4. Determine whether W is a subspace of R³. a. W = {(x-1, x,x) x ER} b. W = {(3x, 0,-x)|x = R} 3 x 0 - X
4. Determine whether W is a subspace of R³. a. W = {(x-1, x,x) x ER} b. W = {(3x, 0,-x)|x = R} 3 x 0 - X
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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Question
A and B
![**Problem 4: Determine whether W is a subspace of \( \mathbb{R}^3 \).**
**a.** \( W = \{(x - 1, x, x) | x \in \mathbb{R}\} \)
The vector representation is:
\[
\begin{bmatrix}
x - 1 \\
x \\
x
\end{bmatrix}
\]
**b.** \( W = \{(3x, 0, -x) | x \in \mathbb{R}\} \)
The vector representation is:
\[
\begin{bmatrix}
3x \\
0 \\
-x
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faea2220e-5b79-4f4c-ba0b-cd87c88bb3af%2F6abe0969-3c96-4fe7-b09e-46bbf32714a3%2Fs7wxghm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4: Determine whether W is a subspace of \( \mathbb{R}^3 \).**
**a.** \( W = \{(x - 1, x, x) | x \in \mathbb{R}\} \)
The vector representation is:
\[
\begin{bmatrix}
x - 1 \\
x \\
x
\end{bmatrix}
\]
**b.** \( W = \{(3x, 0, -x) | x \in \mathbb{R}\} \)
The vector representation is:
\[
\begin{bmatrix}
3x \\
0 \\
-x
\end{bmatrix}
\]
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