Q2. Consider the subspace W of R' spanned by the vectors: wi = W2 = , W3 = W4 = 4 0. 1. Are the vectors w1, w2, w3, wa linearly independent? If they are not, find a largest independent subset of these vectors, i.e. find a basis for W. 2. Find dim(W). 3. Is the vector u = E W? If yes, write u as a linear combination of the basis you found in (1). If not, justify.
Q2. Consider the subspace W of R' spanned by the vectors: wi = W2 = , W3 = W4 = 4 0. 1. Are the vectors w1, w2, w3, wa linearly independent? If they are not, find a largest independent subset of these vectors, i.e. find a basis for W. 2. Find dim(W). 3. Is the vector u = E W? If yes, write u as a linear combination of the basis you found in (1). If not, justify.
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
![Q2. Consider the subspace W of R spanned by the vectors:
37
wi =
1
W2 =
-5
, W3 =
11, W4
4
1. Are the vectors w1, w2, w3, wa linearly independent? If they are not, find a largest
independent subset of these vectors, i.e. find a basis for W.
2. Find dim(W).
3. Is the vector u =
E W? If yes, write u as a linear combination of the basis
you found in (1). If not, justify.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4eadaff-773b-47b7-a8e5-75d27ef2bc22%2Fa3e08e58-21de-495e-b0ff-e26dd8307879%2Futyfqlh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q2. Consider the subspace W of R spanned by the vectors:
37
wi =
1
W2 =
-5
, W3 =
11, W4
4
1. Are the vectors w1, w2, w3, wa linearly independent? If they are not, find a largest
independent subset of these vectors, i.e. find a basis for W.
2. Find dim(W).
3. Is the vector u =
E W? If yes, write u as a linear combination of the basis
you found in (1). If not, justify.
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