Let V be a 3-dimensional vector space with a basis B (v1, v2, V3). Let B' = (w1, w2, w3) where wi = v1 + v2 + v3 w2 = 2v1 + 3v2 + 2v3 w3 = vị + v2 + 2v3. Which of the following is the change of basis matrix from B' to B? (1 1 1 a) 2 3 2 1 1 1 2 1 b) 1 1 2 2 4. -2 c) 1 1. 4 d) -2 1 1 e) There is no change of basis matrix since B' is linearly dependent and not a basis of V.
Let V be a 3-dimensional vector space with a basis B (v1, v2, V3). Let B' = (w1, w2, w3) where wi = v1 + v2 + v3 w2 = 2v1 + 3v2 + 2v3 w3 = vị + v2 + 2v3. Which of the following is the change of basis matrix from B' to B? (1 1 1 a) 2 3 2 1 1 1 2 1 b) 1 1 2 2 4. -2 c) 1 1. 4 d) -2 1 1 e) There is no change of basis matrix since B' is linearly dependent and not a basis of V.
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
![Let V be a 3-dimensional vector space with a basis B
(v1, v2, V3). Let B' = (w1, w2, w3) where
wi = v1 + v2 + v3
w2 = 2v1 + 3v2 + 2v3
w3 = vị + v2 + 2v3.
Which of the following is the change of basis matrix from B' to B?
(1 1 1
a) 2 3 2
1
1
1 2
1
b)
1
1
2 2
4.
-2
c)
1
1.
4
d)
-2
1
1
e) There is no change of basis matrix since B' is linearly dependent and not a
basis of V.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94333a95-5c4b-414c-a3d0-38d702a5346a%2F058cfb39-9248-45b3-9de2-6fbfe285ec47%2F6wgqpda_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be a 3-dimensional vector space with a basis B
(v1, v2, V3). Let B' = (w1, w2, w3) where
wi = v1 + v2 + v3
w2 = 2v1 + 3v2 + 2v3
w3 = vị + v2 + 2v3.
Which of the following is the change of basis matrix from B' to B?
(1 1 1
a) 2 3 2
1
1
1 2
1
b)
1
1
2 2
4.
-2
c)
1
1.
4
d)
-2
1
1
e) There is no change of basis matrix since B' is linearly dependent and not a
basis of V.
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