Let S be a set containing the two column matrices shown S = first column be us and the second column be u Let = 2 -{{[]}-{]}}- Find the projection of onto S. First normalize S. Then calculate 3 < ảv, uì > uì + < v, už > úž. Let the
Let S be a set containing the two column matrices shown S = first column be us and the second column be u Let = 2 -{{[]}-{]}}- Find the projection of onto S. First normalize S. Then calculate 3 < ảv, uì > uì + < v, už > úž. Let the
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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![Let \( \mathcal{S} \) be a set containing the two column matrices shown:
\[
\mathcal{S} = \left\{ \left\{ \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} \right\}, \left\{ \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} \right\} \right\}.
\]
Let the first column be \( \vec{u}_1 \) and the second column be \( \vec{u}_2 \).
Let \( \vec{v} = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix} \).
Find the projection of \( \vec{v} \) onto \( \mathcal{S} \). First normalize \( \mathcal{S} \). Then calculate:
\[
\langle \vec{a} \vec{v}, \vec{u}_1 \rangle \vec{u}_1 + \langle \vec{v}, \vec{u}_2 \rangle \vec{u}_2.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F494356ae-2db7-448e-a147-892d80022497%2F05eb94ce-c59a-4b77-85af-ef26f8d382e0%2F8b1a6qs_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( \mathcal{S} \) be a set containing the two column matrices shown:
\[
\mathcal{S} = \left\{ \left\{ \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} \right\}, \left\{ \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} \right\} \right\}.
\]
Let the first column be \( \vec{u}_1 \) and the second column be \( \vec{u}_2 \).
Let \( \vec{v} = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix} \).
Find the projection of \( \vec{v} \) onto \( \mathcal{S} \). First normalize \( \mathcal{S} \). Then calculate:
\[
\langle \vec{a} \vec{v}, \vec{u}_1 \rangle \vec{u}_1 + \langle \vec{v}, \vec{u}_2 \rangle \vec{u}_2.
\]
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