4. Which of the following subsets of R³ constitute a subspace of R³? [Here, x = (₁, §2, §3).] (a) All x with §₁ = ₂ and §3 = 0. (b) All x with ₁ = - ₂ + 1. (c) All x with positive 1, 2, §3. (d) All x with ≤₁ − ₂ + 3 = k = const.
4. Which of the following subsets of R³ constitute a subspace of R³? [Here, x = (₁, §2, §3).] (a) All x with §₁ = ₂ and §3 = 0. (b) All x with ₁ = - ₂ + 1. (c) All x with positive 1, 2, §3. (d) All x with ≤₁ − ₂ + 3 = k = const.
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
![4. Which of the following subsets of R³ constitute a subspace of R³?
[Here, x = (₁, §2, §3).]
(a) All x with §₁ = ₂ and §3 = 0.
(b) All x with ₁ =
-
₂ + 1.
(c) All x with positive
1, 2, §3.
(d) All x with ≤₁ − ₂ + 3 = k = const.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15b7304-cc73-4505-92c3-23aa2fda4f71%2Fc7ecc5bc-788b-4a06-a0f3-4f9c71b351ae%2Fgkxdwha_processed.png&w=3840&q=75)
Transcribed Image Text:4. Which of the following subsets of R³ constitute a subspace of R³?
[Here, x = (₁, §2, §3).]
(a) All x with §₁ = ₂ and §3 = 0.
(b) All x with ₁ =
-
₂ + 1.
(c) All x with positive
1, 2, §3.
(d) All x with ≤₁ − ₂ + 3 = k = const.
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