Let H be the set of all vectors of the form is a subspace of R³? H = Span{v} for v = 5t t . Find a vector v in R³ such that H = Span{v}. Why does this show that 7t
Let H be the set of all vectors of the form is a subspace of R³? H = Span{v} for v = 5t t . Find a vector v in R³ such that H = Span{v}. Why does this show that 7t
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 \( H \) be the set of all vectors of the form
\[
\begin{bmatrix}
5t \\
t \\
7t
\end{bmatrix}
\]
Find a vector \( \mathbf{v} \) in \( \mathbb{R}^3 \) such that \( H = \text{Span}\{\mathbf{v}\} \). Why does this show that \( H \) is a subspace of \( \mathbb{R}^3 \)?
\[ H = \text{Span}\{\mathbf{v}\} \text{ for } \mathbf{v} = \boxed{\phantom{000}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2a7103f-3a9d-4561-85c8-a7795199028a%2Fd673744c-544c-47f4-b8c4-98eb681ceb38%2Fpgl54s_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( H \) be the set of all vectors of the form
\[
\begin{bmatrix}
5t \\
t \\
7t
\end{bmatrix}
\]
Find a vector \( \mathbf{v} \) in \( \mathbb{R}^3 \) such that \( H = \text{Span}\{\mathbf{v}\} \). Why does this show that \( H \) is a subspace of \( \mathbb{R}^3 \)?
\[ H = \text{Span}\{\mathbf{v}\} \text{ for } \mathbf{v} = \boxed{\phantom{000}} \]
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