-2st] Let W be the set of all vectors of the form 3s + 5t t - 2s H v = Find vectors ū and 7 in R³ such that W = span {ū, v}.
-2st] Let W be the set of all vectors of the form 3s + 5t t - 2s H v = Find vectors ū and 7 in R³ such that W = span {ū, v}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
Let \( W \) be the set of all vectors of the form
\[
\begin{bmatrix}
-2s - t \\
3s + 5t \\
t - 2s
\end{bmatrix}
\]
Find vectors \( \vec{u} \) and \( \vec{v} \) in \( \mathbb{R}^3 \) such that \( W = \text{span} \{ \vec{u}, \vec{v} \} \).
**Solution Format:**
\[
\vec{u} =
\begin{bmatrix}
\text{(Fill in)} \\
\text{(Fill in)} \\
\text{(Fill in)}
\end{bmatrix}
, \quad
\vec{v} =
\begin{bmatrix}
\text{(Fill in)} \\
\text{(Fill in)} \\
\text{(Fill in)}
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F329038e6-522f-4245-8c94-7b937a205b4b%2F53b70b22-d3e9-4dca-a4f7-7a6d4a8de7dc%2Fkd22oa7_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Let \( W \) be the set of all vectors of the form
\[
\begin{bmatrix}
-2s - t \\
3s + 5t \\
t - 2s
\end{bmatrix}
\]
Find vectors \( \vec{u} \) and \( \vec{v} \) in \( \mathbb{R}^3 \) such that \( W = \text{span} \{ \vec{u}, \vec{v} \} \).
**Solution Format:**
\[
\vec{u} =
\begin{bmatrix}
\text{(Fill in)} \\
\text{(Fill in)} \\
\text{(Fill in)}
\end{bmatrix}
, \quad
\vec{v} =
\begin{bmatrix}
\text{(Fill in)} \\
\text{(Fill in)} \\
\text{(Fill in)}
\end{bmatrix}
\]
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