3t – 5s Let W be the set of all vectors of the form 3s + 3t Find vectors i and i in R such that W = span {i, ú}. -2s – 5t
3t – 5s Let W be the set of all vectors of the form 3s + 3t Find vectors i and i in R such that W = span {i, ú}. -2s – 5t
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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![The image contains a mathematical problem related to vector spaces. It reads as follows:
"Let \( W \) be the set of all vectors of the form:
\[
\begin{bmatrix}
3t - 5s \\
3s + 3t \\
-2s - 5t
\end{bmatrix}
\]
Find vectors \( \vec{u} \) and \( \vec{v} \) in \( \mathbb{R}^3 \) such that \( W = \text{span}\{\vec{u}, \vec{v}\} \."
There are also two empty vector boxes labeled \( \vec{u} = \begin{bmatrix} \quad \\ \quad \\ \quad \end{bmatrix} \) and \( \vec{v} = \begin{bmatrix} \quad \\ \quad \\ \quad \end{bmatrix} \), indicating where the solutions should be written.
This exercise involves finding two vectors in three-dimensional space whose linear combinations span the given set \( W \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2192a9f0-1ae9-4ed3-a35b-fc11f1172fc0%2F255255dc-dacd-4de4-8538-66ec685d98dd%2Faeb7ast_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical problem related to vector spaces. It reads as follows:
"Let \( W \) be the set of all vectors of the form:
\[
\begin{bmatrix}
3t - 5s \\
3s + 3t \\
-2s - 5t
\end{bmatrix}
\]
Find vectors \( \vec{u} \) and \( \vec{v} \) in \( \mathbb{R}^3 \) such that \( W = \text{span}\{\vec{u}, \vec{v}\} \."
There are also two empty vector boxes labeled \( \vec{u} = \begin{bmatrix} \quad \\ \quad \\ \quad \end{bmatrix} \) and \( \vec{v} = \begin{bmatrix} \quad \\ \quad \\ \quad \end{bmatrix} \), indicating where the solutions should be written.
This exercise involves finding two vectors in three-dimensional space whose linear combinations span the given set \( W \).
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