{v}_2, \ldots, \vec{v}_p\) be nonzero real valued vectors in \(\mathbb{R}^5\), such that \(\vec{u}\) is orthogonal to each \(\vec{v}_k\). Show that \(\vec{u}\) is orthogonal to each vector in the \(\text{SPAN}\{\vec{v}_1, \vec{v}_2, \ldots, \vec{v}_p\}\).
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