For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. T s-3t s+t 5t :s, t in R (a) Find a basis for the subspace. A basis for the subspace is . (Use a comma to separate answers as needed.)
For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. T s-3t s+t 5t :s, t in R (a) Find a basis for the subspace. A basis for the subspace is . (Use a comma to separate answers as needed.)
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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![For the subspace below, (a) find a basis for the subspace, and (b) state the dimension.
\[
\left\{
\begin{bmatrix}
s - 3t \\
s + t \\
5t
\end{bmatrix}
: s, t \in \mathbb{R}
\right\}
\]
---
**(a) Find a basis for the subspace.**
A basis for the subspace is \(\boxed{\phantom{x}}\).
(Use a comma to separate answers as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2ba40f3-5b99-4806-a053-ede02cf82fa8%2F23c3e9cc-f6f0-4f9a-bb1f-258b60efad83%2Fnlprr9_processed.png&w=3840&q=75)
Transcribed Image Text:For the subspace below, (a) find a basis for the subspace, and (b) state the dimension.
\[
\left\{
\begin{bmatrix}
s - 3t \\
s + t \\
5t
\end{bmatrix}
: s, t \in \mathbb{R}
\right\}
\]
---
**(a) Find a basis for the subspace.**
A basis for the subspace is \(\boxed{\phantom{x}}\).
(Use a comma to separate answers as needed.)
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