Exercise 1. Which of the following subsets of R³ are actually subspaces? a. The plane of vectors (b,, b2, b3) with bị = b2. b. The plane of vectors with b, = 1. c. The vectors with b,b,b3 = 0. d. All linear combinations of v = (1, 4, 0) and w = (2,2, 2). All vectors that satisfy bị + b2 + b3 = 0. f. All vectors with bị < bz s b3. е.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.2: Orthogonal Complements And Orthogonal Projections
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Exercise 1. Which of the following subsets of IR3 are actually subspaces?
a. The plane of vectors (b,, b2, b3) with b, = b2.
b. The plane of vectors with b, = 1.
c. The vectors with b, b,b3 = 0.
d. All linear combinations of v = (1, 4, 0) and w = (2,2, 2).
All vectors that satisfy b, + b2 + b3 = 0.
All vectors with bị s bz < b3.
е.
f.
Transcribed Image Text:Exercise 1. Which of the following subsets of IR3 are actually subspaces? a. The plane of vectors (b,, b2, b3) with b, = b2. b. The plane of vectors with b, = 1. c. The vectors with b, b,b3 = 0. d. All linear combinations of v = (1, 4, 0) and w = (2,2, 2). All vectors that satisfy b, + b2 + b3 = 0. All vectors with bị s bz < b3. е. f.
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